Home

SMOS L1 Processor Algorithm Theoretical Baseline Definition

1. k x X x x Px KK x xxxix x x x x x X x x x x xx Kk xxx x 8 JAB ABC ABd 01 402 403 404 Ans Ane Ane Ans 410 41 1 A12 A13 A14 A15 A18 A17 A18 A19 A20 A2 t ecd ecd B cd 60 1 602 603 604 eos Ene o7 Bos Bos BO 1 81 2 8 13 8 4 1 B 16 817 18819
2. ZN SMOS L1 Processor n um deim s Algorithm iue s ENGENHARIA M Theoretical Baseline page vi 3 3 1 1 Geometrical rotation 63 3 3 1 1 1 Waldteufel and Caudal Implementation 63 3 3 1 1 2 Duesmann and Zundo Implementation 65 3 3 2 Geolocation 66 3 3 2 1 Pixel Brightness Temperature computation 67 3 3 2 2 Pixel Radiometric Accuracy computation 67 3 3 2 3 Pixel Observation Angles computation 68 3 3 2 4 Pixel Footprint Shape Computation 69 3 3 2 5 Apodisation window computation 69 4 Open Issues 71 5 ANNEX G matrix Blocks 78 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 e C iti SMOS L1 Processor pate 29 10 10 deim s Algorithm ENGENHARIA Theoretical Baseline page viii List of Figures Figure 1 Time sequence for dual polansation motdle aieo 6 Figure 2 Time sequence for full polarisation mode niii ie cte cet eth sese cta eh 6 Figure 3 Full polarisation scene ODUDUE vor citi oci t ban cd tuus pa 7 Figure A Pull polarisation LO data reordering uiii roin inei io tib oe i ti saec 7 Figure 5 Logical organization of LO data nominal rada 10 Figure Antenna indexing inthe SMOS tast
3. a PUR Moondir Po I dir l E Ny 0 0 fo v n p E m 7 2 Vul pe dr kj kj E 2 em c Moon ref i y QQ Ts FS c m Back UD Vig POF ortnm latum pis j 1 9 9 J fh E 6 B iE 1 5 Uys Vig dL 49 9 4 fo In these formulae taken from RD 12 and RD 13 the temperature of the sky has to be retrieved from an auxiliary sky map and the spatial coordinates corresponding to Sky coordinates entering the FOV are Jerem atum This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Eq Eq 114 Eq 115 Eq 116 Eq 117 Eq 118 Eq 119 Eq 120 121 113 Code SO DS DME L1PP 0011 SMOS L1 Processor 29 10 10 deim s Bi Algorithm ENGENHARIA Theoretical Baseline computed with the help of pointing CFI the temperature of background Earth is considered constant for each snapshot and computed such that the average Brightness Temperature of the resulting image is Zero Ju pus 0 0 dir 0 0 Vin ref 0 0 Eas dir 0 0 ioi ref 0 0 Pk 0 0 Eq Earth V Pq 0 0 122 Earth The term is the antenna temperature at a given polarisation which for horizontal a
4. measurement from that scene It must be computed combining the Sky observed Brightness Temperature distribution with the NIR antenna patterns The observed Sky distribution is computed using PVT and AOCS to obtain the instrument pointing direction and the Galaxy Map layer with the averaged NIR values T 2 9 E d dn Eq 78 m eUnitCircle 1 m The antenna noise injection temperature is computed as 1 Ty 715 Pul Eq 79 NA where the attenuation coefficients and physical temperatures are defined as in Section 3 1 5 3 Additionally two parameters are computed to be used in NIR AR mode First This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 J C iti SMOS L1 Processor pate 29 10 10 deim s LE Algorithm E ENGENHARIA J siwe Theoretical Baseline page 38 of 89 Is 2 1 80 hi This value is then used to compute T T T z A T 0 T E LycLaLpa N LyclaLpa and also Eq 81 eee x D LR 1 T ko CIP m OG Z T air oo UT These last values are stored in the NIR calibration product in the NIR A Data Set All the parameters in the previous two Eqs have the same meaning as in Section 3 1 5 3 1 3 1 9 2 NIR AR Calibration The NIR AR mode is used to calibr
5. Theoretical Baseline abra are measured from a uncorrelated load in LICEF LU mode uncorrelated noise injection Vua is denormalised as shown in Section 3 1 5 3 1 2 while Veg and Va denormalized as the LICEFs visibilities Then when the instrument is in LICEF LA mode looking at cold sky this value is used together with the antenna temperatures L5 Eq 39 and V to compute 1 a Val Al T d LA ab i 84 Ange Wile where n is computed from the antenna temperature and the temperature of the U load by T v Eq 85 m Tu Using y during measurement in NIR A mode assuming that the cross coupling between channels is equal the value denormalised correlation induced by cross coupling is computed by 29 T Eq 86 where is now computed from T y and Since NIR A the antenna is measured only half of the time we have 2 blind __ Eq 87 As for the leakage factor 2 itis computed NIR A mode when looking at the cold sky by 1 di Veal V Eq 88 SE al 1 2c Vor Eq 89 qi i Tyson n where 77 is NIR pulse length both in NIR A when looking at cold sky is the corrected noise injection temperature transferred to the VAP plane through Eq 50 but using T as it is measured during cold sky calibrati
6. cos Q jsin Q Eq 11 M jsinQ M and M are easily computed and the quadrature corrected correlations are computed through Eq 7 Since it is obtained directly from the instrument s own output the quadrature corrected correlation can be considered as instrument output 3 1 4 Amplitude and In Phase Error Correction The correction parameters for amplitude and in phase errors are computed from MIRAS output while in correlated noise injection mode The outputs of these computations are then used in conjunction with the system temperatures measured in observation mode to calibrate the visibilities This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C n SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA yf Theoretical Baseline 47 of 89 3 1 4 1 Power Measurement System calibration The four point measurement technique is based on a linear model of the PMS A measured PMS voltage at receiver v depends on the system temperature as AD 6 T sysk T extk tT Eq 12 V G T t a T Sys Sys where is the system noise temperature is the external temperature is the PMS offset G is the PMS gain and a is the PMS 27 order linearity correction although this parameter is not used and instead the
7. Vies tae Eq 153148 In order to ensure a circular footprint on the ground the process must be initiated backwards i e given the Earth pixel a ground circular footprint is considered and projected onto the antenna frame as an This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor pate 29 10 10 deim s MG ENGENHARIA Ue s Theoretical Baseline page 70 of 89 ellipse This ellipse is the desired output of the 3dB contour for the Array Factor computed in Eq 152447 which will require a specific window for that purpose First we will deal with the computation of the ellipse equation in the antenna frame of a circular ground footprint The following diagram illustrates some angular relationships like Fig 14 Earth CM Figure 15 Angular relationships for pixel The transformation of the coordinates of any vector from the X Y Z to the x y z frames must be expressed as a product of the following rotations amp cos 0 sin cos sing 1 0 0 X 0 1 0 sing cosg 0 10 cost sint Y sine 0 cose 0 0 1 40 sint cost Z where f is the tilt angle of the antenna arctan y x is the azimuth angle from the nadir and is the arc between the nadir and the point position from the centre of the Earth assumed as spherical It is obtained solving the following equati
8. p bas jn Uu Eq 98 Where Ta is the system temperature used to denormalize the correlations Finally a weighted average is applied taking into account the estimations from the two adjacent calibration point in the orbit This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C ngn SMOS L1 Processor pate 29 10 10 deim s Algorithm EU ENGENHARIA 7 siwae Theoretical Baseline Page 42 of 89 3 1 11 PMS cold sky calibration 3 1 11 1 PMS characterisation The CAS calibration procedure can be validated when the instrument is in deep sky measurement by calibrating the PMS in the same way as the NIR is calibrated and then comparing both calibration sets of parameters A calibration sequence has been designed for this process and it will be recognised by the L1PP First we define a method to calibrate the PMS gain in orbit Gi by using the U load as WARM noise Vy the receiver output when looking ate cold sky COLD noise G _ Vu Vsky E WE SKY Eq 99 A H V where 7 are the physical temperatures of the receivers when in Uncorrelated noise injection and Tos are retrieved from the cold sky map as in Section 3 1 9 The PMS offset and attenuator ratios can also be computed if the PMS 4 point voltages are redefined as v PMS output voltage for deep sky mode with attenuator
9. SO DS DME L1PP 0011 Fg XY C SMOS L1 Processor pate 29 10 10 deim s Bii Algorithm ENGENHARIA M Theoretical Baseline dien where 5 and s are the modulus of the switch S parameters relating port C or V with port L in the k receiver dependent on physical temperature 77 is the ohmic efficiency of the antenna k in H or V mode v are the PMS voltages for the antenna k measured while the visibilities are retrieved are the PMS calibrated offsets and are the PMS calibrated gains also dependent on physical temperature A further correction to PMS 2 order linearity needs to be applied before the plane transition as is explained in Eq 36 in the next section 3 1 5 2 Arm system temperatures The MIRAS SMOS configuration uses a distributed approach to inject noise in the three arms of the instrument Each arm is divided in three sections with 6 receivers each denominated quite simply segments 1 2 and 3 The following assumptions were made 2 EVEN noise sources 0 and J placed at ports 0 and B of the 2 ODD noise sources and placed at ports and y of the 18 PMS placed at the HUB 3 NIR placed at port 1 of the HUB 6 PMS placed at first segment of each arm 6 PMS m placed at second segment of each arm oOo 6 PMS n placed at third segment of each arm The hub PMS calibration method of section 3 1 4 1 can be extended and
10. So introducing the definition of PMS gain from Eq 12 for each segment we have the values of system temperature in terms of PMS output v gain and offset DE 2 2 _ 40 HV _ Sia sys Ny yi 2 2 _ 40 HV _ s 8 EM 2 Eq 3 Sia Vm m 2 _ 2 _ as Vi Vota S 2 YQ Sia G 3 1 5 3 NIR temperatures This section was based on the description of NIR calibration procedures in RD 16 and on the latest In Orbit Calibration Plan AD 6 For more information please refer to those documents This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C n SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA JF Theoretical Baseline 26 of 89 3 1 5 3 1 NIR brightness temperatures 3 1 5 3 1 1 Dual polarisation temperatures In dual polarisation mode the NIR brightness temperatures are computed from data retrieved in NIR A mode namely the NIR pulse length and the measured noise temperature A yr AB A AA y AB with AA Tro Eq 39 AA us T nM AB BAT Tua AB OAT where 77 are the pulse lengths and polarisations is the physical temperature of the antenna patch
11. Temperature scene using steering 30 of MIRAS instrument 20 40 60 0 80 0 100 120 A 20 40 6 80 100 120 20 4 8 10 120 Figure 11 XI left image and ETA right image coordinates proposed for the G Matrix format The distribution of 128x128 elements must be arranged in a vector form of 16384 elements placing elements row after row Additionally the complete size of G is dependant on the level of coupling that exists between polarisations This coupling is due to the cross polar antenna patterns of each receiver in each polarisation and finite input switch isolation included in the antenna pattern measurements through TRF port The complete G matrix can be expressed as in the following figure taking all the previous data into account This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 2f XY age 2 SMOS L1 Processor 29 10 10 deim s Bii Algorithm ENGENHARIA swe Theoretical Baseline Boi en Cx xc RI Jic Xxx Rin m C C Ry X C c 07 0 X vem ntencunm perci C c ex x Ry XX CACY x Re Figure 12 matrix decomposition C and X are co cross polar Antenna Patterns is the Fringe Wash Function multiplied by the complex exponential term see Appendix 5 If the level of the cross polarisation p
12. Code SO DS DME L1PP 0011 e SMOS L1 Processor pate 29 10 10 deim s Algorithm EHGENHARIA s Theoretical Baseline page 7 of 89 2 1 1 1 Dual Polarisation Mode In dual polarisation mode each scene will be a complete HH or VV mode measurement with the upper triangle of the correlator matrix containing the iq raw correlations and the lower triangle containing the ii raw correlations Therefore each scene can be calibrated and processed individually The complete array of visibilities in the star domain can be obtained by taking the complex conjugates of the opposite elements in the correlations matrix 2 1 1 2 Full Polarisation Mode In the case of full polarisation mode however data within each scene will contain information about different cross polarisation measurements This is depicted in the following picture Sub interval T3 Arm pal Arm pol Arm C H pol ASIC 01 ASIC 02 WH Sub interval T2 Arm pol Arm B H pol Arm pal Sub interval T1 Arm H pol Arm pol Arm ASIC 00 ASIC 01 ASIC 02 Wh ASIC 02 ASIC 00 Wh ASIC 00 HH ASIC 01 HN ASIC 03 ASIC 04 HH ASIC 05 HN ASIC 05 ASIC 03 HN ASIC 03 WH ASIC 04 Do vy ASICO4 ASIC 05 vy VH ASIC 08 HH ASIC 06 ASIC 07 HN ASIC 07 WH ASIC 08 Wh ASIC 08 ASIC Whi ASIC 06 WH ASIC 07 Do
13. These operation modes are switched on demand in order to inject noise in the radiometers and measure calibration coefficients for several elements The procedures are described in detail in AD 5 and AD 6 2 1 2 1 Uncorrelated Noise Injection Uncorrelated Noise is generated locally at each LICEF with the purpose of detecting any offset that may happen in the correlators 2 1 2 2 Correlated Noise Injection Correlated Noise is injected through the Noise Sources following a certain strategy described in the AD 5 and AD 6 Additionally attenuators may be activated on the PMS elements and delays introduced in the path of the correlated signals Not only the APID is used to determine the processing strategy but also additional parameters in the ancillary packet like the CMN Last Executed Command and FWF delay are needed in order to properly identify and process the calibration data 2 1 2 3 External Calibration modes These operation modes are switched on demand in order to calibrate the NIR elements PMS gains and offsets and also to image sky or moon scenes that may be used for the Flat Target Transformation or G Matrix calibration in orbit The APID is commanded to change to APID EXC DUAL APID EXC FULL depending on the polarisation mode or APID EXC C and APID EXC U for noise injection calibration while measuring external targets However not all packets with the previous APIDs are used for NIR calibration it also depen
14. Vol 42 No 8 pp 1677 1682 RD 24 Coliander et al MIRAS reference radiometer A fully polarimetric 2005 NIR IEEE Transactions on Geoscience and remote sensing Vol 43 No 5 RD 25 Campbell S L and Meyer Generalized Inverses of Linear Transformations 1991 C D Jr New York Dover RD 26 SO TN UPC PLM 0048 MIRAS EM tests at INTA facilities 2 6 RD 27 SO RS CASA PLM 0050 CCU Requirements Specification 3 3 RD 28 SO TN UPC PLM 0054 In Orbit LICEF and CAS receiver temperature 2 1 calibration RD 29 Zundo B Duesmann On ground BT Frame of Reference TN 3 3 SO TN ESA GS 5873 Table 2 Reference Documents 1 4 Naming and Mathematical Conventions Throughout this document polarisations H and V are used to refer to the antenna reference frame Other documentation within the project use only H and V to refer to the ground reference frame and reserve X and Y for the antenna reference frame It should be taken into account when reading the current document that all data produced with the presented equations using H and V parameters shall be expressed in the antenna reference frame unless otherwise indicated This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C SMOS L1 Processor 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline page 5 of 89 F
15. Where t is the tilt angle of the instrument 32 5 X and Y are the polarisation axes in the antenna frame and Ey and Ey are the polarisation axes in the pixel frame Ey is orthogonal to the PS and PO directions and Ey is orthogonal to Ey and PS The angles may be computed using the following expressions as defined in RD 14 _ We Eq arccos 138139 sintcos cosfsin sin arcsin Sing Eq sin 139140 costsin sintcos sing E 9 usin n 140 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 1 XY C SMOS L1 Processor 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline 65 of 89 Where is measured from the X axis and positive clockwise in the XYZ reference frame and gis the in plane geometrical rotation between polarisation frames The above expressions are valid for the range for the range E z the angles must be simply computed as sinfcosQ sing iB 141142 acp costsin sintcos sing Eq 511 142143 The final geometrical rotation value from pixel frame to antenna frame is given by 2 The antenna frame observation angles can also be obtained using the Cartesian coordin
16. v alus NUM Vig INI v 5 05 amp Co T NL gg gg 7 O Eq 18 By t 1 5 00 p ret EO where k a are the modulus of the S parameters relating the k receiver with the noise source dependent on physical temperature The term M will be measured with HOT noise temperature while the term B is measured with WARM noise temperature The normalised values at time delays shall be used to estimate the FWF shape coefficients as it is described in RD 16 The value of fIF is the intermediate frequency computed as the central frequency minus the local oscillator frequency both values are contained in the PLM ADF The FWF estimated values at the origin are then computed the antenna polarisation reference planes by gh 0 _ 85 0 eus Vk LH Vj ef Eq 19 Where S and S are the phases of the switch S parameters relating port C and or V with port L in the k receiver dependent on physical temperature and v are the antenna patterns absolute phases Only the FWF at the origin needs to be translated to the antenna plane the shape values FWF at time delays will be a function of g 0 The g values are complex and will be used to correct amplitude and in phase errors The values shown in Eq 19 can only be computed for pairs of receivers that share the same Noise Source as correlated noise can only be injected through the same Noise
17. 2346 complex elements plus 3 real elements from the measurement Vy with the same amount of values 2346 complex 3 real and with 3303 complex elements The total number of input real valued elements is then 2346 2 3 2 3303 2 15996 In order to understand the origin of these numbers it must be clear that in H or V polarisation the amount of signals correlated is always 72 but of these only 69 are in either H or V polarisation The remaining 3 are signals being correlated by the LICEF NIR receivers in the opposite polarisation so only 69 68 2 complex correlations are measured which is the source for 2346 The NIR elements are also measuring the total power of the image which is the source for the remaining 3 real elements The case for HV polarisation is fully explained in RD 10 and shall not be repeated here The required output are the Brightness Temperature values in all polarisations and Ty are real valued whereas is complex valued Assuming a default size of 128x128 the total number of output real valued elements is 128 128 4 65536 Of course the size can be reduced to 64x64 although a bigger sampling grid means that more detail is introduced in the System Response Function by using a finer antenna pattern grid This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 EN C LI LUE SMOS L1 Processor 29 1
18. Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline 79 of 89 Making the sum over and explicit and expanding for the indices H V Eq 181496 becomes HT HH p HH HH HV p HV HH p HV HV HV p HH Eq Mir Rar SI Paa 182472 VV _ pVH HH VH HV VV Eq IU tr ES 183128 HV pVH HH DHV AHV pVH Eq k TES F f R riy F F R ali 184179 _ P HH p HV VH P HH VH Eq uper OP Wg eid Rag FEO ES Rg SEE Rg 185480 Now using T T and expanding the complex numbers we have HH HH DHH p HH y E P Riva 7 P HV vv PER pa a Ame DHH pHV HV 186181 Rs sp HH HV BR E Rl H EP E fax Vv er 7 WV pVH Eq NN 187182 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor pat 29 10 10 deimos DD gt mu ENGENHARIA J s Theoretical Baseline page 80 of 89
19. Cartas t LITT M E 168163 _ 1 2cos 9 1 2 12 cosgsing 2 72 cospgsing Eq B Fol ika bata cos sin array cos Unt sin 169164 _ 1 of BH cos sin amp org BUR S Eq di zd tEn cos tabs Laba cos 0 sin PONI sin 8 170165 The angle of the first semi axis with respect to the axis is _ 2 5 arcan 22 171166 and the semi axis are defined by Eq E Acos 2Bsin cos Csin 5 172462 E A Asin 5 2Bsin cos C cos A sin sin COS cos 173168 Once we have the desired ellipse parameters in the antenna frame it is required to find a suitable apodisation window whose Equivalent Array Factor 3dB contour fits that ellipse For this purpose a previous study described in RD 15 shows how to adjust a 2D window based in Kaiser windows This apodisation window expression is the following 2 2 1 d I 174469 p Where Jp is the Modified Bessel Function of the First Kind and has the following expression E 175420 k 0 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C SMOS L1 Processor 29 10 10 deim s Algorithm ENGENHARIA 7 siwae Theoretical Baseline 74 of 89 The alpha parameter in each Kaiser window drives the ta
20. E20 B2 1 cA CAd cd con coz cos coe co7 cog cas ctc o 12 613 14 c15 c16 c17 c t8 c t9 cao c21 Tx Ix KKK TKK x x x xxx x x x x xxu x x Boon 503 caps x C03 C21 Figure 9 Baselines covered by the same Noise Sources Even and Odd Eq 20 a IE om E wef So I 1 a gt 90 La Amplitude and phase estimations need to be done at CIP Calibration Input Plane plane and they are achieved by using the closure relationships method proposed in RD 7 In this method the value of the
21. Figure 3 Full polarisation scene output HV info VH info ASICO3 T2 ASICO6 ASICO3 T1 ASICOG6 T1 ASIC01_T2 j ASICO2_T3 j ASICO1 T1 j ASICO2_T1 j ASICO3 T1 ASICO7 T3 ASICO3 T2 ASICO7 T2 ASICO1 T1 j ASIC05_T3 j ASIC01_T2 j 1 05_ 2 ASICO6_T1 ASICO7 T2 ASICO6 ASICO7 ASICO2 T1 j ASICO5 T2 j ASIC02_T3 j ASICO5_T3 j Figure 4 Full polarisation LO data reordering This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 y C n SMOS L1 Processor 29 10 10 deim s Ri Algorithm im ENGENHARIA Jf Theoretical Baseline 8 of 89 In order to process the full polarisation data the ASIC data in the three top scenes as they are received in LO must be rearranged in order to retrieve same cross polarisation brightness temperatures It has been decided that this reorganization will only be done after L1a data has been produced namely in the Image Reconstruction module In fact each scene for full polarisation measurements is self contained calibration wise What this means is that each scene even if it has information about different cross polarized modes has all the necessary information to be amplitude and phase calibrated For more information on this subject RD 10 can be consulted 2 1 2 Internal Calibration modes
22. Viva tiv S EPPP R yah tE PE R ya 1282 a E UP EI Ru P EP RA n F DHH pVv pVV 7 HV i ISSN Ral T Rigs Mo den 128 tas 25 il Aa dL PIRA TR in ik ui d FP R k p MT EP Rs Jp ti EPR ya n ET p HV HV HV e HS AYER va Ral au DF From Eqs 188183 and 189184 it is easily checked that Vie ye 50 we only need e g Eqs 186484 188483 which can be rearranged as J J HH jj J J A i HH AHH PF F HH Rir HV p HH HV EP BEP YR n HV B HH J D Eq pU 190185 a wR HV Ry rx Te que k Eq 191186 Riva 4 J This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission 2an y SMOS L1 Processor 55 T ENGENHARIA JF Theoretical Baseline 81 of 89 VL E aN ae Eq E Ral 192487 CE P PI Vija D P F R ya HEP Rl d Eq Em e E nC 193188 P a i n Eq EP EP EPEP R mE 194189 CEET EP Vi U FP a ri
23. applied to the PMS in the arms Two sets of PMS voltage readings can be obtained from EVEN and ODD noise sources In the first segment the PMS can be calibrated using the NIR at port 1 of the HUB when driven by the common ODD noise source Due to the symmetry of the temperature at port C of each of the 6 PMS receivers we can calculate RD 17 Si Y 5 v v C la 1 9 2 1h _ 70 Tas n NS2 Ts Eq 27 415 d m Va IS WaT Vin where the noise source temperatures are averaged from the measurements of the receivers in the hub excluding the NIR channels Since the offset term can be calculated from both sources EVEN and ODD it can be written as 5 28 where This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 e SMOS L1 Processor pate 29 10 10 deimos qae d ENGENHARIA Theoretical Baseline Page 24 of 89 0 0 0 0 ui ofl 0 0 0 0 Var T T Vu Vai Eq 29 QE uu Ta EE a a a a Vj Vay T Viu Please note that for the last segment in each arm Eq 27 is not used since there is only one noise source available While this averaging can be done for the offsets the same can not be done for the gains since these depend on the S Parameters of the paths connecting the LICEFS with each Noise Source Making use of
24. are converted from the calibration plane to the H and V Input planes through qe Lois per ee m i rec L rec pUv DCv DCv Eq 54 obe per DCh DCh and then into the antenna planes by t Llin by by tL LI Eq 55 HAP __ LH HIP Te Tu L2h T LL LNCh 11 1 DL Where is the total receiver noise temperature at the antenna plane rec The coefficients present in the previous computation are found using the following relations The receiver temperature between antenna patch input plane and antenna intermediate plane H or V is This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q iti SMOS L1 Processor pate 29 10 10 dei m s Algorithm Issue 2 10 ENGENHARIA Ur Theoretical Baseline 31 of 89 Triva Livn 1 56 The receiver temperature between the antenna intermediate plane and the input connector plane or V is Dag isa Das Eq 57 The receiver temperature between the input connector plane and output connector plane is Linca 7 DT Eq 58 The receiver temperature between the output connector plane and LICEF input connector plane is Tr v Lava a DTr Eq 59 The parameters used in the previous equations measured on ground are Receiver temperature between
25. averaged values for the other variables does not introduce relevant errors These averaged values are SSS 35psu SST 15 C wind speed 5m s wind direction 0 North Usage of this model is considered as the baseline for computing the Reflected Sun contribution to be subtracted in visibilities For the Direct Moon contribution it is treated as a point source Similar to the Sun method the brightness temperature is self estimated over the position where the Moon is located using CFI The effect of the reflected Moon is negligible The equation to be solved is reduced then to the following expression where the input now is the differential visibilities and the expected output is the variation of Brightness Temperatures over a constant value Pq Fe or D OF j2z uy vr t wy Jl AT ADI ue E E Vig Wy v Eq 1 6 deo a ra 123 Or in matrix form This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Jan SMOS L1 Processor pat 29 10 10 4 D NEM oim ae ENGENHARIA Theoretical Baseline Page 54 of 89 AW g7 ATP Tyy GS GL Gy X AT D Eq 124 AV GP AT 6 7 The final result of the brightness temperature is obtained from the output of this previous equation plu
26. components For the dual pol case after the raw normalized correlations are computed Eq 2 the full ks correlations matrix can be simply built by transposing the elements measured below the This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C ngn SMOS L1 Processor pate 29 10 10 deim s Algorithm ENGENHARIA 7 siwae Theoretical Baseline Page 14 of 89 diagonal and the full ju correlations matrix must be built using the complex conjugate when transposing elements For full pol mode the LO data must be previously re arranged as described in Section 2 1 1 2 The main diagonal values are only used for the quadrature correction since they do not define any baseline each element corresponds to an auto correlation 3 1 2 LO decoding and fundamental calibration equations To obtain the digital correlations from the correlator counts the following transformation is used N yoz Eq 1 C max where is the maximum number of counts is an integer from O to Nomas the digital ii iq correlations or raw normalised correlations Tange from 0 to 1 The raw normalised correlations between antennas k and j and for each polarisation and cross polarisations the in phase and quadrature values ii and 14 are converted into normalised correlations u by solving t
27. coordinate system reference frame amp units nomenclature Table 1 Applicable Documents 1 3 2 Reference Documents 2 0 S jiu N S A Ut Ww RD 1 EE MA DMS GS 0001 1 Earth Explorer Mission CFI Software MISSION 1 5 5 090313 CONVENTIONS DOCUMENT RD 2 PE TN ESA GS 0001 Earth Explorer Ground Segment File Format 1 3 Standard RD 3 EE MA DMS GS 0002 3 Earth Explorer Mission CFI Software GENERAL 2 0 7 2 080731 SOFTWARE USER MANUAL RD 4 SO IS DME L1PP 0014 SMOS 11 Processor Input Output Definition 2 3 Document RD 5 SO IS DME L1PP 0002 SMOS L1 Product Format Specification 2 3 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission deimSs Critical ENCGENHARIA software Code SMOS L1 Processor pate Algorithm Issue Theoretical Baseline page SO DS DME L1PP 0011 29 10 10 2 10 RD 6 SO IS DME L1PP 0003 SMOS L1 Auxiliary Product Format 2 3 RD 7 Butora M Mart n Neira Fringe Washing Function Calibration in Aperture 2003 A L Rivada Synthesis Microwave Radiometry Radio Science Volume 38 Issue 2 pp 15 1 RD 8 David M Le Vine amp Saji Faraday rotation and passive microwave remote 2000 Abraham sensing of soil moisture from space Microwave Radiometer Remote Sensing Earth s Surf Atmos P Pampaloni and S Paloscia Eds VSP BV Th
28. e Next 528 rows with calibrated visibilities of elements in arm B in polarisation against elements in arm C in V polarisation Same order as above i e first LICEF BC 03 against CA 03 then LICEF BC 03 against LICEF CA 01 V then LICEF BC 03 against LICEF C 01 until the 23 element LICEF 03 against LICEF C 21 Next is LICEF 01 against LICEF 03 then LICEF BC 01 against LICEF C 01 and so on until all elements in arm C are correlated with LICEF 01 Please note that this row does not include the correlation against LICEF CA 01 V This ordering continues until the last element correlated is LICEF 21 against LICEF C 21 e Next 528 rows with calibrated visibilities of elements in arm in polarisation against elements in arm A in V polarisation Same order as above i e first LICEF CA 03 against LICEF AB 03 then LICEF 03 against LICEF AB 01 V then LICEF CA 03 against LICEF 01 until the 239 element LICEF 03 against LICEF A 21 Next is LICEF 01 against LICEF AB 03 then LICEF CA 01 against LICEF A OI and so on until all elements in arm A are correlated with LICEF 01 Please note that this row does not include the correlation against LICEF AB 01 V This ordering continues until the last element correlated is LICEF 21 against LICEF A 21 e Next 528 rows with calibrated visibilities of elements in Arm C in H polarisation against elements in Arm B in V polarisat
29. is the angle between the local normal at each pixel and the pixel to satellite direction whereas the azimuth angle is the angle measured between the pixel to satellite direction projected in the local tangent plane and the local North direction These angles shall be computed with the help of the CFI functions using the spacecraft position and the latitude longitude and altitude coordinates of each pixel in the Earth fixed grid This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q C PES SMOS L1 Processor pate 29 10 10 deim s Bir Algorithm ENGENHARIA Theoretical Baseline pag TAMEN 3 3 2 4 Pixel Footprint Shape Computation Beyond these computations the pixel shape is obtained as the projection onto the Earth fixed Grid of the 3dB contour of the Synthetic Antenna Directional Gain This projection is approximated by an ellipse in which its major semi axis is oriented with the azimuth observation angle The Synthetic Antenna Directional Gain also known as Equivalent Array Factor may be computed in the antenna frame by following the expression 43 2 Um hd E E Ymn 2 17 Eq AF E tans mn cm J 152147 n Where W ttnn Van is the apodisation function computed before 7 is the fringe washing function which accounts for the spatial decorrelation betw
30. objective is to have an independent source for the antenna temperature not related to the NIR measurements The basic principle behind this formulation is presented in RD 28 and is repeated here below The System temperature at LIP plane when the switch is in U position is given by the following equation poer 45 Eq 92 sysk Where is receiver temperature at LIP plane and T pyg is the physical temperature of the U Load LICEF isolator However since the PMS is calibrated at CIP plane we must write system temperature at this plane n T us Eq 93 2 Sick And now taking into account that this system temperature can be retrieved by the PMS as per Eq 65 the receiver temperature at LIP plane can be recovered from PMS measurement as 2 UC 4 Sul Eq 94 re sysk This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C ngn SMOS L1 Processor pate 29 10 10 deim s Ml Algorithm ENGENHARIA 7 siwae Theoretical Baseline Page 41 of 89 Note that PMS gain at CIP plane must be temperature corrected to have Tun This is directly achieved as the U load is incorporated to the short calibration sequences where PMS gain is calibrated simultaneously Now the magnitude we want to retrieve is receiver temperature at VAP HAP plane when the switch is in A V H posi
31. off Lp v PMS output voltage for uncorrelated noise injection mode with attenuator off Lp Q v PMS output voltage for deep sky mode with attenuator L v PMS output voltage for uncorrelated noise injection mode with attenuator on I and by using Yi V4 Ne v m v v ary ba Ok The PMS gains can be compared to the ones computed in Section 3 1 5 4 by translating the deep sky calibrated gains to the CIP plane This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 ES C iti SMOS L1 Processor pate 29 10 10 dei m s Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline Page 43 of 89 Sial mee Eq 101 Mak IS A H V where 77 are the antenna ohmic efficiencies and the switch S Parameters are the ones defined in the previous sections A measure of the relative error is computed as G m k Eq 102 A H V 3 1 11 2 CAS and receiver temperature validation The cold sky measurements can also be used to validate the CAS plane translation coefficients computed from ground data The coefficients used for comparison are defined as 2 2 end __ IS IS Nk Q2 o e esr Eq 103 A H V The equivalent coefficients can be computed from deep sky measurements when during shor
32. s Mr Algorithm ENGENHARIA 7 siwae Theoretical Baseline Page 45 of 89 3 2 1 System Response Function The instrument s System Response Function is determined by the following equation as referenced in RD 19 but accounting also for the real antenna positions which may not be on the same plane and so the third cosine director coordinate w has to be included F mE i Pq p u v Il n k 7 n j 7 B d sss mm 1 E n XI i Eq 109 Where the following parameters are presented EE 7 is the normalised antenna radiation pattern of receiver in polarisation p expressed in cosine domain coordinates n Q isthe antenna solid angle of receiver in polarisation p T rec is the averaged physical temperature of the receivers multiplied by the Dirac delta 5 to represent that it is not applicable when the polarisation indexes p and q are not equal i e cross polarisation 715 the Fringe Washing Function term that accounts for decorrelation effects in the path of the correlated signals This equation relates the calibrated visibilities measured by the instrument with the Brightness Temperature scene that is being observed Due to the nature of the double integral and expressing the visibilities and Brightness Temperatures matrices as vectors this relationship can be expressed as a matrix vector multipl
33. the differential on the above equations results in dX sin cos r cos 0 cos r sin sin dY sinOsin dr r cos 8 sin r sin cos oS dZ cos dr rsin d That can be expressed in form of another rotation matrix M X rcos cos rsinOsin sinOcos d dY rcosOsin rsinOcos sinOsin d dZ 0 cos 9 dr s So variations in the coordinates in the pixel reference frame can be related to angular and radial variations in the antenna frame using the expression This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor pate 29 10 10 deim s Algorithm we T ENGENHARIA Jr Theoretical Baseline page 72 of 89 cos cos cos sing cost sin sint cos sing sint sin cost dyp sing cos Cost cos sint x sin cos sin sing cost cos sint sin sing sint cos cost Eq rcos cos rsinOsin 40 161156 x rcos sing rsinOcos sinOsin x d L x d rsin 0 cos Q dr dr In which the complete rotation matrix can be called L Thus if a circular pixel of radius R on the Earth surface is required and contained in the local tangent plane at the pixel position the following expression can be imposed 1 fe dXp E dis dys dyp 1 1 16245
34. the following relationship between the Fourier transforms of FWF values for pairs of receivers that use FWF for pairs of receivers not connected to the same noise source k and j can be computed by using the same noise source kl mj and Im Not all of these closures can be made with the direct measurements from Fig 9 As such a series of closures will be found consecutively trying to use as many direct measurements as possible In the following figure the number of closures to compute the FWF for each pair of receivers is displayed This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C iti SMOS L1 Processor 29 10 10 dei m s Algorithm Issue 2 10 ENGENHARIA Ur siwe Theoretical Baseline page 21 of 89 FWF number of closures gt new method 1 5 Figure 10 Number of closures needed to compute the FWF for each pair of receivers There are however a number of baselines that do not have any possible closure for the estimation of the FWF namely the ones between receiver LICEF A21 and all the receivers in arms B and C and the ones between the receiver LICEF 21 and all the receivers in arm C amounting to a total of 72 baselines For these remaining pairs of receivers the FWF will have to estimated by computing the average amplitude value at CIP plane of the measured elements and assigning it
35. the same symmetry the calibration temperature for receivers m in the second segment can be calibrated with C 70m 206 mf BC2 poa Sy 2 Eq 30 Vom T uw since in the first segment can play the role of NIR when both segments are driven by the common noise source p Since the PMS have been calibrated already we have pr MI PR 5 Van Min Nap Voi 7 Vogt Is P zs T 2 T DL 2 51 Vat Vii Mal Vin Y Vit 5 m Eq 31 E Vg 12 Min T al Ty Ts 7 Ins 5 NS2 51 Vi Vin Vay Vit Sul yielding ET y y y 5 IM C _ zum 21 ll la B 2 Eq 32 Ven Vs vi Sia Moreover the taking into account that each noise source drives 12 receivers 6 PMS in each segment can be used as NIR and the results averaged in order to improve the results The previous will then transform into f vh Sial vi Sia 6 S 6 mp Ts 15 33 EL CN s va lS i Finally the same procedure can be applied to the third segment for the PMS n 2 C _ Yn Val 5 Y y Von in 709 Eq 34 sysm sysl my This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Co
36. to take into account the incidence angle effect In the case of the Direct Sun and Moon the distribution is taken as a point source setting the computed value over the appropriate spatial coordinates and zero for the rest In the case of the Reflected Sun it has been mentioned before that it shall use a distribution computed using a reflection model with averaged auxiliary parameters The averaged physical temperature of the receivers is taken from the Lla HKTM measurements and is set as constant in the entire xi eta integration domain The Brightness Temperature distribution entering through the backlobes has an effect that is highly dependant on the level of the backlobes radiating patterns which are very low It is most probable that the only worthy contribution will come from the Sun when it is illuminating the back of the instrument However in order to take into account the backlobes contribution to the visibilities the average backlobes antenna patterns are used The Flat Target Response measurement is described in the following section This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C ns SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline 55 of 89 3 2 2 1 Flat Target Transformation This process shall compute a transformation similar to th
37. to the baselines that were not measured Phase estimation for these remaining pairs of receivers is achieved by first solving the system of equations determined by a 0 0 6 Eq 21 g Where 04 is FWF phase of the baseline k j at plane are the phase of receivers j and respectively and 6 is the non separable error The system is solved initially by assuming that the non separable errors are negligible The system is over determined as there are 1296 equations and only 72 unknowns As a reference phase is required the phase of receiver LICEF A01 shall be taken as 0 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 1 XY C SMOS L1 Processor 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline Once the best solution is found for each receiver phase the non separable error be estimated for those baselines that are not covered by any closure by computing the average value of the error between the measured FWF phase and the solutions of the receivers phases as per the next equation 9 mean 8 Sh Eq 22 The FWF phase is then estimated by using a modified version of equation 21 0 0 0 Eq 23 3 1 5 System Temperatures Computation In measurement mode the visibilities must be amplitude and phase corrected wi
38. will be computed as Eq 26 y n Eq 65 The U load system temperatures and Fringe Washing Function at the origin are then used together with the quadrature corrected correlations compute the visibilities offset UCrpUC UC 575 55 85 SUC __ YS Eq 66 3 1 7 Error Compensation 3 1 7 1 Visibilities Calibration The final step for calibrating visibilities is to de normalise them with the system temperatures computed in the measurement mode calibration This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission IN Code SO DS DME L1PP 0011 e C iti SMOS L1 Processor pate 29 10 10 deim s Algorithm ENGENHARIA Theoretical Baseline Page 34 of 89 __ H Vrp HV I Ts M kj Eq 67 and apply the in phase and amplitude error corrections as well as removing the offsets computed previously The visibilities offsets are corrected with the switch S parameters retrieved using the physical temperature at calibration time 5 30 uy Eq 68 i DECEM EUM The final equation will thus be g E be V 77 a Vy Eq 69 Kj where is a coefficient to adjust the influence of the visibilities offsets in the final calibrated visibility This coefficient is defined as an integer number 0 1 or 2 indicating if offset correction is needed for baseline kj Additionally as
39. 0 10 deim s Algorithm ise ENGENHARIA 7 siwae Theoretical Baseline 47 of 89 Thus the unique G matrix is composed by 15996 rows and 65536 columns with real valued elements Using a real valued matrix is preferred as it reduces the size and ensures that the output in Brightness Temperatures for H and V is real valued Rows in the G matrix are generated from particularising the general Eq 109 for a pair of LICEF receivers k j indexes and polarisation values of the antenna patterns and Brightness Temperature p q indexes The rows are ordered as follows The first 2346 2 3 rows correspond to polarisation calibrated visibilities p and are The next 2346 2 3 rows correspond to V polarisation calibrated visibilities p and are V The final 3303 2 rows correspond to HV polarisation calibrated visibilities is and is V Going into more detail The first 3 rows correspond to the zero baselines as measured from the for polarisation The first row corresponds to the NIR AB measurement then BC and last CA The next 2346 rows correspond to the real values of the polarisation calibrated visibilities as received from the L1a products and ordered in the same approach as shown in figure 11 in chapter 4 3 1 3 of RD 5 ie first element is the calibrated visibility of LICEF AB 03 against LICEF AB 01 next is LICEF AB 093 against LICEF A 01 etc until the sixty n
40. 2 0 0 Er Then if the dependency calculated above between pixel centred coordinates and antenna frame spherical coordinates is introduced the following expression is obtained V 0 0 Lon LR L L by 40 Ly Ly 0 p OL L 1 40 1 163158 La L4 L4 0 0 0 L Ly La dr It can be easily seen that for negligible variations in the radial direction the classic equation of an ellipse is obtained in the antenna frame Of course this assumption is not valid for high incidence angles where the radial direction is almost tangent to the Earth Eq Lj Ly dO 2 Ly Ly L L dd 5 dj 164159 Deriving the 4 77 coordinates from Eq 149144 the variations are expressed as cos 10 165160 sing Eq dg d d sin 0 et sin y 166161 Substituting these expressions and transforming the differential elements into discrete increments the following equation of an ellipse in the antenna frame is defined This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SQ DS DME L1PP 0011 d Critical SMOS L1 Processor Date 29 10 10 el m OS Algorithm Issue 2 10 ENGENHARIA Jr Theoretical Baseline page 73 of 89 2 2 A A 2 B dAE An C An 167162 where the ellipse coefficients are cos sin gt Eq Ac E 2
41. 9 10 10 deim s Bi Algorithm ENGENHARIA M Theoretical Baseline pag mares The way to compute the different coefficients is shown in AD 6 It consists on using the measurements at time lags Ts 0 and from Eq 19 for estimating the parameters A to The equations to be used are le T A sinc B T C sy 0 A sine B C PEUT su T A sine B T C arg 27 _ a T e t 0 S Eq EEG 1 re ej 1 131132 2 T p aga 0 The FWF is measured independently for H and V polarisation and also for the paths of the in phase and quadrature signals meaning that for the same visibility there are two different values of the FWF One is applicable to the real part component of the visibility while the other is applicable to the imaginary part of the component The following equation shows this behaviour in detail E US Vy Jo j2m ug vgn wyOF TP 1 T FP EMF Pia 7 rec k 6 7 6 7 Eq 07 T G m T9 Gum ura 1 2 i 49 09 2 smt 1321 dk j The LICEF coordinates which are used to compute the applicable u v baselines Eq 109 can be taken from their initial measured positions in an Auxiliary Data File or an elastic model may be applied to obtain them as a function of time Regardless of the approach UPC has already modelled devia
42. A rm emm Finally the coefficients 7 are computed from the NIR pulse lengths by the following rules This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 J C iti SMOS L1 Processor pate 29 10 10 deim s Ml Algorithm E ENGENHARIA Ur siwe Theoretical Baseline page 30 of 89 i n zn mm 1 1 n 7 7 min UNUM Eq 52 n 3 7 2 1 1 By expanding all the coefficients of Eq 48 the full equation for T and T is obtained 1 Re L Aug Ts Tys M fi Kine 1 LES 8 Eq 53 The terms f and ra are the corrections for cross coupling and leakage computed during the NIR calibration process Section 3 1 9 3 Moreover Eq 53 has been further simplified from Eq 48 by using the definition of quadrature corrected correlations Eq 7 The values are computed in VIP since both NIR LICEF are switched to the NIC and subsequently to the antenna using the VIP port The procedure to transform the FWF 0 to the antenna plane is the same as described in Eq 19 but taking care to use the combination of H and V polarisation needed in this case and noting that the final plane is still VIP for both polarisations 3 1 5 3 2 NIR receiver noise temperatures LV CIP LH CIP The receiver noise temperatures measured in LICEF LC LC2 mode see Section 3 1 8 2
43. Baseline bd cran e If v sqrt 3 NEL 1 d 2 then goes from 11 4 to 11 d in incremental steps of d If v sqrt 3 NEL 2 d 2 then has the values 23 d 2 19 d 2 to 19 d 2 in incremental steps of d and 23 d 2 Notice that the elements 21 d 2 are not present e f v sqrt 3 NEL 3 d 2 then has the values 12 d 9 d to 9 d in incremental steps of d and 12 4 Notice that the elements 11 d and 10 d are not present e Finally if v gt sqrt 3 NEL 3 d 2 and v lt sqrt 3 NEL d then goes NEL d v sqrt 3 to NEL d v sqrt 3 in incremental steps of d The order followed is shown in the next picture For the 1395 element vector the baselines are taken first from left to right then from bottom to top starting from the centre of the star 0 0 Le the first 24 elements are the ones with v 0 and ordered by increasing u the next 42 elements are the ones with v sqrt 3 d 2 and ordered by increasing u from negative to positive and so on until the 1395 elements are covered 20 20 Figure 13 J matrix baselines ordering For the case of HV polarisation where the vector is 2791 elements long the complete star must be covered In this case the ordering is similar to the one adopted above The first element is the zero baseline u 0 v 0 the next 1395 elements are ordered like it has been described left to right then bottom to top and the remaining 1395 element are order
44. C 01 H against all other receivers in arm B in V polarisation Le LICEF 01 against LICEF BC 03 LICEF BC 01 against LICEF BC 01 V LICEF BC 01 against LICEF B 01 etc until LICEF BC 01 against B 21 Next 22 rows with calibrated visibilities of all receivers in arm B in H polarisation against LICEF BC 01 V excluding LICEF BC 01 against LICEF BC 01 V whose equation is presented in the point above Le LICEF BC 03 against LICEF BC 01 LICEF B 01 against LICEF 01 V etc until LICEF 21 against LICEF BC 01 V Next 23 rows with calibrated visibilities of LICEF 01 against all other receivers in arm C in V polarisation Le LICEF CA 01 against LICEF CA 03 LICEF CA 01 against LICEF CA 01 V LICEF 01 against LICEF C 01 etc until LICEF CA 01 against LICEF C 21 Next 22 rows with calibrated visibilities of all receivers in arm C in H polarisation against LICEF CA 01 V excluding LICEF CA 01 H against LICEF CA 01 V whose equation is presented in the point above Le LICEF CA 03 against LICEF CA 01 V LICEF C 0I against LICEF CA 01 etc until LICEF C 21 against LICEF CA 01 V The following and last 3303 rows correspond to the imaginary values of the HV polarisation calibrated visibilities as received from the L1a products and ordered in the approach that has been just described Columns in the G matrix are generated from particularising the general Eq 109 for a certain pai
45. DE rud di J d UL AP EP SL Lar SEM Eng RB Rg These elements are represented in Figure 12 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission
46. Housekeeping Telemetry Microwave Imaging Radiometer by Aperture Synthesis Noise Distribution Network Noise Injection Radiometer Power Measurement System Position Velocity Time orbital vector Root Mean Square Error Satellite Housekeeping Telemetry SMOS Performance Simulator Temperature Brightness at Horizontal polarisation Temperature Brightness at Vertical polarisation Total Electron Content This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SMOS L1 Processor pate Algorithm Theoretical Baseline page SO DS DME L1PP 0011 29 10 10 2 10 ENGEN ARIA oftware TM Telemetry TOA Temperature Of Antenna UPC Universidad Polit cnica de Catalufia VTEC Vertical Total Electron Content 1 3 Applicable and Reference Documents 1 3 1 Applicable Documents AD 1 SO SOW CASA PLM 0380 SO RS ESA PLM 0003 SMOS DMFE LIPP 0014 SO TN CASA PLM 0017 SO TN UPC PLM 01 SO TN UPC PLM 0019 ECSS E 40B SO TN CASA PLM 0279 SO PL CASA PLM 0022 AD 2 AD 3 AD 4 AD 5 AD 6 AD 7 AD 8 AD 9 Level 1 Processor Prototype Development Phase 2 and Support Activities Statement of Work SMOS System Requirements Document SMOS 11 Processor Input Output Data Definition SMOS Payload Technical Description IN ORBIT CALIBRATION PLAN SMOS In Orbit Calibration Plan Phase C D ECSS E 40 Software Engineering Standards SMOS PLM Command and Control Definition of
47. RODUCTION 1 1 1 Purpose and Scope 1 1 2 Acronyms and Abbreviations 1 1 3 Applicable and Reference Documents 2 1 3 1 Applicable Documents 2 1 3 2 Reference Documents 2 1 4 Naming and Mathematical Conventions 4 2 Instrument Operation Modes 6 2 1 1 Measurement modes 6 2 1 1 1 Dual Polarisation Mode 7 2 1 1 2 Full Polarisation Mode 7 2 1 2 Internal Calibration modes 8 2 1 2 1 Uncorrelated Noise Injection 8 2 1 2 2 Correlated Noise Injection 8 2 1 2 3 External Calibration modes 8 2 1 2 4 Test mode 8 3 Algorithm Steps 9 3 1 Level 0 to Levella 9 3 1 1 LO data structure 3 1 2 LO decoding and fundamental calibration equations 14 3 1 3 Quadrature Error Correction 16 3 1 4 Amplitude and In Phase Error Correction 16 3 1 4 1 Power Measurement System calibration 17 3 1 4 2 Fringe Washing Function Estimation 18 3 1 5 System Temperatures Computation 22 3 1 5 1 Hub system temperatures 22 3 1 5 2 Arm system temperatures 23 3 1 5 3 NIR temperatures 23 3 1 5 3 1 NIR brightness temperatures 26 3 1 5 3 1 1 Dual polarisation temperatures 26 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission SMOS L1 Processor dei m A Critical me ENGENHARIA 7 Theoretical Baseline 3 1 5 3 1 2 Full polarisation temperatures 3 1 5 3 2 NIR receiver noise temperatures 3 1 5 3 3 LICEF NIR ba
48. and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 1 XY C LI LINE SMOS L1 Processor 29 10 10 deim s Bi Algorithm ENGENHARIA Uu swe Theoretical Baseline PUR 3 3 1 lonospheric Correction Ionospheric correction requires the computation of the Faraday rotation angle based on the Total Electron Content TEC and the geomagnetic angles at boresight Later on the values can be particularised at each pixel by simply using the incidence 0 and azimuth angles from the spacecraft to the pixel shown in Fig 14 The geomagnetic angles can be computed using the IGRF 10 model valid until 2010 and available as an Auxiliary Data File and the IGRF FORTRAN code available from NSSDC The required inputs at any time are the S C geodetic longitude and latitude the time in decimal years and the altitude The expected outputs are the magnetic field strength in Tesla F as well as the magnetic inclination I and declination D in degrees The TEC can be obtained from several sources the first one is the IRI2001 model available as well from NSSDC in FORTRAN code the second one is the IGS combined TEC map produced by UPC and available daily as Auxiliary Data File at ftp gage152 upc es rapid_iono_igs The IRI2001 model is based on the 11 year Sun solar cycle and requires as input the geodetic longitude and latitude the time and the altitude as well as several configura
49. antenna plane and antenna intermediate layer Receiver temperature between antenna intermediate layer and antenna input plane Ti yc Receiver temperature between antenna input plane and antenna output plane Receiver temperature between antenna output plane and LICEF input plane Lj Attenuator between antenna LICEF input plane in C port and LICEF output plane 3 1 5 3 3 LICEF NIR baselines system temperatures For LICEF NIR baselines while the LICEF system temperature can be computed in the usual way Sections 3 1 5 1 and 3 1 5 2 the NIR system temperature needs to be computed in a different way making use of the antenna temperature the receiver temperature described above the noise temperature in the antenna plane and a the NIR pulse length information The noise injection level T gt is translated to the antenna plane through Eq 50 and the VV HH Tos equivalent system temperature is defined as Eq 60 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission AA Code SO DS DME L1PP 0011 Criti SMOS L1 Processor pate 29 10 10 s Ml ine y ENGENHARIA Jr Theoretical Baseline page 32 of 89 where VA p VAP Tojs Lay iln Eq 61 qu mp c Sys v rec phy UU rpLH CIP T ord E T de TTG with amp as the complex Dicke Switch isolation and Lpp LL L L where the attenu
50. arameters T and T have to be computed from NIR pulse lengths the FWF 0 values and the phase corrected correlations The 3 and 4 Stokes parameters are retrieved by using This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 2f XY C n SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA Ur Theoretical Baseline page 29 of 89 T 0 llr i aja abu Eq 47 L 0 sini f qi The factors in the previous computation must be retrieved from a set of measurement and calibration data The steps to obtain these are shown below First the correlations are used to compute the factor arcsin u oer arcsin 4o And the g are gain parameters computed as 1 1 85 a c bh Eq 49 where g is the Fringe Wash Function at the origin applicable to the two LICEF correlation within NIR I the system temperatures computed through Eq 61 and 7 is the noise injection temperature from Eq 41 converted to the antenna plane by rid 4 NA vh Ln 2 NA vh Lvh L2 vh is Tus Eq 50 with Ta and T defined in the next section Ll vh Additionally parameter A from Eq 49 is dependant on the condition77 gt 7 as shown in the following equation Ty gt WEE HI IIT em Eq 51 My sys sys C
51. arisation Brightness Temperature Fourier Components The next 1395 columns correspond to the imaginary components of the V polarisation Brightness Temperature Fourier Components The next 2791 columns correspond to the real components of the HV polarisation Brightness Temperature Fourier Components with the zero baseline as the first column The next 2791 columns correspond to the imaginary components of the HV polarisation Brightness Temperature Fourier Components with the zero baseline as the first column The distribution of elements within each sub group of 1395 columns follows the order described next This ordering is based on reporting only the baselines with positive v coordinate and u positive for v20 The v coordinate for the upper half of the baselines goes continuously from 0 to sqrt 3 NEL d where NEL 21 and d 0 875 in incremental steps of sqrt 3 d 2 The u coordinate of the upper half of the baselines follows the mathematical rules defined as e If v 0 then goes from d to 24 d in incremental steps of d e Tf v gt 0 and v lt sqrt 3 NEL d 2 then goes from NEL d v sqrt 3 to NEL d v sqrt 3 in incremental steps of d This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 1 XY C SMOS L1 Processor 29 10 10 d 1 m YS ritica Algorithm Issue 2 10 ENGENHARIA Theoretical
52. arisation p expressed in director cosines coordinates 77 is the antenna solid angle of receiver j in polarisation k 8 J np T the averaged physical temperature of the receivers and is multiplied here by the Dirac delta rec S E represent that it is not applicable when the polarisation indexes p and are not equal e 4 isthe Obliquity Factor given by 1 amp 1 e is Delay Time given by u vn fy 7 is the Fringe Washing Function term normalised at the origin which accounts for decorrelation E 8 8 g effects in the path of the correlated signals and it is assumed a sum over indices 4 4 Here the director cosine coordinates are given by i54 ZnT in the instrument s coordinate system and u v are the baseline coordinates In matrix form discretising the director cosine coordinates as amp 7 this becomes 128 CERE Eq dr Lim Rok 181476 T 2 V where T c X o 5 7 2 7 hi and the sum over c gg PAF k 070 index k 1 128 is implicit 5 It is assumed a regular discretisation in kok otherwise the discretisation step sizes must be also included This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 1 XY C SMOS L1 Processor 29 10 10 dei m s ritica
53. ate the NIR R mode by computing the noise injection temperature in the reference branch Tygo This is done by applying LL ry T ju a o 1 Eq 82 e Lys where T is used instead of the noise coming to the V H OPR planes since there is no noise injection 16 Section 4 3 is defined as 1 Posi egg Eq 83 Lpr Los where all the coefficients have the same meaning as in Section 3 1 5 3 but are reference values hence the subscript R 3 1 9 3 Leakage and cross coupling calibration To account for cross coupling between the different channels of the NIR and leakage from the noise injection channels to the remaining ones the factors cross coupling and 17 leakage must be extracted and used to compute the correction functions f and i that calibrate the values of the third and fourth Stokes parameters Section 3 1 5 3 1 2 Several modes of the instrument are needed to collect all the data necessary for this computation The denormalised correlations extracted in each mode are listed here V are measured in LICEF LA mode when looking at the cold sky V are measured in NIR A mode when looking at the cold sky This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 2 XY C n SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA JF
54. ates of the S C and the Cartesian coordinates of the pixel plus the instrument attitude rotation matrix and additionally miss pointing like Best Fit Plane deviation Using this last method the pixel coordinates do not need to be restricted to the Reference Ellipsoid but they can be expanded with the local altitude value using a Data Elevation Model This process of orthorectification would be done with the help of the EE CFI functions This method is no longer used in v2 0 but its description is kept for historical reasons 3 3 1 1 2 Duesmann and Zundo Implementation In RD 29 an alternative method to compute the geometric rotation angle is proposed It consists on calculating the emission basis vectors in the Earth s surface and the Ludwig 3 polarization basis vectors on the instrument frame and from them extract the geometrical rotation angle This method is the algorithm baseline for L1PP v2 0 onwards The emission basis vectors in the topocentric frame of the pixel are calculated from the observation angles as Ehe rnc BU gus UP Eq 143 He topocentric ee C08 0 s n Eve soi cos 0 cos Eq 144 sin 2 topocentric To calculate the Ludwig 3 basis vectors on the satellite one must start by defining the target vector from MIRAS the satellite to the pixel 7 This document is property of DEIMOS Engenharia and cannot be distributed or duplicate
55. ating the visibility sample V 2 the corresponding frequency sample can be computed as X X y lt Z noon 528 8 2 e Eq 111 0 Where 40 is the wavelength value at the central frequency of operation 4 my for a typical value of 0 fo of 1413 5MHz Computation of the spatial coordinates is done in a hexagonal grid but put in a rectangular matrix according to the following formulation for an array steering of 30 The corresponding frequency coordinates are also shown Their outputs are 2 matrices with the coordinates of all points in the spatial and frequency domains according to the resolution specified This ordering was presented in RD 22 u v 2k ir Eq 112 1 1 Ks J3N d En en Where is the resolution required typically 128 d is the distance between adjacent receivers in wavelengths typically 0 875 and k and kz are the indexes of the matrix from 0 to 1 It must be noticed that the computation has to be performed according to the hexagonal quadrant where the indexes are since the centre baseline is the first element of the matrix this accounts to subtracting NT from the indexes depending on the part of the hexagon being retrieved The most complete G matrix is built for the full polarisation processing case as the dual polarisation G matrix is a subset of it The input data in the case of full polarisation are three vectors of calibrated visibilities with
56. ator parameters have been used in Eqs 56 59 It has to be remarked that the Dicke Switch Isolation is provided in the NIR ADF and that it must be interpolated to the corresponding temperature of the NIR unit ph h v 3 1 5 4 A After measuring the 4 voltages from each PMS the calibration parameters for the hub are obtained through Eqs 14 and 16 RD 17 lying system temperatures to PMS calibration Vig Var Vo T vj 7 Va 7 y 7 V Von Vik Eq 62 2 So Tar 2 S82 51 and for the PMS 1 m n in each of the three arms and C through _ 1 odd even Voffl m m 2 afim Vaim v _ Vina alan E 63 dies _ E 8 Virag Vis Vat mn 5 Viima Vitas G mn To Jak where the system temperatures differential for each segment can be related to the measured one at the hub by please note that for the last segment on each arm the offset is computed with the only noise source available and that there is no averaging This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor 29 10 10 dei m s Critical Algorithm Issue 2 10 ENGENHARIA Ur software Theoretical Baseline Page 33 of 89 Stal Man 5 0 Uu cB f vo v9 s 2 5 Sal vi Sul T i vm ta la E S
57. atterns is negligible when compared to the co polar patterns to be addressed in a foreseen study during Phase 4 then the above G matrix may be split into three independent G matrices each one related to one polarisation only The format of the H and V polarisation G matrix shall be the same while the HV G matrix shall be a bit bigger as shown above see Appendix 5 The antenna patterns shall be measured on ground for each receiver and depending on the image reconstruction method it shall be possible to calibrate validate these patterns in orbit The fringe washing function shall be also calibrated in orbit for several baselines those sharing noise sources and it shall be estimated for the rest of baselines through the procedure described in the previous chapters Again depending on the image reconstruction method the FWF calibration shall be applied differently 3 2 2 Foreign Sources Correction This removal procedure for Foreign Sources has been developed and implemented by A Camps et al in SEPS and it is described in RD 12 and RD 13 This procedure starts by subtracting the Earth and Sky contribution from the calibrated visibilities that have been produced as Lla output Sun and Moon direct and reflected contributions are also removed after following some considerations Effects from the antenna pattern backlobes and the receiver s physical temperature are also corrected This document is property of DEIMOS Engenharia and can
58. cally in order to initialise the model parameters In flight there shall not be any more measurements of the antenna patterns so it is required to validate calibrate the coefficients using known scenes This calibration process is still TBD The LICEF filters model has been descoped from the parametric G generation and the Lla calibrated FWF shape shall be used instead 3 2 3 3 Mathematical inversion Stabilised approach The mathematical inversion of G is a common approach for both algorithms It is based on a band limited regularisation which is equivalent to This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q SMOS L1 Processor pate 29 10 10 deim s Bi Algorithm S ENGENHARIA Ur swe Theoretical Baseline 2 min V GT Eq 1 P T 0 86 Where Py plays the role of a regularisation parameter This method was proposed by Anterrieu in RD 11 and is applicable to any algorithm based on G Matrix not only to the Parametric one It consists in a reduction of the domain applicability by creating the J Matrix The G Matrix operates between Calibrated Visibilities and Brightness Temperatures whereas the J Matrix operates between Calibrated Visibilities and Brightness Temperature Fourier Components T After being computed the J Matrix is mathematically inverted using the pseudo inverse approach J as de
59. cent arms For example the elements between arms A and B are labelled AB This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 2 XY C n SMOS L1 Processor 29 10 10 d el m s ritica Algorithm Issue 2 10 ENGENHARIA Ur Theoretical Baseline 11 of 89 ele OOK OS A 1 PDA 1 f pas NS A 1 DO LCF C 04 LCF C 19 ARM A PD H 01 OS H1 NIR CA 01 PD Il 02 Figure 6 Antenna indexing in the SMOS instrument Using this nomenclature it is possible to clarify the data organization in the LO format Figure 7 Note that the output starts with the elements in the hub LCF AB 03 in the case of arm A followed by the two separate outputs from the LICEF NIR in horizontal and vertical mode NIR AB 01 H and AB 01 V in the case of arm A and only then we have the arm receivers outputs A 01 to LCF 21 The LO data also contains correlation data between each antenna and a stable signal of 0 or 1 In Fig 5 these correlations are colour coded in red and are stored in between the cross correlations data Finally the diagonal of the logical data matrix contains the autocorrelations between the quadrature and in phase outputs for each antenna Above the diagonal for nominal layer LO data the cross corre
60. computed through the 4 point method lt lt The equivalent to the previous equations in this case is odd odd AA Vo Vir rk odd odd Vox G Ea 107 ye ye G me ce f lr k rk even even CC Vox G There will be 3 sets of coefficients and 3 sets of each with 11 values for k The comparison between ground and sky coefficients is done as eC 20log dB Eq 108 even C eC 20log 3 2 Level 1a to Level 1b This processing level further refines the L1a data by removing influential sources from the calibrated visibilities and it also performs what has been called the Image Reconstruction The first activity consists then in removing external sources Sky Sun Moon etc from the calibrated visibilities while the second one consists simply in reconstructing the Brightness Temperature distribution out of the calibrated visibilities This latter reconstruction can be performed using two different algorithms which are also described We shall first start with the theoretical definition of the problem by studying the equation that rules the instrument s output moving later on the procedures to be used for each Image Reconstruction Algorithm This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C ngn SMOS L1 Processor pate 29 10 10 deim
61. coordinates e g Blackman window In the case of strip adaptive the coefficients are also a function of the xi eta coordinates The method for W computation is shown in the last chapter of this section In case Foreign Sources correction removed a constant Earth Brightness Temperature Eqs 115 and 122 the equivalent of Eq 125 has to be applied here in order to add back the subtracted quantity This is not applicable to full polarisation scenes as the Earth is not subtracted for HV pol reconstruction 3 3 2 2 Pixel Radiometric Accuracy computation Additionally the radiometric accuracy is computed for each pixel and polarisation The equation for doing this is the following This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 2f XY C n SMOS L1 Processor 29 10 10 deim s Bi Algorithm ENGENHARIA Ur Theoretical Baseline pag Te Pq h 2 a4 AT 1 4 7 Sys Eq aa GE 9 B c wol 151446 Where the different parameters are 4x is the solid angle of the antenna and can be approximated by T for the current LICEFs where D is the averaged directivity of the LICEFs for the corresponding polarisation For full polarisation D is computed as JD D G amp m is the averaged LICEF receiver directional power Gain function normalised so that it is unity at boresigh
62. cument is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C SMOS L1 Processor pate 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA Uu Theoretical Baseline 28 of 89 T U load Approximated by T Tep Physical temperature between radiator output plane and LICEF input plane Shall be approximated from and T as Tos Ty Cabv 43 ES is Trj Cabh 2 Finally the coefficient B is computed as pcm East Ps Zu Eq 44 By es 5 npa b La and Eq 39 is applied The resulting brightness temperature is further corrected by m 2 Tus a Cay ER E pat PA Eq 45 ve tC h T A0 on m E T us j where the parameters c and d are parameters measured on ground and used to compensate the uncertainty in the front end characterization first and second order Los are computed by T A v Dh 46 Dus LS Wm Ah tlh LL AA and T is the antenna temperature during calibration see Section 3 1 9 and stored with the NIR A data i e with physical temperatures measured at the time of calibration 3 1 5 3 1 2 Full polarisation temperatures In the case of the processing of full polarisation scenes the NIR brightness temperatures are computed as in the dual polarisation case but the 3 and 4 Stokes p
63. d m s EINE ENGEN ARIA software Theoretical Code Issue Date Name Prepared by A Guti rrez Checked by J Barbosa Approved by J Barbosa SMOS L1 Processor Algorithm Baseline Definition SO DS DME L1PP 0011 2 10 29 10 10 Function Signature Project Engineer Quality A Manager Project Manager DEIMOS Engenharia Av D Joao Lote 1 17 Torre Zen 10 1998 023 Lisboa PORTUGAL Tel 351 21 893 3013 Fax 351 21 896 9099 E mail mai lto deimosedeimos com pt DEI All Rights Reserved No part of this document may MOS Engenharia 2010 be reproduced stored in a retrieval system or transmitted in any form or by any means electronic mechanical photocopying recording or otherwise without the prior written permission of DEIMOS Engenharia Code SO DS DME L1PP 001 1 SMOS L1 Processor pate 29 10 10 deimos lir c Bee a M ENGENHARIA Theoretical Baseline page This page intentionally left blank This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 001 1 e SMOS L1 Processor pate 29 10 10 d m OS Algorithm Issue 2 10 ENGENHARIA Ur Theoretical Baseline EE Document Information Contract Data Classification Internal L1 Public Contract Number 4000101241 10 1 Industry L1 Contract Issuer ESA Confiden
64. d E it is possible to obtain the corresponding alpha values which produce such an elliptically distorted Equivalent Array Factor This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C SMOS L1 Processor 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline 76 of 89 The following image shows the graphical method for E 0 024 and E 0 018 which consists in plotting the curves as a function of the alpha values that produce Array Factors having those E and E values and finding the intersection of both curves There shall be two solutions one indicating that the major semi axis is oriented along the 6 direction and the other indicating that the minor semi axis is oriented along the direction In this image it is also shown a red line indicating the Beam Efficiency that corresponds to those two alpha values which in this case is 58 Please refer to RD 15 for additional information Fig 18 Alpha parameters for E 0 024 0 018 Delta value is 15 A system of analytical equations has been derived in RD 15 by INETI after implementation of the equations above The system of equations computes the Kaiser parameters Ou and Ow out of the relationship between the ellipse semi axes in the antenna frame The coefficients used in that system of eq
65. d without its written permission Code SO DS DME L1PP 0011 2f XY C n SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA Jr Theoretical Baseline 66 of 89 cos sin cos cos 9 Eq 145 sin 0 MIRAS r and with it define two auxiliary vectors and Ny MIRAS MIRAS MIRAS r u aux lt MIRAS MIRAS MIRAS Vaux Xu x MIRAS MIRAS aux Xu 146 MIRAS MIRAS N MIRAS __ Vaux Xu y MIRAS MIRAS Xu aux y These auxiliary vectors are used to calculate the Ludwig 3 vectors MIRAS MIRAS L N Xr x gt mes x p MIFAS 147 N MIRAS x y MIRAS L MIRAS _ y y z MIRAS MIRAS x MIRAS MIRAS s Having and L to the same referential the polarization angle is obtained as shown in the following equation L T MIRAS humas L E a arctan ERO es Eq 148 MIRAS For further details please refer to RD 29 3 3 2 Geolocation This objective of the geolocation requirement is to compute the Brightness Temperature values expressed at Top of Atmosphere over pixels in an Earth fixed grid ISEA That the values are expressed at TOA means that the Faraday and geometrical rotations are not corrected in L1c The pixel coordinates are defined in an Auxiliary Data File using longitude latitude and altitude The
66. de SO DS DME L1PP 0011 Q C Pru SMOS L1 Processor pate 29 10 10 deim s Bi Algorithm due ENGENHARIA Theoretical Baseline pag du A and again using the fact that the PMS m have already been calibrated and can be averaged we have 2 2 6 jp ln B P T n Von Sar Vin Vig Sms Vit Sia T Ea 35 Sys 36 Y _ 7 2 B B ph 2 NS2 NS1 q m l 1 1 Von Vin Is Vom Vim Sil Vo Vi Siel After computing the system temperatures at CIP for all receivers 7 a further 2 order linearity 55 correction must be performed using the deflection parameter measured on ground C 2 eg 0 Eq 36 k The objective is to apply again the previous equations but using these new voltages as a starting point in order to obtain a final system temperature p i e computing again new offsets and gains with Eq 27 35 To extract the system temperature at the antenna phase centre the following plane translation between calibration and antenna planes is made H mode exemplified 2 H UTR 551 m n m 2 T Eq 37 SYSt TR where s and s are the modulus of the switch S parameters relating port C and H with port LCl m n LHI m n L for PMS dependent on physical temperature and 77 15 the antenna efficiency in horizontal mode The same procedure must be applied for the vertical measurement modes
67. deflection C from Eq 36 is used instead It should be noted that in case the linearity correction is enabled Eq 36 should be applied to all input PMS voltages before using them in the remaining equations If two external noise temperatures are used Tc WARM and HOT and if an attenuator is used to switch the system gain between two values G and G L we have four possible PMS measurements Va T G ci T Var Vog G en 1 Eq 13 G Va Tez T L The estimated calibration parameters are obtained as VogVay Vik Vak e Gy ess 2k 4k lk 3k Eq 14 x ae k E and the estimated system temperatures with the calibrated PMS data will then be gc E Toon 7 Toy Eq 13 sysk G Voy T Vik As can be seen from Eq 14 only a differential knowledge of the calibration temperatures is needed The attenuator value is not needed In the case of relative amplitude calibration a single noise source is used delivering two calibration temperatures 75 WARM and 75 HOT to port 0 of the NDN The NIR will measure two This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q PLoS SMOS L1 Processor pate 29 10 10 deim s Bir Algorithm s ENGENHARIA Theoretical Baseline pag T temperatures and Tysz at the port 1 of
68. discovered by ESTEC during November 2007 the offset correction for baselines involving NIR LICEF needs to be corrected with a factor 2 due to the different integration time in which the NIR LICEF are providing correlations the rest of the time it operates as a NIR During IVT campaign it was seen that offset correction is only required for baselines sharing the same Local Oscillator so for the current time there shall be three configurable processing options No offset correction a j O for all baselines C Offset correction 1 for all LICEF baselines and 2 for all NIR LICEF baselines Local Oscillator Offset Correction 1 only for LICEF baselines sharing the same Local Oscillator i e the LICEF for those baselines are linked to the same 2 only for NIR LICEF baselines sharing the same Local Oscillator 3 1 7 2 Redundant Space Calibration This method is based on the fact that there are redundant baselines measured that should be measuring the same value in case this is not true it can be attributed to separable amplitude and phase errors associated to each receiving chain As this method is very sensitive to non separable errors in SEPS it has only been applied to calibrate non normalised visibilities to correct for error terms associated to the path between the antenna and the input switch that is for all the antennae along the arms The
69. ds on the status of other processing flags The procedures are also described in detail in AD 5 2 1 2 4 Test mode This operation mode is not described in AD 5 or AD 6 as it is a built in test mode with a fixed output in all correlators It is described in section 10 3 3 of AD 4 The APID APID TEST shall identify it This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 y N C ns SMOS L1 Processor pate 29 10 10 deim s Ri Algorithm ENGENHARIA Jf Theoretical Baseline 9 of 89 3 ALGORITHM STEPS In the next part a description of the processing steps needed to complete the transition from one product to the next is provided This document shall describe the processing methodology and how to extract information but it shall not attempt to group activities into processing modules This task is performed in the System Concept document RD 9 and in the respective Detailed Processing Model documents 3 1 Level O to Level1a This processing step extracts calibration parameters and offsets from calibration data and applies them appropriately to the measurement data It is responsible for decoding the original packetised science and ancillary data and converting it into engineering units Most of the calibration procedures presented in this section have been gathered from AD 5 and AD 6 3 1 1 LO data struc
70. duplicated without its written permission SO DS DME L1PP 0011 Code SMOS L1 Processor pate 29 10 10 deim gt s co 7v EHGENHARIA M Theoretical Baseline page 10 of 89 Q1 92 Q24 1 x 0 025 Q26 Q4B 1 x 0 049 050 072 1 x 3 8 5 3 723 3722 3721 3697 Figure 5 Logical organization of LO data nominal layer N the integration time used For dual polarisation mode the value of N is the maximum number of counts which is a function of the sliding window of the DICOS and is 65437 while for full polarisation mode it is 43625 In Fig 3 there is only the representation for the LO nominal layer In fact there is a redundant layer of LO data which contains the Q I correlations instead of I Q correlations and QQ instead of In the remainder of this document we will only address the processing of the nominal layer data being the redundant layer processing essentially the same Whenever there are differences in the equations for each layer they will be explicitly presented C max C max The following figure depicts the counting schema of the LICEF and LICEF NIR receivers for each arm As can be see the elements in the hub can be assigned to each arm by extending the arm direction into the hub as far as the hub centre For those elements in the hub in a region between arms the arm the naming convention AD 9 incorporates the labelling for the two adja
71. e Netherlands 89 96 RD 9 SO DS DME LI PP 0006 SMOS L1 System Concept 2 9 RD 10 SO TN DME L1PP 0024 SMOS 11 Full Polarisation Data Processing 1 6 RD 11 IEEE Trans Geosc and Anterrieu A resolving matrix approach to 2004 Remote Sensing Vol 42 synthetic aperture imaging radiometers No 8 2004 RD 12 A Camps M Vall llossera Sun Effects In 2D Aperture Synthesis Radiometry 2004 Duffo M Zapata Imaging Their Cancellation IEEE Corbella Torres Transactions on Geoscience and Remote Sensing Barrena 42 6 1161 1167 ISSN 0196 2892 RD 13 A Camps M Vall llossera Impact and Compensation of Diffuse Sun 2005 N Reul F Torres N Scattering in 2D Aperture Synthesis Radiometers Duffo I Corbella Imagery IGARSS Seoul Korea July 25 29 2005 RD 14 P Waldteufel G Caudal About Off Axis Radiometric Polarimetric 2002 Measurements IEEE Transactions on Geoscience and Remote Sensing RD 15 SMOS DMS TN 5100 Adaptive Apodisation Function Development 1 2 Technical Note RD 16 SO TS HUT NIR 0005 NIR Calibration and Characterisation Plan 5E RD 17 SO TN UPC PLM 0010 Distributed Amplitude Calibration by the Two 1 0 Level Approach RD 18 SPS TN GMV PL 0003 SMOS End to End Performance Simulator SEPS 4 1 Architectural and Detailed Design Document RD 19 A Camps I Corbella Polarimetric Formulation Of The Visibility 2006 Torres M Vall llo
72. e Eq 113 with the exception that it will only encapsulate the contribution corresponding to the receivers physical temperature but at the same time it will make unnecessary the correction for the constant Earth term This transformation is first based on the measurement of a set of FTT auxiliary correlations obtained while the instrument is pointing to the deep sky u v During these measurements the Brightness Temperature of the zone being observed shall also be stored 7 as well as the average of the physical temperature of the receivers T T zT 7 V uv V uv T Eq 126 per In this way we can write now Eq 113 as AV u v v u v Vo u v i u v u v mi u v Eq 127 After cecosseedlieors the Brightness Temperature Fourier components 17v have tobe coreeted for inthe followi x A TP T b 4 Y Pq T 5 7 Eq 128 3 2 3 Image Reconstruction This processing step requires two separate functionalities The first one is to compute the System Response Function which shall be performed based on a calibration timeline and the second one is to use that calibrated System Response Function to reconstruct the calibrated visibilities already corrected for foreign sources This last step is not reversible as it shall not be possible to perform corrections once the Brightness Temperature Fourier Components are calculated in case the G matrix chan
73. e Welt aiu oscar tak ean Gi E cen Van hp 11 Ligute 7 Correlations orders in LO nominal data packets aao o areae a s ced kac posui dada 12 Figure 8 Simplified organization of LO nominal layer science 13 Figure 9 Baselines covered by the same Noise Sources Even and Oddq sees 20 Figure 10 Number of closures needed to compute the for each pair of 21 Figure 11 XI left image and ETA right image coordinates proposed for Matrix format 50 Figure 12 G matrix decomposition C and X are co and cross polar Antenna Patterns and R is the Fringe Wash Function multiplied by the complex exponential term see Appendix 5 Figure 13 J matrix baselines Ordering 2 ro E 61 Figure 14 Geolocation and projection angles RD odes i paste a ear 64 15 For ias n a d P adt ba Cl rr on cdd eol o e ond vta S 70 Fig 16 Major semi axis of elliptical 3dB contour of as a function of alphaU x axis and alphaV axis Delta is constant at TRO 75 Fig 17 Minor semi axis of elliptical 3dB conto
74. e known for all the pixels they shall be used to compute the different values at each pixel specifically The output data information is written into the Llc products first starting with a reference to the snapshots in which the measurements were made which include OBET UTC PVT AOCS and magnitudes of the removed foreign sources TEC and geomagnetic angles and the averaged physical temperature of receivers Following that the data is ordered by pixels where for each pixel it is indicated the numeric identifier to the ISEA grid and the number of BT measurements available Each of the measurements is composed of the BT component measured real for and V complex for HV incidence 8 and azimuth p observation angles radiometric accuracy Faraday rotation angle geometric rotation angle pixel footprint elliptical major and minor semi axes and quality flags 3 3 2 1 Pixel Brightness Temperature computation The Brightness Temperature computation to be performed for each pixel uses a Discrete Fourier Transform using as input the brightness temperatures Fourier Components T u v produced as L1b output the u v baselines coordinates the apodisation window coefficients W u v and the xi eta coordinates of that particular point The equation used is the following j2zt u E v E T 6 0 7 usus e d i 150145 In the nominal case the apodisation window W coefficients are constant regardless of the xi eta
75. e redundant layer as Eq 3 tius uu Eq 4 7 r jui 7 The redundant data will only be used in the case of failure of the nominal layer Please note that Eqs 3 and 4 account for the only difference in the processing of nominal or redundant data The processing of time delays is only important for the FWF shape computation but it should be noted that the real parts of the delayed signals must be switched to build the complex correlations After computing 44 all the subsequent processing is unchanged The complex correlations are theoretically related to the calibrated visibilities through the equation 1 DV e mir o Eq 5 ii gi where is the fringe washing function at the origin for the corresponding pair of filters indicated by the sub and superscripts and are the calibrated visibilities The system temperatures are the sum of the antenna temperature and the receiver noise temperature referred to the theoretical antenna phase centre and including antenna ohmic losses The objective of the calibration procedures is to compute the system temperatures and the FWF values at the origin to recover the calibrated visibilities The final calibrated visibilities are computed as AD 6 _1 UV UH V 5V H __ i V H Sy VV HH _ p VV HH yp V H Eq 6 Ton Tos M UVY UH __ UV 0 p DUM SYS j where is def
76. ed in the same way as well but inverting the sign of the resulting u and v coordinates i e it changes to ordering from right to left then top to bottom This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C SMOS L1 Processor 29 10 10 deim s Bii Algorithm ENGENHARIA Theoretical Baseline EUM It is important to define a common format so that the L1b output is coherent and can be interpreted 3 2 3 3 2 J Matrix inversion As the J matrix relates the Brightness Temperature Fourier Components with the Calibrated Visibilities once it has been generated the J matrix needs to be inverted in order to obtain T u v The inversion is achieved by using the pseudo inverse J V Eq Teu 136437 P 3 2 3 3 3 J Matrix application The result of multiplying J by the calibrated visibilities V is the brightness temperatures Fourier Components T u v expressed in the frequency star domain The calibrated visibilities must be ordered in a very precise way in order to match the way in which the J and G matrix were generated This ordering is described in chapter 3 2 1 as it is equivalent to the rows ordering of the System Response Function Visibilities for H and V polarisation in two consecutive integration times must be used in dual polarisation mode while visibili
77. een antennas It is j i mW calibrated as part of the nominal processing but it can also be approximated by d where W is the relative bandwidth of the filters i e bandwidth divided by the central frequency i usus are the baseline coordinates in the frequency domain d is the antenna element spacing 0 875 2 7 are the coordinates of the resulting pixel centre viewing direction in the antenna frame fois the central frequency 1413 MHz The resulting distribution over the antenna frame cut at half of the maximum 3dB will yield contour circular or elliptical that must be projected over the Earth As mentioned the major semi axis is oriented along the azimuth 5 observation angle so it is only necessary to project two points to compute the ellipse axes on the ground 3 3 2 5 Apodisation window computation In the nominal case i e no strip adaptive the apodisation window is simply a function of the u v baseline coordinates For the Blackman window the expression is the following 2 2 2 2 0 08 cos rd gd In which the MIRAS SMOS case for a Y shaped array has already been taken into account and 21 and d 0 875 This apodisation window when used in Eq 150145 produces a circular footprint in the antenna frame which is later projected into an elliptical footprint over the Earth s surface
78. ernal Calibration Mode and T is the value of T during on ground calibration stored NIR ADF file As for the coefficient B it is computed through 1 PON S Ts Rv DRv Eq 73 Bay T Ly Low with 1 L L Tus s Der i Der Uv Lp Lii 74 L L Du 3 Tr n Tu Ly Lp Lorn After applying Eq 71 the CAS noise temperature is further corrected through the equivalent of Eq 45 i i 2 LV CIP 7 CIP CIP Tys F te T i dg 7 NS v NS v ONO v Eq 75 i 2 LH CIP _ _ CIP S ovo dy with measured in NIR A mode during NIR calibration with an external target see Section 3 1 9 1 3 1 8 2 Reference receiver noise temperatures The receiver noise temperatures at CIP planes are computed through the PMS measurements obtained when the instrument is in LICEF LU mode inside the PMS calibration sequence by using the following equation 2 Sex LV C P matic LCk recy SyS S ln phUk VE me LVk UC _ k off where Toss Gear Eg 76 LH CIP UC k recy Sys 2 7 phUk M 7 where vi are the PMS voltages when the instrument is in uncorrelated noise injection mode but taking care to use the voltage offsets and gains from the appropriate NIR LICEF unit and the rest of the terms are identical t
79. es are used 1396 In HV polarisation no other value is changed from zero and all the non redundant baselines are used 2791 A 2D Inverse Fast Fourier Transform is performed on the resulting complex matrix which will generate a new complex matrix In or V polarisation as the input matrix is Hermitian the output matrix is real valued This new NrxNr complex matrix is ordered in vector format zero padded to form a 4 real valued vector and multiplied by G as shown in Figure 12 Notice that depending on the polarisation being used the zero padding of the vector in the figure may vary e g if the vector corresponds to H polarisation the V and HV polarisation components must be filled with zeroes This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 1 XY C SMOS L1 Processor 29 10 10 deim s Bi Algorithm ENGENHARIA Theoretical Baseline pag OTN The resulting vector of the matrix vector multiplication is a complete column of the J matrix applicable to the baseline Continue the loop until all columns of J have been computed The J matrix contains the same number of rows and ordering than that of the G matrix which has already been explained in chapter 3 2 1 However the number of columns is now dependant on the u v frequency domain and i
80. ges It shall be necessary to start over from the calibrated visibilities to obtain new results with the new G matrix This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C n SMOS L1 Processor 29 10 10 deim s Bi Algorithm ENGENHARIA Theoretical Baseline 56 of 89 In the following sections two algorithms for generating the System Response Function are described On ground characterised G Matrix and Parametric G Matrix which have been selected as baselines The DLR Learning Approach which was also investigated is not described as it is not part of the baseline although it has similarities to the Stabilised one Inputs to both algorithms are the same requiring Calibrated visibilities Lla Matrix ADF In fact the only difference between these two methods is the approach in how to compute that G matrix as the format of the G matrix is shared by both of them Once the G matrix is computed and or calibrated the inversion method is the same passing by a mathematical reduction based on a band limited approach 3 2 3 1 On ground characterised G Matrix This G Matrix is built based solely on input data available such as calibration data and auxiliary data files This method has been already implemented in SEPS and was developed by the Universitat Polit cnica de Catalunya The
81. he non linear equation proposed in sin ug a Qc 1 ui with Eq 2 o 1 1 Qu 2xixyus iiq FE E Uu 1 u Where the values of X Ne are built using the correlations of I and Q channels with constant 1 and 0 channels using the following expressions in which x 15 the correlation of I channels to all zeros first vertical red line in Fig 5 and x is the correlation of the I or Q channels to all ones ty 1 le oe 1 Xi 5 to xu Xi z 0 zn x mno o ii T iig Equation 2 has to be solved iteratively using as first solution sin n 1 Note that in AD 6 the equations are written based on and QI correlations This document approach is not inconsistent with that formulation see Section 9 of AD 6 only the equations are based on the nominal layer data II and IQ correlations This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q C a ee SMOS L1 Processor pate 29 10 10 deim s 105 Algorithm S ENGENHARIA Theoretical Baseline pag m After computing the digital correlations complex normalised correlation of baseline kj can be written for the LO nominal layer and any time delay as qi uy My M My Ps 2 Hi Cr jus and for th
82. ication hereafter referred as G matrix V u v 2 amp m Eq 110 This G matrix is dependant on the antenna patterns the fringe washing function the u v frequency samples of w is the out of plane coordinate and the spatial samples 4 7 of BT In order to obtain the Brightness Temperature distribution that generated a certain measured calibrated visibilities it is only required to invert G by whatever method is more appropriate The first step is to specify the u v frequency samples and corresponding spatial samples for the resolution selected that match the instrument configuration The u v frequency samples and the off plane component w are determined by the location of the receivers in the instrument whereas the spatial samples are simply chosen based on the desired resolution The preferred option is to work with a minimum resolution of 128x128 or 256x256 spatial samples If a finer data sampling is desired an interpolation may be performed after the reconstruction This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 EN C LI LUE SMOS L1 Processor 29 10 10 deim s aue ENGENHARIA siwae Theoretical Baseline 46 of 89 The visibilities measurements are taken at specific frequency samples Being x j y and x2 y2 the XY plane coordinates of two antennas gener
83. ined as 0 L Mus jim Nominal layer Eq 7 Mi L Mj ME jim Redundant layer This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C SMOS L1 Processor pate 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA JF Theoretical Baseline 16 of 89 with index g H V or U and T Sys in Eq 6 is the value of the fringe washing function at the origin is the quadrature corrected normalised correlation and in turn has the following parameters Oj 8 My cos jsin 2 8 2 2 9 0 0 7sin The terms in these equations other than the complex correlations are computed during three calibration procedures quadrature phase amplitude and offset are the system temperatures during measurement The parameter g 3 1 3 Quadrature Error Correction The quadrature correction is computed for all instrument modes outputs and applied before any other processing is done This approach obtains the term which is directly estimated from the measured normalised auto correlation between an antenna in phase and quadrature outputs AD 6 0 arcsin 44 Eq 9 After knowing and defining 9 kj 2 Eq 10 Oj 8 E ME Eq 8 transforms into
84. ing data from the first year is the short term drift component of the L1 attenuator in orbit using data from the first year T isthe reference Tp7 at which the previous 3 coefficients were obtained T isthe physical temperature of the radiator of the antenna antenna patch during the current measurement e 0 15 the physical temperature of the radiator of the antenna antenna patch during the NIR calibration sequence Attenuator between antenna intermediate layer and antenna input plane As for the coefficient several intermediate temperatures must be computed First the thermal noise contributions are computed from T jl NL a l Ta L L L P 1 m Ly 2h Eq 42 n 2 L fi gt i y Lyc v L Ly Lp Lp 1 a fi y Uh Ly Ch Ly Ly h Ly Lys Loan P To where Physical temperature of the radiator of the antenna antenna patch Physical temperature of the intermediate layer of the antenna Physical temperature of the attenuator in reference noise injection channel Lyc Attenuator between antenna input plane and antenna output plane L Attenuator between antenna output plane and LICEF input plane L Attenuator between antenna LICEF input plane in or V port and LICEF output plane Physical temperature measured inside the LICEF between U Load and isolator This do
85. input data required for the G Matrix are LICEF antenna patterns Auxiliary Data File Fringe Washing Function shape L1a Product Data LICEF spatial coordinates Auxiliary Data File Antenna patterns shall be measured once on the ground and a static Auxiliary Data File shall be generated with the measurements These measurements shall be done at three different frequencies the central operation frequency and another two at plus and minus a B bandwidth Their use in the G Matrix construction is done through a weighted average as expressed in the next equation extracted from RD 20 la B xs B qk Gm fS Dg 1 Dp ng Eq REME GC M E OFT EN fo ET ix ap B ru 6 7 fy OP 6 7 fy The Fringe Washing Function shape is calibrated estimated as part of the nominal calibration campaign by injecting correlated noise and introducing time lags in the correlated signals An Lla product file is generated every time this type of calibration is performed This process is described in section 3 1 4 2 and its output is used to compute a set of coefficients for approximating the FWF shape amplitude by a sinc function and the FWF shape phase by a quadratic function 5 2 Eq A sine B t C e 129130 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Re Im Code SO DS DME L1PP 0011 if XY C SMOS L1 Processor 2
86. inth element LICEF AB 03 against LICEF C 21 The next element is then LICEF AB 01 H against LICEF A 01 and so on until LICEF AB 01 against LICEF C 21 The next one is LICEF A 01 against A 02 etc until LICEF A 02 against LICEF 21 This ordering continues until all LICEF correlations have been inserted and not including correlations with LICEF_NIR in V polarisation i e correlations with receivers LICEF AB 01 V LICEF BC 01 V and LICEF CA 01 V The next 2346 rows correspond to the imaginary values of polarisation calibrated visibilities following the same order as above The next 3 rows correspond to the zero baselines as measured from the for V polarisation The first row corresponds to the NIR AB measurement then BC and last CA The next 2346 rows correspond to the real values of the V polarisation calibrated visibilities as received from the L1a products and ordered in the same approach as shown in figure 11 of RD 5 i e first element is the calibrated visibility of LICEF AB 03 against LICEF AB 0I V next is LICEF 03 against LICEF A 0l etc until the sixty ninth element LICEF AB 03 against LICEF C 21 The next element is then LICEF AB 01 V against LICEF A 01 and so on until LICEF AB 01 against LICEF 21 The next one is LICEF A 01 against LICEF_A_ 02 etc until LICEF A 02 against LICEF C 21 This ordering continues until all LICEF correlations have been inserted and
87. io zi T Te x al IS px yo y 5 7 Ns2 Eq 64 2 S i m Saal y y zm v Mi z Tia Ta 2 Vs IS ho ES i gt 1 3 5 It has to be taken into account that in order to correct the PMS linearity term this process must be done 2 in two iterations as indicated in Eq 36 and only the second iteration PMS voltage is used to compute the final PMS gain offset and the System Temperatures 3 1 6 Correlator Offset correction All receivers from the same segment should have zero cross correlation when connected to separate uncorrelated noise sources In order to have this behaviour the residual offset must be calibrated through periodic injection of uncorrelated noise in the receivers The cross correlations are quadrature corrected and de normalised yielding a set of visibilities The measured visibilities are then stored in memory and subtracted from all subsequent visibilities measured in normal observation mode or during calibration Uncorrelated noise injection will be done at various points of the orbit and at various temperatures More than one offset per visibility will be stored as a function of the temperatures of the LICEFs involved in the generation of the visibility The subtractions are performed at the level of de normalised visibilities so the U load temperatures during uncorrelated noise injection
88. ion Same order as above i e first LICEF CA 03 against LICEF BC 03 then LICEF CA 03 against LICEF BC 01 V then LICEF CA 03 against LICEF B 01 until the 23 element LICEF 03 against LICEF B 21 Next is LICEF CA 01 against LICEF 03 then LICEF CA 01 against LICEF B 01 and so This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor pate 29 10 10 55 MA m ENGENHARIA software Theoretical Baseline Page 49 of 89 on until all elements in arm B are correlated with LICEF_CA_01_H Please note that this row does not include the correlation against LICEF_BC_01_V This ordering continues until the last element correlated is LICEF_C_21 against LICEF_B_21 Next 23 rows with calibrated visibilities of LICEF_AB_01_H against all other receivers in arm A in V polarisation Le LICEF AB 01 against LICEF AB 03 LICEF AB 01 against LICEF AB 01 V LICEF AB 01 against LICEF A 01 etc until LICEF AB 01 against LICEF 21 Next 22 rows with calibrated visibilities of all receivers in arm A in H polarisation against LICEF AB 01 V excluding LICEF AB 01 against LICEF AB 01 V whose equation is presented in the point above Le LICEF AB 03 against LICEF AB 01 V LICEF A 01 against LICEF AB 01 V etc until LICEF A 21 against LICEF AB 01 V Next 23 rows with calibrated visibilities of LICEF B
89. lations are between in phase I and quadrature Q outputs for each of the antennas while below the diagonal the cross correlations are the between the in phase outputs of both antennas For more information on the LO data structure refer to documents RD 27 and RD 5 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 d e Critical SMOS L1 Processor pate 29 10 10 el mos Algorithm Issue 2 10 EHGENHARIA Me Theoretical Baseline page 12 of 89 Arm A m eg i 5 Tj i T gt E e z 5 5 5 3 al M M E 5 M M lt lt m m d m m Sag ui a 2i gl x ul ul ul 9 ul 25225 99 S22 G 9 3 2 9 9 l corr LCF AB 03 N H NIR_AB_01_H aN H E m lt NIR AB 01 V m c LCF A 01 Eu LCF A 20 N B E E E LCF A 21 E E l 1 corr 9 M L LCF BC 03 B L E NIR BC 01 H N NIR BC 01 V LCF_B_01 lt LCF B 20 N LCF B 21 m E Seb mi LIN LCF_CA_03 u m NIR_CA_01_H m B o NIR CA 01 V LCF C 01 lt LCF C 20 E E LCF C 21 m m Figure 7 Correlations ordering in LO nominal data packets Therefore the data accessible on the nominal correlations layer according to AD 8 consists
90. nd vertical polarisation can be computed from the instrument output NIR and for cross polarisation contribution it is computed from the self correlations between LICEF_NIR in H and V ports The term yn 0 0 1S Earth the same one as in Eq 115 but without the term for the Earth constant temperature The temperature and position of the Sun and Moon needs to be computed for both Direct and Reflected contributions For the Direct Sun contribution it is treated as a point source computing the position in the antenna frame using the pointing CFI together with the spacecraft position and attitude The magnitude of the Sun Brightness Temperature at that position can be retrieved from the measured data itself by doing an FFT on the uncorrected calibrated visibilities and computing the brightness temperatures over that exact position This FFT is performed assuming ideal FWF one averaged antenna pattern and perfect positioning of the receivers In case other methods to obtain the Sun BT are available like models external measurements etc they can be used instead of the self measurement as the Sun position is known For the Reflected Sun contribution Sun reflection over Oceans shall be modelled through several auxiliary parameters namely the Sun BT wind speed and direction and Sea Surface Salinity and Sea Surface Temperature As demonstrated in RD 13 the effect of the Sun BT is dominant in the modelling of the reflected source and using
91. nnel is missing Their values however are easily retrieved from the 1 0 and Q 0 correlations due to the fact that 1 0 and 1 1 values as well as and Q 1 values are complementary No 1 0 1 1 for example Cmax So at any given integration time where all receivers are configured in a unique polarisation H or V only the following data shall be useful as the rest of the data shall be in the opposite polarisation 2346 correlations between I channels of different receivers 1 1 2346 correlations between I and channels of different receivers 1 Q 69 correlations between I and 0 channels 0 d d 69 correlations between I and channels of same receiver No 1 Q 69 correlations between and 0 channels 0 The Error Correction module will nevertheless process all LO data in the same processing step using the 72 signals for each antenna 66 LICEF 2 3 LICEF NIR An even more simplified logical organization of the useful data in a scene is depicted in the following diagram correlations I Q auto correlations correlations Figure 8 Simplified organization LO nominal layer science data The composite matrix will be used to define two symmetric matrices the us correlations full matrix containing the real components and the correlations full matrix containing the imaginary
92. not be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 J C iti SMOS L1 Processor pate 29 10 10 deim s Algorithm Ee ENGENHARIA M Theoretical Baseline page 52 of 89 This means that the reconstruction process does not work on the calibrated visibilities but on a delta value where the Earth Sky Sun and Moon Brightness Temperatures have been removed AV u v uv VI uv Viin adu u v v Vi v The indexes p and q represent the polarisation for which the visibilities have been measured These visibility values are obtained by performing the following integrals In these equations the off plane component entering the Fringe Wash function and the exponential has been simplified to keep each equation in a single line OF is the Obliquity Factor represented by 41 7 TS 1 RE Xa i m gt il UG t Vy w OF Ms oy ae VQ j fo ES fr GE u E v w OF TE GME 66 7 2 Earth amp 4 c Earth y1 E n 49 9 7 fo _ E _ P Eo i 6 1 2 Vy Sun dir Puy di dir y I E N y 0 0 Py E 2234 e a a w OF v re o i up cSun ref 1 Q Q Jo oum dir Fr EE Em 7 T Vig T w OF j2a ug vyn wyOF
93. not including correlations with LICEF NIR in H polarisation i e correlations with receivers LICEF AB 01 LICEF BC 01 and LICEF CA 01 Please refer to figure 11 of RD 5 for a visual representation of the order followed The next 2346 rows correspond to the imaginary values of the V polarisation calibrated visibilities following the same order as above The next 3303 rows correspond to the real values of the HV polarisation calibrated visibilities as received from the L1a products and ordered in the following approach Please refer to figures 10 and 11 of RD 10 orange cells for a visual representation of the description This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 y C ngn SMOS L1 Processor pate 29 10 10 deim s Algorithm ise ENGENHARIA 7 Theoretical Baseline Page 48 of 89 First 528 rows with calibrated visibilities of elements in Arm in polarisation against elements in Arm B in V polarisation Le first LICEF AB 03 against LICEF BC 03 then LICEF AB 03 against LICEF 01 V then LICEF AB 03 against LICEF B 01 until the 234 element LICEF AB 03 against LICEF B 21 Next is LICEF AB O01 against LICEF 03 then LICEF AB 01 against LICEF 01 and so on until all elements in arm B are correlated with LICEF AB 01 H Please note that this row does not include the co
94. o Eq 26 NIR LICEF PMS gains and offsets are computed in the following section This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C SMOS L1 Processor 29 10 10 dei m s ritica Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline 37 of 89 The explanation for this receiver noise temperature estimation can be found in more detail in section 3 1 10 3 1 8 3 NIR LICEF Receiver gains and offsets The NIR LICEF receiver gain and offsets are also found though the 4 point method Measurements from NIR modes LICEF LC and LICEF LC2 are used in the equivalent of Eq 14 GY Voy Vik PMS 7 TLV CIP pLV CIP NS2 1 _ Von Vik p aP Eq 77 2 1 i _ Vig Vax Va 7 Vig T The voltage offsets are computed from noise injection from the ODD Noise Sources configuration 3 1 9 NIR absolute calibration through external sources In order to calibrate the remaining parameters of the NIR the next measurement steps must be made Look at a cold scene in NIR A mode Look at a cold scene in NIR AR mode Look at a cold scene in NIR LA mode 3 1 9 1 NIR A Calibration The parameters T and Tj are calibrated periodically in flight by measuring a known scene The values T and T represent the expected
95. o obtain a fitting window This methodology can be seen in the following example where contour plots are made for equal semi major and semi minor axes values against alpha values This represents the initial tabulation and it should only be performed once The way to perform this tabulation is to compute the Equivalent Array Factor according to Eq 152147 using an array of fixed alpha and 6 values Once the Array Factor is computed the 3dB contour is fitted with an ellipse from which the E E2 parameters can be obtained This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 iti SMOS L1 Processor pate 29 10 10 dei m s Algorithm Issue 2 10 ENGENHARIA Jr siwe Theoretical Baseline page 75 of 89 a variation for delta 15 25 20r eem 0 032 0 03 0 028 0 026 0 024 0 022 0 02 0 018 0 016 Fig 16 Major semi axis of elliptical 3dB contour of AF as a function of alphaU x axis and alphaV y axis Delta is constant at 15 b variation for delta 15 25 20r 10 15 20 25 0 028 0 026 0 024 0 022 0 02 0 018 0 016 0 014 Fig 17 Minor semi axis of elliptical 3dB contour of AF as a function of alphaU x axis alphaV y axis Delta is constant at 15 Thus for 6 15 and for any combination of values of an
96. objective of the Geolocation process is to compute for each of the pixels observed the corresponding Brightness Temperature and observation angles the radiometric accuracy the Faraday and geometric rotation angles the footprint major and minor semi axis and a set of quality flags The first step is to identify which pixels of the ISEA grid are contained within the extended alias free FOV EAF FOV for one particular snapshot This is done by first projecting the EAF FOV contour onto the ISEA grid and gathering the points falling inside Once identified the incidence and azimuth angles in the antenna frame are computed for each of the pixels which also correspond to the xi eta coordinates according to the following equation This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C iti SMOS L1 Processor 29 10 10 deim s Mili Algorithm S ENGENHARIA Ur Theoretical Baseline page 67 of 89 sin cos Eq 7 sin sin 149444 Based on a land sea mask the pixels are separated into two different loops pure sea pixels are flagged for OS Llc processing land and mixed pixels are flagged for SM Llc processing Additionally pixels belonging to the alias free FOV not extended are flagged as well as pixels near the border or on the diagonals of the antenna frame 77 Once the antenna frame coordinates ar
97. of 2556 correlations between I channels of different receivers No 2556 correlations between I and channels of different receivers Q 72 correlations between I and channels of same receiver Q 72 correlations between and 0 channels Q 0 d 72 correlations between I and 0 channels 0 d 72 correlations between I and 1 channels 7 1 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 N C SMOS L1 Processor pate 29 10 10 d e 1 m g S r Algorithm Issue 2 10 ENGENHARIA J Theoretical Baseline pae 48 correlations between and 1 channels 1 36 control correlations between 1 and 0 channels 4 for each ASIC Since each LICEF NIR has two separate output channels one for each polarisation mode only 69 signals from the receivers will be used at a time when doing the image reconstruction of the scene In H polarisation measurement mode for example the horizontal outputs of the LICEF NIR will be used and the vertical polarisation outputs will be discarded However the data calibrated from LO to Lla are the complete 72 signals from all receivers For correlations between antennae and stable signal it should be noted that the total information for correlations between the channels and the 1 cha
98. on This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 df nN C iti SMOS L1 Processor pate 29 10 10 deim s Algorithm E ENGENHARIA J Theoretical Baseline page 71 of 89 n Eq sin tan 1 5 cos Earth 155450 with R as the Earth radius H the orbital height and as the nadir angle of the considered point Expanding the rotation matrix K it has the following coefficients Zz cos cos cos sing cost sin sint cos sing sint sin cost X E Eq y cost AMEN sint Y 156454 Z sin cosg sin sin cost cos sint sin sin 0 sint cost J Z In order to calculate the projection of an antenna beam contour on the ground it is necessary to define a link between the variations of the coordinates in the antenna frame and the coordinate variations in the coordinate frame defined in the plane tangent to the Earth surface in the considered point Now expressing the position of point P in the reference system SXYZ can be done using spherical coordinates in the antenna frame r X r sinOcos Y r sin sing 157152 Zp 6 The distance r can be computed assuming a spherical Earth by means of the expression Eq r E T UL y i 2R parih H sat E COS MUT Computing
99. on This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C non SMOS L1 Processor 29 10 10 deim s Algorithm 240 ENGENHARIA 7 siwae Theoretical Baseline Page 40 of 89 Using 2 during measurement in NIR A mode the denormalisation factor due to noise leakage is computed by noise Jl Eq 90 Where this time is the antenna noise injection temperature and 77 is pulse length both in NIR A while the instrument is in science measurements s blind In conclusion the correction functions f and Ls are computed during measurement by solving and V and then using f Re V 7 Va Val 91 fy Dive eva vu 3 1 10 Receiver Noise Temperature Monitoring As of September 2006 a new step has been introduced in the PMS calibration sequences In this step the instrument is in Uncorrelated Noise Injection configuration with the NIR LICEF also in LICEF LU configuration The purpose of this step is to measure the System Temperatures with the switch in U position at the same time and temperature as the rest of PMS calibration is performed and use it to derive the Receiver Noise Temperature This way the Receiver Noise Temperature can be characterised in the same way as the PMS gain and offset are and be computed during nominal science observations The
100. or each pixel in Llc the information of Brightness Temperatures is retrieved along chosen polarisations e g TX and TY polarisation directions are parallel to Za and Ya directions on the Antenna Reference frame but for the scope of simplicity on the current document from now on these measurements are referred only as Brightness Temperature values Throughout the document whenever the superscript is used it denotes the complex conjugate of the value to which it is applied Indexes in the S Parameters definitions also denote specific components unless otherwise noted k represents receiver positions s represents noise sources and numerical values represent the NIRs LICEF channel modes are indicated as superscripts with H for horizontal polarization V for vertical polarization U for uncorrelated noise injection and C for correlated noise injection representing the switch from which the signal being correlated is coming This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C SMOS L1 Processor 29 10 10 d m s ritica Algorithm Issue 2 10 ENGENHARIA Ur Theoretical Baseline 2 INSTRUMENT OPERATION MODES This chapter shows briefly the instrument possible operation modes as taken from section 6 of the AD 5 where the in orbit modes are described These operation modes are also reflected in
101. pering capabilities of the apodisation meaning that higher values of alpha provide higher tapering The baselines are normalised with the same 2 2 maximum value Prax Aus x Rotation is introduced by making a linear combination of the u and v coordinates and applying the apodisation along those new directions as it is shown in the following equation u ucos Eq v 5 8 6 176171 The problem to be solved would be to find the and coefficients by forcing that the Equivalent Array factor as computed in Eq 152147 particularised at the semi axes points needs to be half of the maximum measured at xi eta 0 The expression has been simplified considering FWF unity on the right side of the equations u v g ma 177472 yxw u v eb Substituting Eqs 174169 and 176171 in the above one it results in an equation system with two unknowns 1 cos vsin usind vcosd i Shed amp l x p max P max 2 2 gt A uerus x1 max max Eq 2 2 178123 1 cos vsin usin vcos ix a Lala pd 2 u y 2 2 peu x1 TETT xen Which unfortunately cannot be solved analytically so the solution is to tabulate the alpha values for a set of ellipse parameters E E2 and and interpolate among them t
102. r of coordinates in the antenna frame amp 7 indexes and polarisation values of the antenna patterns and Brightness Temperature p q indexes The order of the columns is the following 9 9 9 The first 128x128 columns correspond to H polarisation Brightness Temperatures The next 128x128 columns correspond to V polarisation Brightness Temperatures The next 128x128 columns correspond to the real components of the HV polarisation Brightness Temperatures The final 128x128 columns correspond to the imaginary components of the HV polarisation Brightness Temperatures This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission lt Code SO DS DME L1PP 0011 e SMOS L1 Processor pate 29 10 10 deim s Algorithm m EXSENHARIA Theoretical Baseline page 50 of 89 Going into more detail each distribution of 128x128 elements corresponds to the SMOS natural hexagonal grid represented in a rectangular matrix The centre 0 0 is the first element of the distribution The generation of i elements within the matrix is done according to Eq 112 by moving the two indices k and k from 0 to 127 or the final resolution desired Some considerations have to be taken to account for the fact that we are dealing with a hexagonal domain as depicted in RD 22 The following figures show the resulting 77 distribution of values for a 128x128 Brightness
103. rical Harmonics are expressions that satisfy the spherical harmonic differential equation which is given by the angular part of Laplace s equation in spherical coordinates The spherical harmonic Yin 90 of degree and order m with l lt lt l is a complex valued function of the spherical coordinates 6 0 7 and ge 0 27 It is related to the associated Legendre s polynomial Pim x with 1 1 by the relation 21 1 1 Eq Por 133134 Y 0 9 Spherical Harmonics provide orthonormal base for representation that can be used to approximate the LICEF pattern diagram once it has been measured over a discrete grid The method for approximation is to express the antenna pattern as a series of Spherical Harmonics B 7 0 6 gt Es 12435 1 0 m With being specific coefficients that are computed doing the scalar product of each Spherical Harmonic base with the discrete LICEF pattern Er 0 9 Y 9 In practice the summation over cannot be done to infinite and it must be truncated typically to a few elements This means that the coefficients must be optimised to minimise the quadratic error in the approximation and the retrieval process turns out to be iterative using the scalar product described above as a first approximation This process needs to be performed only once when all the LICEF antenna patterns are measured on ground empiri
104. rrelation against LICEF BC 01 V This ordering continues until the last element correlated is LICEF A 21 against LICEF B 21 e Next 528 rows with calibrated visibilities of elements in arm A in polarisation against elements in arm C in V polarisation Same order as above i e first LICEF AB 03 against LICEF CA 03 then LICEF 03 against LICEF CA 01 V then LICEF AB 03 against LICEF C 01 until the 23 element LICEF 03 against LICEF C 21 Next is LICEF AB 01 against LICEF CA 03 then LICEF AB 01 against LICEF C 01 and so on until all elements in arm C are correlated with LICEF AB 01 H Please note that this row does not include the correlation against 01 V This ordering continues until the last element correlated is LICEF 21 against LICEF 21 e Next 528 rows with calibrated visibilities of elements in arm B in polarisation against elements in arm A in V polarisation Same order as above i e first LICEF BC 03 against LICEF AB 03 then LICEF 03 against LICEF 01 V then LICEF BC 03 against LICEF A O1 until the 234 element LICEF BC 03 against LICEF A 21 Next is LICEF BC 01 against LICEF 03 then LICEF 01 against A 01 and so on until all elements in arm A are correlated with LICEF 01 Please note that this row does not include the correlation against LICEF AB 01 V This ordering continues until the last element correlated is LICEF B 21 against LICEF 21
105. s the constant background Earth temperature contribution that was subtracted earlier Results are only meaningful in the extended alias free FOV delimited by the Earth replicas now that the Sky replicas contributions have been eliminated T Eq 125 B B Earth In full polarisation mode it must be remarked that the physical temperatures of the receivers is not applicable to HV polarisation so the corresponding correction term is zero The Galaxy Map used as baseline contains measurements for HV polarisation and these shall be used when correcting full pol visibilities However there are no sources for Sun or Moon temperatures in HV pol so they shall be assumed to be zero New information in this regard may come during commissioning and never before that As it can be seen from Eqs 123 124 the formula can be also expressed as a matrix vector multiplication and the only requirement to remove foreign sources is to have the latest G matrix available and be able to compute the Brightness Temperature distribution of the sources to be removed In the case of the Sky the distribution is taken from the Galaxy map and set to zero for those spatial coordinates that are not part of the sky area In the case of the Earth the distribution is taken as constant based on Eq 122 and set to zero for those spatial coordinates that are not part of the Earth area The distribution may be taken using a model instead of a constant value
106. s restricted to the number of non redundant correlations that the instrument shall be measuring For MIRAS the number of non redundant visibilities is 2791 forming a star shape in the u v plane and is only dependant on the number of receivers per arm and the Y shape of the instrument Thus the number of columns for this matrix is 11164 This number comes from 1395 complex elements plus one real element that is measured for H or V polarisation plus 2791 complex elements measured for HV polarisation Again the total size of the matrix is dependant on the level of coupling between polarisations through the cross polarisation antenna patterns If they can be considered negligible the J matrix can be split into three separate and independent matrices one for each polarisation For the column elements ordering it follows the ordering indicated below The first column corresponds to the real component of the zero baseline for the H polarisation Brightness Temperature Fourier Components The next 1395 columns correspond to the real components of the polarisation Brightness Temperature Fourier Components The next 1395 columns correspond to the imaginary components of the H polarisation Brightness Temperature Fourier Components The next column corresponds to the real component of the zero baseline for the V polarisation Brightness Temperature Fourier Components The next 1395 columns correspond to the real components of the V pol
107. scribed in RD 25 so that the Brightness Temperature Fourier Components may be obtained after a simple matrix vector multiplication T J V 3 2 3 3 1 J Matrix generation This method requires to compute the matrix J whose size is much smaller than G as it merely relates the calibrated visibilities to the brightness temperatures Fourier components The number of these Fourier components is equal to the number of non redundant baselines 1396 for H and V polarisation and 2791 for HV polarisation The matrix J is computed by using G to create the expected calibrated visibilities for some specific Brightness Temperatures These specific Brightness Temperatures are computed by setting to unity each of the non redundant baselines in the star domain and perform a normal 2D IFFT on the resulting distribution Each computed set of Brightness Temperatures for each of the non redundant baselines results in a complete column of the J matrix The method can be modelled in the following way Enter a for loop for each of the non redundant baselines which correspond to a particular U V position the order to be taken is described in RD 6 Using Eq 110 an NrxN4 complex matrix is created for the u v baselines with zero in all positions except for the U V position where the complex number 1 1 is set In H or V polarisation the complex number 1 1 is also set in the U V position and only half of the non redundant baselin
108. selines system temperatures 3 1 5 4 Applying system temperatures to PMS calibration 3 1 6 Correlator Offset correction 3 1 7 Error Compensation 3 1 7 1 Visibilities Calibration 3 1 7 2 Redundant Space Calibration 3 1 8 NIR calibration 3 1 8 1 NIR R mode measurements 3 1 8 1 1 Reference CAS noise temperature 3 1 8 2 Reference receiver noise temperatures 3 1 8 3 NIR LICEF Receiver gains and offsets 3 1 9 NIR absolute calibration through external sources 3 1 9 1 NIR A Calibration 3 1 9 2 NIR AR Calibration 3 1 9 3 Leakage and cross coupling calibration 3 1 10 Receiver Noise Temperature Monitoring 3 1 11 PMS cold sky calibration 3 1 11 1 PMS characterisation 3 1 11 2 CAS and receiver temperature validation 3 2 Level 1a to Level 1b 3 2 1 System Response Function 3 2 2 Foreign Sources Correction 3 2 2 1 Flat Target Transformation 3 2 3 Image Reconstruction 3 2 3 1 On ground characterised G Matrix 3 2 3 2 Parametric G Matrix 3 2 3 3 Mathematical inversion Stabilised approach 3 2 3 3 1 J Matrix generation 3 2 3 3 2 J Matrix inversion 3 2 3 3 3 J Matrix application 3 3 Level 1b to Level 1c 3 3 1 Ionospheric Correction SO DS DME L1PP 0011 29 10 10 2 10 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission
109. set of equations for this purpose is expressed in phase and amplitude as RD 18 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission 7 Code SO DS DME L1PP 0011 LU Pe SMOS L1 Processor pat 29 10 10 deimosB MEM uoc uo E ENGENHARIA J Theoretical Baseline page 35 of 89 Lk t Jk raw 35 Eq 70 In In g In g In V Where and amp are the indexes of adjacent antennae in the same direction along the arms spaced the minimum distance d These baselines should measure the same correlations and any difference between measurements is attributed to the separable phase and amplitude errors As a starting assumption the phase of the first element in the first arm is set to 0 and its amplitude is set to unity The set of equations is solved for f and This method amplifies the amplitude errors so UPC recommends in AD 5 that it be used only for phase calibration and only after having made Noise Injection Calibration for calibrating the path after the switch so that only the path antenna to switch is covered by RSC 3 1 8 NIR calibration By NIR calibration two sets of different sets of measurements are defined While in NIR A mode the NIR measures the brightness temperatures and acts in parallel as a LICEF forming mixed baselines In NIR R mode the NIR is measuring the CAS noise level and
110. source This means that the total number of elements that can be measured is 1296 see next figure and for the rest of the pairs the values should be estimated based on these measurements This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission 2 10 29 10 10 20 of 89 SO DS DME L1PP 0011 Code Date Issue Algorithm SMOS L1 Processor Theoretical Baseline page software deim s lilii ENGENHARIA JE 1 1 1 1 IX jx TK PPK TKK TKK x x xix xxix x x x x x xx X x x x x x x x x xx X Xx Xx X X x Xx X x EA x
111. ssera N Function Equation Including Co And Cross Polar Duffo Antenna Patterns IEEE Geoscience and Remote Sensing Letters Vol 2 No 3 pp 292 295 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission deimSs Critical EHCGENHARIA software Code SMOS L1 Processor pate Algorithm Issue Theoretical Baseline page SO DS DME L1PP 0011 29 10 10 2 10 RD 20 A Camps Torres The impact of Antenna Pattern Frequency 2006 Corbella N Duffo M Vall Dependence in Aperture Synthesis Microwave llossera M Mart n Neira Radiometers IEEE Transactions on Geoscience and Remote Sensing Vol 43 No 10 pp 2218 2224 RD 21 I Corbella Torres L band Aperture Synthesis radiometry Hardware July Camps J Duffo Requirements and System Performance IGARSS 2000 M Vall llossera 00 Proceedings of the IGARSS 00 Hawaii USA RD 22 Camps J L The Processing of Hexagonally Sampled Signals January Corbella F Torres with Standard Rectangular Techniques Application 1997 to 2D Large Aperture Synthesis Interferometric Radiometers IEEE Transactions on Geoscience and Remote Sensing GRS 35 pp 183 190 RD 23 Corbella et al The visibility function in interferometric aperture 2004 synthesis radiometry IEEE Trans Geoscience and Remote Sensing
112. subscript 0 indicates the temperature during calibration and A and B are coefficients computed as is explained in the following paragraphs The coefficient A can be computed simply from L LT yay Eq 40 Lh L Ty h where T is the corrected noise injection temperature computed from the noise injection level measured during calibration see Section 3 1 9 1 by is 177 v oan Pu Eq 41 Tu Lant h lh Ta with the parameters defined as u n Sensitivity to physical temperature gradient please check RD 16 Section 5 3 3 T Is the physical temperature of the noise source 5 the physical temperature of the noise source during calibration see Section 3 1 9 1 y Attenuator between antenna plane and antenna intermediate layer computed as Ly D v R m i Bay T z T out in which E is the L1 attenuator value measured on ground This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 iti SMOS L1 Processor 29 10 10 dei m s Algorithm Issue 2 10 ENGENHARIA Theoretical Baseline 27 of 89 L isafixed LI attenuator error characterised in orbit using data from the first year 15 the long term drift component of the L1 attenuator in orbit us
113. t This data is retrieved from the antenna patterns ADF for each polarisation For full polarisation G 2 77 is computed as dis the distance ratio between receivers 0 875 LT is the averaged System Temperature measured by the PMS system which has been used to de normalise the Lla calibrated visibilities Bis the equivalent receiving frequency bandwidth in Hz currently being 19 MHz 7 is the effective integration time and is equivalent to Where ris the integration time and ce is the coefficient that accounts for the 1 bit correlation oversampling and hermiticity c g 1 81 as quoted RD 21 Tis considered as 1 25 for and V polarisation measurements and 0 85 for HV polarisation measurements 2 xxt accounts for the apodisation window and redundancies in the u measurements where W is the apodisation window term for each u v baseline and R is the redundancy level of that same baseline 1 e number of times that the baseline has been measured 1 for non redundant baselines greater than 1 for the rest as fef 1 P before fo is the central frequency and fo is the low frequency whose values are 1413 and 1403MHz accounts for the local oscillator factor where B is the bandwidth mentioned 3 3 2 3 Pixel Observation Angles computation Afterwards the incidence 8 and azimuth observation angles are computed The incidence angle
114. t calibration the following values are collected v PMS voltages for WARM noise injection even and odd PMS voltages for HOT noise injection even and odd WARM temperature measured in NIR R Ty HOT temperature measured in NIR R After these values are stored the coefficients must be computed for the hub in the first place 1 hub _ NS2 1 34A hub __ hub 104 Vox lk where N are the 6 paths from the hub Noise Sources to the NIRs and there are 12 values for For the odd noise sources we have T T odd _ NS2 NS1l oad Eq 105 Vak T Vik This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C ngn SMOS L1 Processor pate 29 10 10 deim s Algorithm sue 240 ENGENHARIA siwae Theoretical Baseline Page 44 of 89 where are the 3 paths from the odd Noise Sources to the NIRs and there are 10 values for The CAS differences plane translation coefficients are then compared by hub Mea eC 20log AT Em Eq 106 eC 20l0g a dB Nk As for the case of the receivers that are driven by a Noise Source without a direct path to the NIRs the coefficients must be computed using as reference the gain of the receiver closest to the hub in each group sharing the same Noise Source The gain used as reference is the one
115. ted for all possible pairs of receivers without repetition This gives a total of NV N 1 2 pairs to be eceivers Receivers computed The amplitude of the FWF is computed using data from the relative amplitude calibration approach using the system temperatures computed during calibration with correlated noise injection Three different measurements are made at the three different time delays needed Special care has to be taken in the computation of the M terms for the two time delays t and 1 The baseline for the time delay is given from a Local Oscillator at 55 84 MHz and the value shall be retrieved from the PLM ADF As mentioned in RD 26 Equations 3 4 and 7 must be adjusted for the effect of the time delay The net effect is that the real part of 44 t has to be computed from the correlations at time delay f and viceversa Additionally the quadrature error correction computed in Eq 9 has to be taken from the zero delay self correlations as otherwise the quadrature error is badly estimated The resulting equations for the fringe wash amplitude term g at the hub at time delays T t 0 t_ are AD 6 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q SMOS L1 Processor pate 29 10 10 deim s Bi Algorithm ENGENHARIA Ur Theoretical Baseline pag om v
116. th the parameters computed in calibration mode While the quadrature offset and in phase corrections are straightforward to apply since the coefficients have been computed during the noise injection modes the de normalisation of the calibrated visibilities will rely on the computation of the system temperatures in the reference planes at the time of each measurement First the correct PMS parameters must be retrieved from auxiliary or previous calibration data indexed by physical temperature The correct parameters will be the ones computed ate the closest physical temperature to the one at measurement time If the temperature change between calibration and observation times is AT nk Eq 24 the gain and offset of the PMSs during observation is computed using AT pny and the PMS sensitivity to physical temperature G 1 S phy 100 Eq 25 C Voff Voge Voge The sensitivity terms S7 and al will be characterized on ground as well as in orbit during the phy phy calibration procedures 3 1 5 1 Hub system temperatures Using Eq 15 one can express the calibration temperature at the receiver k and the system temperature at the antenna plane as _ Vor SYSk E 2 Eq 26 T HH V _ pHCVC s SYS COUP Sys 2 sel vk This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code
117. the the calibration external temperatures As there are three NIRs in the MIRAS instrument the values Tys and 2 will be the average of the noise temperatures measured by each NIR each NIR has two outputs H and V and will in fact provide two measurement of the noise temperature in NIR R mode which will also be averaged This averaging of the NIR signals reduces the noise and possible systematic errors The equivalent system temperatures at the LICEF receivers port k and j of Tcsi and For example AD 6 2 Tesar mA sir Eq 16 Ts IS AT 1517 where AT and are the noise contributions from due to its physical temperature is the S Parameter of the path connecting receiver k with a noise source s while is the S parameters of the path connecting the NIR with the same noise source Rearranging Eq 16 and inserting into Eq 15 the system temperature can be written as 2 Y YV S _ k offk k ks Lu p Toz To Vox Voy IS C usa Eq 17 3 1 4 2 Fringe Washing Function Estimation The estimated values of the fringe washing function at the origin are used as a parameter to correct amplitude and in phase errors Together with the values at two different time delays it will also be used later during the image reconstruction process The fringe washing function needs to be estima
118. the APID of the LO instrument source packets containing the information transmitted There are two main observation modes and 4 calibration modes although in all of them the output format is the same In one integration time each receiver s signal is correlated against the other receivers in an arrangement shown in Figure 5 2 1 1 Measurement modes There are two instrument polarisation modes dual and full polarisation In dual polarisation all arms are in the same polarisation mode In full polarisation one arm is in a cross polarisation mode for 1 3 of the integration time The cross polarized arm is rotated in a clockwise fashion Schematically _ 4 ee ee LLL LLLLL LLLLLLLLDLLLLLLBILLJ Ome 1200 ms 2400 3600 ms 4820 ms Figure 1 Time sequence for dual polarisation mode Oms 1200 ms 2400 ms 3500 ms 4800 ms Figure 2 Time sequence for full polarisation mode This means that in four consecutive integration intervals the instrument will measure two dual polarisation brightness temperature HH and VV and two cross polarized brightness temperatures VH and HV In fact as can be seen from the previous figure the arms in full polarisation mode rotate polarisations four times each mode producing one set of visibilities corresponding to a third of the integration time This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission
119. the gain offset and receiver temperature of the NIR channels Therefore the description of NIR R measurements is included in this chapter since it is a NIR calibration procedure On the other hand the NIR A and NIR R modes themselves must be calibrated The NIR requires two targets as calibration standards The first one is an internal reference load at the inner instrument s temperature The second target is the cold sky Additionally a third mode NIR AR mode will be necessary to calibrate NIR R mode The following description is based on the documents RD 16 and AD 6 3 1 8 1 NIR R mode measurements 3 1 8 1 1 Reference CAS noise temperature The CAS noise temperature used in the System Temperatures Computation Sections 3 1 4 1and 3 1 5 can be computed through Eq 39 reproduced here with the correct coefficients Tys An Bry Eq 71 Dui Ar alh t Brn With A defined as A Tyo i I gt To Lys ee E Rv Eq 72 A Tyron Urn Lacs RA T Ly Lp This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 XY C aes SMOS L1 Processor 29 10 10 deim s Bii Algorithm ENGENHARIA Theoretical Baseline 36 of 89 where all the coefficients have the same meaning as in Section 3 1 5 3 but are reference values hence the subscript Tyro is computed in Ext
120. tial Internal Distribution Unit Copies External Distribution Organisation Jean Claude Debruyn Steven Delwart Archiving Word Processor MS Word 2000 File Name SO DS DME L1PP 0011 Algorithm Theoretical Baseline doc Archive Code SO DS DME L1PP 001 1 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 C iti SMOS L1 Processor pate 29 10 10 deim s Bis Algorithm sue Y ENGENHARIA JF Theoretical Baseline iv Document Status Log Change description Date Approved Delivered to ESA 2004 01 19 Updated to comments from Final Presentation 2004 01 30 Update for Phase 2 CDR 2005 06 30 Updates after CDR RIDs 2005 08 31 Introduction of FTT and NIR calibration 2005 11 04 Revision after L1PP implementation 2006 04 07 Final delivery for Phase 2 activities 2006 06 07 Updates for L1PP V2R 2006 11 15 Reviewed by CASA and ESA 2006 11 24 V3R Delivery 2007 04 09 V3 5 Delivery 2007 07 15 V4 Delivery 2007 11 16 Updated after review for the Maintenance Phase and for 2010 10 29 L1PP v3 5 0 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 e C iti SMOS L1 Processor 29 10 10 deim s Algorithm ENGENHARIA Theoretical Baseline v Table of Contents 1 INT
121. ties for H V and HV polarisation in two consecutive integration times must be used in full polarisation mode For a comprehensive analysis on the HV visibilities ordering and location please refer to RD 10 In fact in order to give the user more configuration flexibility to take into account e g possible hardware failures the temperature frequencies are instead obtained by multiplying by WV T where W is a diagonal matrix whose entries consist of user configurable weights for each baseline These baseline weights whose default value is 1 are obtained from the SM xxxx AUX BWGHT ID Auxiliary Data File 3 3 Level 1b to Level 1c The last steps of the processing consist first on a computation of the Ionospheric data applicable to each snapshot Afterwards the Brightness Temperature values are computed grouping all snapshots into a single swath product The purpose is to provide for each footprint an array of Brightness Temperature expressed at Top of Atmosphere values along with their observation angles Based on the Spacecraft orbital position and also in the instrument s attitude it is possible to compute the antenna frame to pixel incidence and azimuth angles for any pixel on the ground This computation is shown in the next chapter s equations although for implementation purposes it shall be better performed with the help of the Earth Explorer CFI functions This document is property of DEIMOS Engenharia
122. tion This can be written as 1 T i pnuk 1 Max 5 4 P Eq 95 Su If we insert the expression of in the equation above it yields 2 2 IS UC m is T E Eq 96 Note that we are retrieving receiver temperature at VAP HAP plane at the temperature that the short calibration has been performed Hal in spite of the fact that the switch has not been connected either to H or V During the orbit in calibration mode long calibration LICEF receiver temperature can be retrieved as a function of temperature This must be performed at VAP HAP plane This allows to compute receiver temperature sensitivity to physical temperature by linear fit in the same way as performed for PMS gain and offset A H V using a sensitivity value as Now the receiver noise temperature at any orbit position in measurement mode can be computed by finding the two nearest calibrated receiver temperatures and 2 and applying Ts M Ton uas m Ta To Sn LL 0 0 0 0 I5 T dia an Ci Eq 97 Where and T n2 are the temperatures at the orbit position in measurement mode and the are the arguments of latitude for each position It must be pointed out that once receiver temperature is known at this gives an estimate of the antenna temperature seen by the LICEF in measurement mode Tax Dos
123. tion parameters The altitude to be used in this model shall be 450km to match the altitude at which the TEC 1s computed The IGS combined TEC map is an ASCII file with TEC values over a Mercator grid at an altitude of 450km and measured every 2 hours The frequency with which this file is released is every 24 hours The expected output in both methods is the TEC value for the given spatiotemporal coordinates expressed TEC Units 10 9 6e m Computation of Faraday rotation 0 expressed in degrees for each pixel can be computed using Eqs and 4b of RD 8 with the retrieved pixel observation angles 0 TEC and geomagnetic data D w 6950x F xTECx sin I cos xtan x cos 6 D lm 3 3 1 1 Geometrical rotation The geometrical rotation between the polarisation axes in the antenna frame and the pixel frame can be also computed in this module by following the next two procedures 3 3 1 1 1 Waldteufel and Caudal Implementation The following diagram shows the intended angles for a projection of point P into the antenna frame SXYZ This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 df SMOS L1 Processor pat 29 10 10 MM oim ee T H ENGEN ARIA J siwae Theoretical Baseline 64 of 89 Faraday rotation Figure 14 Geolocation and projection angles RD 14
124. tions or errors in the receivers positions as an error in the retrieved Brightness Temperatures 3 2 3 2 Parametric G Matrix The Parametric Matrix Reconstruction algorithm is based on computing a matrix based on independent element modelling Each of the elements used in the G Matrix computation is expressed as a best fitting formulation based on a set of parameters and these parameters are later calibrated validated by observing known Brightness Temperature scenes This algorithm has been developed by E Anterrieu from the Laboratoire d Astrophysique de l Observatoire Midi Pyr n es RD 11 The input data thus required for the G Matrix are This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 Q C ate SMOS L1 Processor 29 10 10 deim s Bi Algorithm ENGENHARIA Theoretical Baseline LICEF antenna patterns radiative model LICEF Filters model combined in pairs they yield the Fringe Washing Function shape for that baseline MIRAS thermo elastic model The models are described in the next paragraphs The LICEF patterns are approximated with Spherical Harmonics using as the first baseline the measurements to be performed by TUD to obtain the initial coefficients During commissioning and operations calibration procedures will turn up new values for such coefficients Sphe
125. ture Input Data at this level is the Digital Correlator System DICOS output the PMS s output voltages and the NIR pulse length outputs as well as the instrument physical temperatures attitude and orientation All these quantities are directly retrieved from the LO product with each correlation encoded in 16bit PMS output voltage has to be transformed into system temperatures by means of manufacturer tables that specify the conversion formulae and characterisation approaches These tables will have measurements throughout the temperature range The in flight measured temperatures will then be used to retrieve the correct parameters The PMS parameters are also calibrated in flight through correlated noise injection to correct for changes in the response and allow for correct values of those parameters to be used The NIR pulse length output is transformed into the L band antennae temperatures using an algorithm provided by the NIR manufacturer Final antenna temperature can be computed as the average temperature of the three NIR receivers although it is also possible to use the three measurements independently The DICOS output consists of correlator counts N for each pair of receiver outputs in addition to correlator counts between each receiver outputs quadrature and in phase and one of two constant channels with 1 and 0 values respectively This document is property of DEIMOS Engenharia and cannot be distributed or
126. uations are described in the next equation and have been set as part of the Strip Adaptive ADF APOD99 2 3 log10 7 2205 4 1 9915102 10 1 0776 log10 0 13022 10210 E n 2 179474 v log 10 ar o 8 4703 1 5081 log 10 w w 0 16293 log 10 w w ji 0 016226 log10 w w This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor 29 10 10 deim s Algorithm ue d T ENGENHARIA software Theoretical Baseline Page 77 of 89 4 OPEN ISSUES Modelling of the Parametric matrix approach is not yet complete although there shall be a This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 2f XY C n SMOS L1 Processor 29 10 10 dei mos ritica Algorithm Issue 2 10 ENGENHARIA Jr Theoretical Baseline 78 of 89 5 ANNEX G MATRIX BLOCKS In this Appendix the expressions for the elements in each G matrix block are derived Rewriting Eq 109 in a slightly different notation the System Response Function is Fee mire Ew 2 1 NN ni j j 2 _ Eq P io ve u v I Pula Jo 5 7 where F 2 7 is the normalised antenna radiation pattern of receiver j in pol
127. ur of AF as a function of alphaU x axis and alphaV elias SS LR LES URS LEER RETENIR 75 Fig 18 Alpha parameters for E 0 024 E 0 018 Delta value is 157 eese 76 List of Tables 1 opio ble oae er ene pa Eoo ida ctu v Da er err rere rire 2 Table 2 Reference DOCUITIGDIS iier tera terree ag ra K dae 4 This document is property of DEIMOS Engenharia and cannot be distributed or duplicated without its written permission Code SO DS DME L1PP 0011 SMOS L1 Processor pate 29 10 10 deimos lir ENGENHARIA J Theoretical Baseline 1 of 89 1 INTRODUCTION 1 1 Purpose and Scope This document describes the SMOS L1 Algorithms Theoretical Baseline explaining in depth all the mathematical and processing operations needed to successfully transform the SMOS LO Data into all the L1 output 1 2 Acronyms and Abbreviations AOCS BT CAS CIP DICOS DLR PEP FFT FOV FTT FWF GSL I HKTM MIRAS NDN NIR PMS PVT RMSE SC HKTM SEPS TBH TBV TEC Attitude and Orbital Control Subsystem Brightness Temperature Calibration System Correlated Noise Input Plane Digital Correlation System Deutschen Zentrum fiir Luft und Raumfahrt Front End Processor Fast Fourier Transform Field of View Flat Target Transformation Fringe Washing Function GNU Scientific Library Instrument

SMOS L1 Processor Algorithm Theoretical Baseline Definition

Contents

Download Pdf Manuals

Related Search

Related Contents