Exposure Time Calculator for LUCI - USER MANUAL -
Contents
1. 10 T FA x 14 k Boltzmann s constant k 1 3807 10773 2 Tss Blackbody temperature After that calculation the flux is normalized to the magnitude given by the user Gaussian Shaped Emission Line The last selectable standard spectrum is a gaussian shaped emission line The parameters are central wavelength FWHM and total flux The magnitude of the source is not a free parameter anymore due to the total flux given by the user NEE Se Se 15 ft or o is given by FWHM 2 35 FLUX the total flux and T the central wavelength 1 2 5 Target Magnitude The input of the source magnitude available for template spectra or blackbody only have to be done in Vega magnitudes Flux density W m nm 0 8 1 1 2 1 4 1 6 1 8 2 2 2 2 4 Wavelength um Figure 2 The six available stellar spectra Flux density arbitrary units m 0 5 1 1 5 2 2 8 Wavelength um Figure 3 The four available galaxy spectra at redshift z 0 1 2 6 Entrance Window LUCI is equipped with an entrance window tilted by 15 It reflects the visible light to a wavefront sensor Two different coatings are available The main pa rameters are listed in Tab 2 while the plots can be found in Appendix EEntrance Windowsappendix E Table 2 Available entrance windows Window 1 Window 2 50 cut on 882 nm 955 nm transmission at 532 nm 0 42 0 12 1 2 7 Filter LUCI s ETC uses transmission data of all filters measured by the2. 0 99 0 98 0 8 onen g g 5 8 a m 0 96 a 0 6 4 A eii 2 H 0 95 5 G a 0 94 B 0 4 E 0 93 ner 0 92 0 91 0 0 0 90 1 6 1 8 2 0 2 2 2 4 0 8 1 0 22 I4 1 6 U8 2 0 2 2 24 length pm Wavelength pm Figure 16 The measured transmission of the entrance window 2 Left The whole transmission curve from zero transmission to full transmission 1 Right The transmission curve zoomed in to a transmission from 0 90 to 1 00 20
3. Exposure Time Calculators Formular Book http www eso org observing etc doc gen formulaBook FLUX95 C Megessier Astronomy and Astrophysics 296 771 778 1995 OH LIN http www eso org instruments isaac oh list_v2 0 dat ROUS00 P Rousselot C Lidman J G Cuby G Moreels G Monnet Astronomy and Astrophysics 354 1134 1150 2000 SKYBA http wwvw gemini edu sciops ObsProcess obsConstraints atm models nearIR_skybg_16_15 dat AIRTRA http unagi gps caltech edu notes bfats2002 STERNS A J Pickles Publications of the Astronomical Society of the Pacific 110 863 878 1998 GALAXS J Bicker U Fritze C S Muller K J Fricke astro ph 0309688 FIL HP http obswww unige ch gcpd filters fi108 html FIL PA H L Johnson Astrophysical Journal 141 923 942 1965 FDR OP W Seifert W Xu LUCIFER Final Design Report Optics LBT LUCIFER TRE 009 ACC RE N Ageorges A Germeroth W Seifert Acceptance Test Report LBT LUCIFER TRE 022 TRANSA http unagi gps caltech edu notes bfats2002 GRATIN Richardson Grating Laboratory http www gratinglab com BARR Barr Assosiates Inc http barrassociates com SKYREF C Leinert et al Astronomy and Astrophysics Supplement 127 1 99 1998 14 A Filter Curves z filter 0 0 g g G 5 rt n a n o a 0 4 E E a E a 5 a 0 g o 0 0 0 0 0 80 0 85 0 90 0 95 1 00 1 05 1 10 1 0 1 1 1 2 1 3 1 4 1 5 Wavelength pm
4. Paschen filter Paschen y fi ED476 1 0 g 5 A a ao A p zi A a HO 0 0 1 24 1 26 1 28 1 30 1 32 1 34 1 07 1 08 1 09 1 10 1 11 1 12 Wavelength um Wavelength um Y filter 00 80 60 40 20 00 0 90 0 95 1 00 1 05 1 10 1 15 1 20 Wavelength pm Figure 13 Narrow band filter curves Part 2 18 B Gratings HD grating with 210 lines mm H K grating with 200 lines mm 0 0 2nd Order 0 0 0 0 0 0 o0 0 v 3 20 qo a o qo fa a 0 0 0 0 Oe 0 0 oD 0 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 0 8 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 Wavelength m Wavelength pm gt g o a a a u u fa Ks grating with 150 lines mm 0 1 nn 12 1 4 16 LE 240 2 2 244 Wavelength pm 0 0 ty Figure 14 The efficiencies of the gratings vs the wavelength for the Non Littrow setup The different orders of each grating are color coded 19 C Entrance Windows Entrance Window 1 Entrance Window 1 1 00 1 0 0 99 0 98 0 8 a 5 amp a 0 96 2 0 6 a E E 0 95 a 5 8 0 94 H 0 4 Mi a a 0 93 0 2 0 92 0 91 0 0 0 90 0 8 1 0 1 2 1 6 1 8 2 0 2 2 2 4 0 8 1 0 12 1 4 16 LE 20 22 2 4 Wavelength pm Wavelength pm Figure 15 The measured transmission of the entrance window 1 Left The whole transmission curve from zero transmission to full transmission 1 Right The transmission curve zoomed in to a transmission from 0 90 to 1 00 Entrance Window 2 Entrance Window 2 1 00 1 0
5. manufac turer BARR The additional numbers are the identifiers for the filters They are stored in wavelength steps of 0 5 nm as well as the previous wavelength dependent datasets The transmission curves of these broadband filters are shown in Figure 4 All available filters including the narrowband filters are shown in Appendix CFilter Curvesappendix C Transmission 0 80 1 20 1 60 2 00 2 40 Wavelength um H K Ks OrderSep Figure 4 Broadband filters used by LUCI The optical filters U B V R and I can be chosen for the input of the object s magnitude only They are originally described in steps of 10 nm U and 20 nm B V R and I FIL HP By linear interpolation the sampling was increased to 0 5 nm 1 2 8 Cameras Three different cameras can be used with LUCI The collimator lenses mirrors and each camera results in three total efficiencies for each camera These values are shown in Table 3 One can read off the efficiency of each optical element in ACC RE Table 3 Efficiencies of the system camera and collimator in different wavelength regimes Camera Z J H K N1 8 0 49 0 52 0 57 0 61 N3 75 0 57 0 63 0 68 0 73 N30 zJ with ADC 0 37 0 43 0 63 0 68 The image scale of each camera is listed in Tab 4 Table 4 Image scale of each camera Camera Scale pix N1 8 0 25 N3 75 0 12 N30 zJ with ADC 0 015 1 2 9 LUCI 1 an
6. scale source Npix s set to 1 for both dimensions of the source light is reflected three times before entering the cryostats If we optimistically assume a reflectivity of 90 for each mirror we get a total efficiency of 0 729 at the bent Gregorian foci Adaptive Optics AO The LBT will provide a deformable secondary mirror for AO observations For this reason the ETC can handle both a seeing limited PSF and a diffraction limited PSF 1 2 3 If the loop is closed different Strehl ratios are possible This depends on the environmental conditions seeing Therefore the value of this parameter is continously changeable 1 2 3 Point Spread Function Diffraction Limited Mode In diffraction limited mode with adaptive optics the PSF is approximately composed of two functions 1 The core This is an airy function of the telescope 2 J D 2 Bessel x r Airy r 12 P D diameter of the telescope mirror u observing wavelength Bessel the the first kind Bessel function of the order 1 2 The halo It is given by a Moffat function B B 1 r Inofiat r Ia plr 1 4 7 Ta Intensity at the distance r with parameters a and 8 a Parameter is used to fix the FWHM for a given 8 6 Parameter to fix the amount of light in the lobes J Distance to the center r Y2 y FWHM 2av2al P 1 An example of such combined PSF is shown in Figure 1 For comparing the peak intensity of an ideal diffraction
7. Exposure Time Calculator for LUCI USER MANUAL Andr Germeroth A Germeroth at Isw uni heidelberg de 15th July 2014 Abstract The exposure time calculator ETC roughly calculates the exposure time of LUCI at the Large Binocular Telescope LBT There is a wide choice of different model spectra available e g different main sequence stars It is also possible to select a blackbody spectrum or a single line spectrum as an object spectrum The main calculations are written in Python and the user interface is web based The web interface provides an additional graphical output that shows the SNR versus Wavelength in spectroscopic mode or SNR vs exposure time in case of a selected imaging mode This document presents the basics of the exposure time calculator The formulae of the ETC and the main characteristics of LUCI are described in detail 1 Basics 1 1 List of Abbreviations and Acronyms AO adaptive optics CWL central wavelength DARK dark current DIT detector integration time e m electro magnetic ETC exposure time calculator EW entrance window FWHM full width at half maximum HTML hyper text markup language LBT Large Binocular Telescope LUCIFER LUCI LBT NIR Spectroscopic Utility with Camera and Integral Field Unit for Extragalactic Research PSF point spread function QE quantum efficiency RON readout noise SNR signal to noise ratio SNR signal to noise ratio for exposure time T SNRp r signal to noise r
8. N _ F A E S Os pectroscopy oo P SA P N number of photons A filter band width P energy of one photon As spectral resolution S light collecting area Qi scale in imaging mode oe exposure time Qs scale in spectroscopy mode In the near infrared regime the SNR for the exposure time DIT is given by the formula SNRp r Norr 3 Norm npix Nsky DARKprr RON DARKp r dark current for 1 DIT Dpix number of integration pixels Nagy sky signal for 1 DIT RON readout noise SNRpi r signal to noise ratio for 1 DIT In imaging mode the user will be asked for the signal to noise ratio for the exposure time 7 SNR The ETC calculates the necessary exposure time to achieve this SNR see also formula 3 T Noprr DIT and SNR SNRoprt UV Norr 4 SNR gt _ _ DIT 5 T SNRpir 5 T total exposure time DIT detector integration time Nprr number of detector integrations SNR signal to noise ratio for exposure time T SNRpir_ signal to noise ratio for one DIT SNR signal to noise ratio for an exposure time of 1 sec 1 2 2 The Telescope Mirrors Both LUCI instruments are going to be first light instruments for the Large Binocular Telescope LBT at the bent Gregorian foci This means that the lIn imaging mode Npix Of a point source is calculated within a 2 FWHM diameter aperture N Npix T sis In spectroscopic mode the program uses npix 2 seeing For an extended
9. The airmass is an additional parameter which influences the transmission The ETC allows six different values for the airmass 1 00 1 25 1 50 1 75 2 0 2 5 The Airmass AM scales the number of photons from the sky background with 2 78719 1074 AM 6 53841 10 AM 1 11979 AM 5 52132 10 16 It is a polynomial fit to observed sky brightnesses from SKYREF For small zenith distances lt 40 it is similar to the van Rhijn s function formula 17 10 1 2 13 Sky Background The sky background in near infrared regime can rapidly change within hours or even minutes For that reason the observer can choose between three different possibilities of sky background templates Sky Brightness given by the User The observer can set a brightness of the sky in 3 WVEGA for the zenith It arcsec is the brightness of the sky for the filter used for the observation Background File Another option is a file This file contains data from sky background mea surements at Mauna Kea for 1 6mm water vapor and the selected airmass see Fig 7 600 T T T T T T T 1 6 mm H O Airmass 1 5 500 F J 400 F 4 300 F al 200 F Photons sec nm arcsec m 0 all au MM A 0 8 1 1 2 1 4 1 6 a8 2 232 2 4 Wavelength um Figure 7 Sky spectrum measured at Mauna Kea for 1 6mm water vapor and an Airma
10. Wavelength um H filter K filter 1 0 ra G A n na 0 E a Eo B 0 0 1 4 1 5 1 6 1 7 1 8 1 9 1 9 2 0 2 1 2 2 2 3 2 4 2 5 Wavelength um Wavelength um Ks filter 1 0 8 a a 0 4 E a E 6 0 a 1 9 2 0 2 41 2 2 2 Wavelength um w N gt Figure 10 Filter curves of broad band filters Part 1 15 Transmission 1 20 fs 40 HKspec Filter ED763 1 ED763 2 1 60 1 80 2 00 2 20 2 40 2 60 2 80 Wavelength um Transmission zJSpec Filter 60030 00 80 60 40 20 00 0 80 1 00 1 20 1 40 1 60 1 80 2 00 Wavelength pm Figure 11 Filter curves of broad band filters Part 2 16 Transmission Transmission Transmission Brackett y filter g 5 A a a 4 p a A a a 2 14 2 15 2 16 2 17 2 18 2 19 2 20 Wavelength um H2 filter 00 80 A 6 k a 60 ui E a A a 40 u 20 00 2 08 2 10 2 12 2 14 2 18 Wavelength pm J low and J high filter 00 80 g G 4 a 60 a d E a g 8 40 4 a 20 00 1 00 1 05 1 10 1 15 1 20 1 25 1 30 1 35 1 40 1 45 1 50 Wavelength pm Fell ED468 ED468 2 1 62 1 63 1 64 1 65 1 66 1 67 Wavelength pm Hel filter 00 80 40 1 05 1 06 1 07 1 08 1 09 1 10 1 11 Wavelength um OH filters OH 1060 OH 1190 1 00 1 05 1 10 1 15 1 20 1 25 Wavelength pm Figure 12 Narrow band filter curves Part 1 17 Transmission Transmission
11. atio for one DIT 1 2 The Exposure Time Calculator 1 2 1 The Formulae This program will be used by observers for scheduling their observations with LUCI The following fixed parameters e telescope transmission light collecting area reflectivity e transmission of the instruments entrance window lenses e quantum efficiency QE of the detector and user defined parameters e object geometry spectrum magnitude e camera scale e filter e grating slit width spectroscopic mode e atmospheric conditions airmass water vapor sky background seeing e adaptive optics is loop closed Strehl ratio e exposure parameters detector integration time total exposure time e signal to noise ratio are used to calculate two auxiliary values E Tatm s Tre x Tinst Trt E QE 1 F Fo 10725 2 Fo flux density for Vega at A 550 nm Fo 3 56 1071 _ FLUX95 mag magnitude of the object QE quantum efficiency of the detector Tatm transmission of the atmosphere Tte transmission of the telescope Tint transmission of the instrument without any filter and grating Tat transmission of the filter used The number of photons that are detected per second can be calculated with 1 2 and the following formula ESO HP Table 1 Formulae for calculating the number of photons from the source Observing mode point source extended source I f N _ FA ES N _ EALESQ MASE TER P TO P ane N _ EASES
12. d LUCI 2 Both instruments are identical their detectors however have different efficien cies The efficiency curves are shown in Fig 5 Efficiency 0 8 1 0 1 2 1 4 1 6 1 8 Wavelength um LUCIFER 1 LUCIFER 2 2 0 2 2 2 4 Figure 5 The efficiency of the two LUCI detectors versus the wavelength The different detectors are color coded 1 2 10 Gratings Three gratings are installed in LUCI All of them were tested for their efficiencies by the manufacturer The company measured in a Littrow setup LUCI reaches about 90 FDR OP of the nominal efficiencies because it is not working under Littrow conditions See Appendix DGratingsappendix D for the plots and ASCII files e High Dispersion grating HD grating with 210 1 mm e H K grating with 2001 mm e Ks grating with 1501 mm 1 2 11 Water vapor in the Atmosphere The water vapor in the atmosphere is the main reason for absorbing light in the near infrared and infrared The transmission of light for three different water vapor levels in the wavelength range from 0 9 um to 2 5 um is shown in Figure 6 The transmittance of the atmosphere for 1mm 1 6mm and 3mm water vapor TRANSA is displayed In the ETC three different values for the water vapor can be selected 1 0mm 1 6mm and 3 0mm Air transmittance 1 0 1 2 1 4 1 6 1 8 2 0 2 2 2 4 Wavelength um Figure 6 Transmittance vs wavelength for three different water vapor levels 1 2 12 Airmass
13. l spectrum stellar galaxy or uniform template 2 Blackbody spectrum 3 Gaussian shaped emission line In imaging mode the stepping of the spectra is 0 5nm This stepping is adjusted to the spectral resolution in spectroscopic mode Template Spectra 6 different model spectra representing various main sequence stars are avail able These are STERNS BOV AOV FOV GOV KOV MOV Figure 2 Their flux densities are normalized to f A 550 nm 3 66 1071 Wm nm 12 In addition 4 different galaxy template spectra are available Figure 3 and GALAXS If a spectrum is allowed to be redshifted the filename must include the phrase galaxy at any position The transformed spectra are calculated by the definition of the redshift A A z o gt A z 1 13 Xo z redshift measured wavelength o rest wavelength Finally a uniform spectrum can be used The first step of creating such a spectrum constant flux density for all wavelengths is to calculate the total flux in the given band pass for a uniform spectrum with an arbitrary flux density After that the flux is calibrated to the target magnitude given by the user Blackbody Radiation The blackbody spectrum is another option that can be chosen The flux density is calculated as a function of wavelength 14 for the user defined tem perature T 1 Ad exp ais 1 Planck s constant h 6 62607 10734 Js c velocity of light c 2 9983
14. limited optical system with a real system the Strehl parameter was introduced I Strehl 8 theo This parameter is the ratio of the observed peak intensity at the detection plane of a telescope or other imaging system from a point source compared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit For calculating the fraction of the halo and core component to achieve a certain strehl ratio the parameter FO is introduced in this ETC It has to fulfill the following equation T T airy function E moffat function E Intensity in arbitrary units 0 0 4 0 3 0 2 0 1 0 0 0 1 0 2 0 3 0 4 arcsec Figure 1 Simplified description of an observed AO PSF It is built by a core Airy function and a halo Moffat function Tobs F0 Ikiry 0 1 F0 Moffat 0 9 Itheo Iairy 0 IMoffat 0 Strehl I airy 0 I Moffat 0 IAiry 0 Strehl FO 10 11 In this mode the SNR is calculated for a disk with a radius of twice the radius of the airy disk Seeing Limited Mode The PSF in this mode is approximated by a Gaussian shaped function In this case the seeing is the FWHM of this function and the SNR is calculated for a disk with a radius of the seeing 1 2 4 Objects Besides the choice of the source s size point source or extended source the observer can select one out of three different types of spectra 1 Mode
15. line BB blackbody with a temperature x R earth radius 6378 km h hight of emitting layer 100 km z zenith distance 1 2 14 Slit Width and Slit Transmission Slit Width Different slit widths between 0 25 and 2 00 can be selected If the width is smaller than the scale of the camera used the width is set to the scale of the camera Slit Transmission First of all the program calculates the number of photons reaching the slit After that it computes the number of photons behind the slit For a point like source it assumes a PSF like a Gaussian or a Moffat Airy disc The hatched area in Figure 9 is the relevant area for transmission The transmitted photons are split into the pixels 1 5 see bottom of Figure 9 For example if 18 photons 12 are passing the hatched area of the slit the light will be split up to 4 5 pixels Pixel 1 2 3 and 4 will detect 4 18 4 5 4 photons each The fifth pixel will count 2 photons 2 d 1 2 3 45 a section of one pixel line of the detector Figure 9 Top Sketch of a slit The hatched area is used to calculate the transmission of the slit The parameter d depends on the observing mode For seeing limited mode it is the FWHM of the seeing In diffraction limited mode it is the diameter of the first minimum of the airy disk Bottom The calculated photons are split into the shaded pixels 13 References ESO HP
16. ss of 1 5 SKYBA Theoretical Background Spectrum A theoretical spectrum is the last possibility for choosing a sky background This spectrum is shown in Figure 8 The fundamental parts of this calculation are the OH line database OH LIN ROUS00 and the transmission data of the atmosphere AIRTRA The ratio of intensities for two lines may change during the night or from observation to observation This is the reason why it is possibile to change the relative intensities via an ini file The predefined values are adjusted to Mauna Kea s night sky spectrum SKYBA For modeling the sky background we assume e OH line absorption due to the light travel through the atmosphere scaled with T e thermal emission of a blackbody with a temperature of 250K scaled with 1 T 11 900 1 6 mm H 0 Airmass 1 5 800 F 4 700 F 4 Photons sec nm aresec m 0 8 1 1 2 1 4 6 8 2 22 2 4 Wavelength um Figure 8 A synthetic spectrum of the sky background e zodiacal emission a blackbody spectrum T 5800 K e increasing intensity with larger zenith distances described by the van Rhijn s function Then the sky background can be described as T OH 1 T BBas0x BBsgo0x Nsky 17 Ne _ wx sin z Nsky number of photons from sky background T transmission of the atmosphere OH intensity of the OH
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