DORT2002 version 2.0 User Manual
Contents
1. A ERF Tryckteknisk Forskning DORT2002 version 2 0 User Manual Per Edstr m Marcus Lehto Mid Sweden University FSCN Report ISSN 1650 5387 2003 18 Internal FSCN Report Number R 03 43 April 2003 OGS 4 to amp l 3 my yY Z Mid Sweden University Fibre Science and Communication Network SE 851 70 Sundsvall Sweden Internet http www mh se fscn FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 2 25 Contents Page ABSTRAC Trunan a e a teensex 3 TEN TROD UC TION rs cctevcc ea tesee ecto a ices debecs ec tacos atone oes e eee 4 De MINS TIN oa vores ces co cecece Sococeen sees besten cuecenccuaceet teveutescesteneuaGacutes Lenccecencceasheseetences 5 2 1 SYSTEM REQUIREMENT runana Ee E E ls oe Gu a cewek 5 ZZ INSTAL ATION noaa a a O 5 2d SETTING S TARI PDanna A ecttabiadeehns atlas 5 3 DORT2002 GRAPHICAL USER INTERFACE eeesesesseesssesssesssesssesssesssesssesssesoe 6 SAGE TENG STARTE D aa EE 6 3 2 PFRFORMING SIMULA ON Sruntararnn t a ake a dauenaenakoetaawsee 7 3a Domda RRR E E E E nme eer en 7 AE E E A OA AE NE EAE A OA E A Dil Ds CUCUA On SENE SE EE EE E ia seiesdapseataeetesieadaetuadeeds 8 Be LOMO OIONS ooi E vinden car E T E Ms ned crac eto usudesdinn 9 2 OUIDUL CODUIONS criti cgeh een elisa nicl aaah toa liven heres aaaehan eda to 10 DDO COI CI OC asi arts hers steals iciaa es dost Sas Sata a AA des aaae Sac eeate tae a a tsalaa deat 10 DD J SAVE2. the output can still be retrieved inside the current MATLAB workspace see section 3 2 10 3 2 6 Calculate When all input parameter fields are filled in press the Calculate button or choose Calculate from the File menu If the parameters are valid the simulation will be performed and the desired output will be generated If any of the parameters defined are invalid an error message will be shown and the parameter must be changed accordingly A note for Windows platforms When a parameter field has been edited the new value visible on the screen will not be read into the application until the user clicks a button clicks the background of the Graphical User Interface or presses Return It is not read into the application when clicking on the menu bar This means that editing a parameter field and directly choosing Calculate from the File menu will cause the old parameter value to be used although it has been edited To be sure to always use the new parameter value the user should either use the Calculate button or always click outside the parameter field or press Return before choosing Calculate from the File menu This unfortunate behavior is consistent with the Microsoft Windows platform conventions and is not an error in DORT2002 On UNIX systems clicking on the menu bar will cause the parameter to be read so this problem does not exist there FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se
3. 3 2 Creating Parameter Files in the MATLAB Command Window A parameter file for the DORT2002 Graphical User Interface is simply a MAT file containing a struct named parameters which contains specified fields The field names and their ranges are given in Appendix A Parameter files can be created outside the Graphical User Interface This can be done using the default_parameters m script file as a template It is always possible to save FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 13 25 any changed parameter set specified in an m file into a MAT file The following example shows how to save the parameters defined in my_parameters m into the file filename mat parameters my_parameters save filename mat parameters 3 3 3 Opening Parameter Files A predefined parameter file is opened by choosing Open parameter file from the File menu If the parameters included in the chosen file are valid as they must be 1f they were saved from the Graphical User Interface the parameters will be extracted otherwise an error message will appear on the screen 3 3 4 Creating Phase Function Library Files A phase function library file is a file containing phase function moments for any phase function to be used in DORT2002 calculations The phase function moments are coefficients of the Legendre polynomial expansion of the phase function and have to be supplied by the user This
4. Internet http www mh se fscn Page 15 25 4 Running DORT2002 from the MATLAB Command Window 4 1 Input When calling DORT2002 from the MATLAB Command Window a complete input parameter struct must be provided as input If not the missing input parameter fields will be set to default during the calculation When creating an input parameter struct the file default_parameters m can be used as a template The input parameters and their ranges are given in Appendix A 4 2 Output The output is returned in a variable as from any MATLAB function result dort2002 parameters The output is a struct containing the desired output fields as defined in the input parameters The fields in the result struct are described in Appendix C The output can also be saved directly as defined in the input parameters in a formatted text file a binary MATLAB file or both FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 16 25 5 Notes on Some Advanced Features 5 1 The N Method and Intensity Correction Procedures To maintain accuracy without a tremendously increased computational burden for cases with strongly forward peaked phase functions the so called 6 N method is used in DORT2002 together with single and second order scattering correction procedures the TMS and IMS methods The intensity correction procedures uses in a special way a larger number of phase function moments than in
5. RESUS METILO ncssaivtencescopssnatuandciscusdcatennaaviinestetsiccuddscsbesesoiiceitassieesesweseeusis Il De 5 CN CAI ssa sk uk hae ana shams ated eae ees ts assests che Il FeO EN cde asta Sade sneaanag aa e a hacen dsiot elaine ean eeabsee aes Il 3 2 10 Interaction with the MATLAB Command Window ccccccccccceeecceeeceeueees Il 33 MANAGING PARAMETER FIE Secene EET came E AES 12 IIe DAVIN TF ONAMNCUCl L O EEEE EEE T E EN 12 3 3 2 Creating Parameter Files in the MATLAB Command Window 12 JIo DCNINS T arameAler T US arn ea a a a oleh tat eebasehse 13 3 3 4 Creating Phase Function Library Files cccccccccccccccccccccscceeeeee esse stteeeseeees 13 4 RUNNING DORT2002 FROM THE MATLAB COMMAND WINDOW 15 NPU ceia aa ait a a ntaleaa eee ataboeiee aes 15 AED OUTPUT nenn a E AEEA E ASG 15 5 NOTES ON SOME ADVANCED FEATURES seeosseossoossosssosssssscossesssesssessseo 16 5 1 THE N METHOD AND INTENSITY CORRECTION PROCEDURES 0000eeeeeee0 16 3 2 BREAKING THF ZIM THA DOORS arrori in r EERE ETA 16 6 AC KNOW LEDGE MENTS sasacessgeccesedccatecsssceectasietcecissiccees deen tines cisecteicaciccis ea CONi oat 18 APPENDIX A THE DORT2002 PARAMETER STRUCT cssssccsssseeeeees 19 APPENDIX B THE DORT2002 PLOT OPTIONS csscosssccssscccscsccssccceecees 22 APPENDIX C THE DORT2002 RESULT STRUCT cccsscccssccccsccsceeeees 24 REFERENCES rer E E 25 FSC
6. all components are properly installed that the MATLAB current directory or search path is set to the folder containing all your DORT2002 files and that the MATLAB version used is version 6 5 or higher To get further help choose Help from the Help menu to open this manual FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 7 25 3 2 Performing Simulations When a DORT2002 simulation is to be performed all parameter fields in figure 1 must be given manually or by opening a predefined parameter file see section 3 3 3 The ranges of the input parameters are given in Appendix A Note that the fields Beam polar angle cosine Beam azimuthal angle Output depth s Output polar angle cosine s and Output azimuthal angle s can be filled in using MATLAB expressions This makes it possible to use MATLAB variables and functions such as pi and cos The fields requiring vector input must be defined using MATLAB vector expressions 3 2 1 Boundary Conditions The upper boundary conditions to be defined are the incident illumination e g any incident diffuse intensity and the direction and intensity of any incident beam At the lower boundary the bottom surface type has to be defined Note that the bottom surface is not the lower surface of the medium but the surface of the underlying medium There are two optional types of the underlying surface a perfectly diffuse surface or no surface If a diff
7. calls the command line version of DORT2002 in the background Most users will prefer the Graphical User Interface since it is so convenient However advanced users may prefer the direct control of all parameters from the command line and the possibility to use DORT2002 as a component in scripts or larger applications 3 1 Getting Started The DORT2002 Graphical User Interface is started by executing the dort2002interface p script in MATLAB When executed the main window will appear on the screen see figure 1 i DORT 2002 Graphical User Interface oa F E oj xi File Help Upper Boundary Conditions Dittuse intensity Beam intensity Beam polar angle cosine Beam azimuthal angle Depth at upper boundan Lower Boundary Conditions amp Diffuse surface No surface Surface reflectance Depth at lower boundary Layer Properties Calculation Settings Half number of channels M3 Output depths Output polar angle cosines Output azimuthal angles Maximum relative error Flot Option E Mean BSOF cume BSOF 3D 1 Fourier mesh fw azimuthal mesh azimuthal 3D jpo AT Output Options B Total reflectance Total transmittance Total absorptance Mean BSDF BSOoF Fourier components jv l azimuthal components E Beam remainder m Sawe results in file Calculate Clear Exit Figure 1 The DORT2002 Graphical User Interface If it does not start check that
8. can be done by separate calculation or by looking up in a table The phase function file itself is simply a MAT file containing a struct phase_function_moments which contains one or more fields with different phase function moments Each field must be a row vector containing the phase function moments ordered by index in ascending order The following example shows how to create a phase function library file containing phase function moments for the Henyey Greenstein phase function with six different asymmetry factors and a Haze L phase function with a specific asymmetry factor The row vectors containing the phase function moments denoted r1 r7 are assumed to be generated previously The struct is generated field by field phase_function_moments henyey_greenstein_gO0p5 rl phase_function_moments henyey_greenstein_gOp9 r2 phase_function_moments henyey_greenstein_gOpO r3 phase_function_moments henyey_greenstein_gm0p9 r phase_function_moments henyey_greenstein_gO0p95 r phase_function_moments henyey_greenstein_gOp r6 phase_function_moments haze_L_gO0p8042 Baw aie This gives a MATLAB struct with fieldnames henyey_greenstein_g0p5 henyey_greenstein g0p9 henyey_greenstein_g0p0 henyey_greenstein_gm0p9 henyey_greenstein g0p95 henyey_greenstein_g0p7 and haze L g0p8042 For simplicity the fieldnames should be chosen such that they give information of which phase function is used and the value of the asymmetry factor A
9. graphs_I_ac_3d_fig Figure number s Save options Simulation_name Name of simulation Ssave_results 0 do not save 1 save output in MAT file Name of MAT file save _results text 0 do not save 1 save output in TXT file Name of TXT file Table 3 Parameters for controlling the output FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 22 25 Appendix B The DORT2002 Plot Options The following table describes the plot options Plot Option Mean BSDF curve 2D plot of the azimuthally a o averaged Bidirectional Scattering Distribution Function BSDF jODSHS LAAS POER The upper curve is the azimuthally averaged BRDF and the lower curve 1s the azimuthally averaged BTDF 3D Plot of the Bidirectional EET File Edit View Insert Tools Window Help Scattering Distribution JDSUSIKAAS Per Function BSDF DORT2002 BSDF The distribution plotted in the positive hemisphere is the BRDF and the _ ae distribution plotted in the wy TELE Sh negative hemisphere is the cae Se BTDF i Wises Sy TV Mute AM A we SUNNY y NN W A FSCN Systems Analysis and Mathematical Modeling Internet http www mh se fscn I Fourier mesh The Fourier component distribution of the intensity as a surface plot I azimuthal mesh Surface plot of the azimuthal components of the intensity 1 e the intensity at the user defined polar angle cosine
10. MATLAB struct of this kind can also be generated using the MATLAB struct command see MATLAB help for more information The phase function library file is then created using the MATLAB save command save filename mat phase_function_moments FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 14 25 The saved phase function library file can then be opened in the Graphical User Interface and the field containing the wanted phase function moments can easily be selected see figure 7 eM x Layer Properties Layer thickness Scattering coeficient Absorption coefficient Phase Function Type Henyey Greenstein jw Predefined phase moments Henvey Greenstein asmmetotactor Phase function moments from filer henyey_greenstein_gOp Fhase function library file thenyey greenstein g0ps jhenyey_greenstein_g0po w n b files phase functio Renren a aneen atipo henyey greenstein_gmOpo henyey greenstein_gOpys henyey greenstein_gOp ok haze L_ goOpso4e Number of phase function moments Figure 7 The window for defining layer properties when using predefined phase function moments Note that the user is responsible for the validity of the phase function moments saved in this manner Therefore only users familiar with how phase function moments for a specific phase function are generated should use this option FSCN Systems Analysis and Mathematical Modeling R 03 43
11. N Systems Analysis and Mathematical Modeling Internet http www mh se fscn R 03 43 Page 3 25 OKO gt 7 gt SMHOKH MATEMATISK MODELLERING DORT2002 version 2 0 User Manual Per Edstrom Marcus Lehto Mid Sweden University S 871 88 Harnosand Abstract The DORT2002 software is a fast and accurate tool for solving radiative transfer problems in vertically inhomogeneous turbid media using a discrete ordinate model geometry DORT2002 is implemented in MATLAB and is adapted to light scattering simulations in paper and print The DORT2002 Graphical User Interface is a tool developed to provide users with a fast and easy way of performing DORT2002 simulations It works as a shell that encapsulates the parameters and the function calls and offers powerful simulations through a mouse click This report gives a thorough description of how to install and use DORT2002 version 2 0 and the Graphical User Interface FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 4 25 1 Introduction DORT2002 is a numerical implementation of a discrete ordinate solution method for the radiative transfer problem in vertically inhomogeneous turbid media The model is based on papers by Edstrom 1 and Edstrom and Lehto 2 which are recommended for those who whish to get a thorough understanding of the model and its features DORT2002 has been developed during the past year and is now a fast and accurat
12. always be added by pressing the Add button 3 2 3 Calculation Settings The Calculation Settings fields found in figure 4 specify the accuracy of the calculation for which depths and angles the results should be calculated and any convergence criterion of the simulation FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 9 25 Calculation Settings Half number of channels HY oo 0 Output depths fo 0 0025 0 005 Output polar angle cosines OF 0 1 0 15 0 2 0 25 0 3 0 35 0e Output azimuthal anglesi D 0 15708 0 31416 0 47124 0 628 Maximum relative error Booo Figure 4 The Calculation Settings frame Since understanding of the calculation settings is crucial for the user these parameters are described more in detail below The parameter Half number of channels N specifies the number of channels a feature of the discrete ordinate model geometry and a parameter of the core calculations A low number of channels decreases the accuracy of the results but gives faster calculations A larger number of channels increase both accuracy and calculation time In order to make efficient simulations the user should be aware of approximately how many channels that are needed in a specific calculation Performance tests show that DORT2002 converges for N 15 20 in most cases This means that a larger number of channels would not increase the accuracy of the results since the
13. e tool for light scattering simulations in paper and print applications The light scattering simulations can be performed using a Graphical User Interface which makes the simulations convenient and accessible It 1s also possible to call DORT2002 directly from the MATLAB Command Window which may be preferred by the experienced user Finally it is possible to embed DORT2002 as a component in a script or a larger application This report is a user manual for DORT2002 version 2 0 and focuses on how to use DORT2002 software rather than describing the theories and implementation in detail Furthermore the main focus is on the usage of the DORT2002 Graphical User Interface since the command line calls are mainly for advanced users with a basic knowledge of MATLAB function calls Section gives references and some general information section 2 describes how to install DORT2002 sections 3 and 4 describe how to use DORT2002 via the Graphical User Interface and from the MATLAB Command Window respectively and section 5 briefly describes some more advanced features included in DORT2002 Tables of the parameter and result structs are given in appendices together with a description of the plot options FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 5 25 2 Installation 2 1 System Requirements Version 2 0 of DORT2002 requires the following from your system e Microsoft Windows 98 original or S
14. e_moments User defined phase N_layers X 1 cell array of moments vectors size 1 lt N and or reals KK N_phase_moments Number of phase moments Vector of positive integers in used in intensity correction 2N 1 600 size procedures IxN_layers phase_moments_check Automatic check for how 0 No phase moments check many phase moments to be 1 Phase moments check used for maximum accuracy layer_thickness Sub layer thickness Vector of positive reals size IxN_layers Table 1 Parameters for characterizing the simulated medium If field TSR_type is set to 1 user must define the surface reflectance rho_n Setting parameter field phase_type to user defined for a certain layer allows the user to define other phase functions than Henyey Greenstein more suitable for the case at hand If so the phase function moments have to be specified If Henyey Greenstein phase function is to be used phase_type should be set to Henyey Greenstein for the specific layer and the asymmetry factor specified in phase_moments FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 20 25 __ Fieldname Description Ramge Calculation Half number of channels Settings N_depths Number of calculation Positive integer depths depth Output depth s Vector of reals in top_depth bottom_depth size N_depths xl N_interpol Number of output polar Positive integer angle cosines mu_interpol Output polar ang
15. econd Edition Windows Millennium Edition ME Windows NT 4 0 Windows 2000 or Windows XP e MATLAB 6 5 e See also the MATLAB system requirements 2 2 Installation DORT2002 is packaged in a zip file containing the software this manual help files and reports on the theory behind the solution method To install DORT2002 extract the zip file into a folder on the target computer Note that all files must be extracted into the same folder 2 3 Getting Started The DORT2002 software can only be used ina MATLAB environment Therefore MATLAB has to be opened before using DORT2002 To access DORT2002 the MATLAB current directory must be changed to the directory containing the DORT2002 files or the directory of the DORT2002 files must be added to the MATLAB search path The DORT2002 simulations can be performed in two ways either through the Graphical User Interface by executing the dort2002interface p script see section 3 or directly from the MATLAB Command Window by executing the dort2002 p script see section 4 FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 6 25 3 DORT2002 Graphical User Interface The DORT2002 Graphical User Interface is a tool developed to provide users with a fast and easy way of performing DORT2002 simulations It works as a shell that encapsulates the parameters and the function calls and offers powerful simulations through a mouse click The interface
16. ed in It is only possible to save a full and valid set of parameters The parameters and their valid ranges are given in Appendix A The parameter file is saved by choosing Save parameter file as from the File menu and defining the target directory and filename The input parameters are checked to avoid input errors and error messages are displayed if any invalid parameters are found The result MAT files stored in previous simulations can also be used as parameter files since the result files also contain the input parameters A note for Windows platforms When a parameter field has been edited the new value visible on the screen will not be read into the application until the user clicks a button clicks the background of the Graphical User Interface or presses Return It is not read into the application when clicking on the menu bar This means that editing a parameter field and directly choosing Save parameter file as from the File menu will cause the old parameter value to be used although it has been edited To be sure to always use the new parameter value the user should always click outside the parameter field or press Return before choosing Save parameter file as from the File menu This unfortunate behavior 1s consistent with the Microsoft Windows platform conventions and is not an error in DORT2002 On UNIX systems clicking on the menu bar will cause the parameter to be read so this problem does not exist there 3
17. et to zero the calculations will be performed using maximum possible accuracy If the full accuracy is not needed a choice of lower maximum relative error will give a significant decrease in computation time in most cases This parameter should however be used with caution see section 5 2 3 2 4 Plot Options DORT2002 offers to present the results in various plots which can be selected in the Plot Options frame see figure 5 FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 10 25 Plot Option E Mean BSOF cume Jw BSDF 3D figure 1 E l Fourier mesh fw l azimuthal mesh figure 2 4 J azimuthal 30 figure s 5 7 Figure 5 The Plot Options frame showing figure numbers for desired plots More detailed information on the different plot options is given in Appendix B When the simulation is carried out the figures numbers of any generated plots will be displayed in the Plot Options frame The figure numbers for each plot are given in ascending order of calculation depths 1 e the lowest figure number corresponds to the smallest calculation depth etc 3 2 5 Output Options The output options define which results to be calculated and returned as output from the simulation More detailed information on the fields in the result struct is given in Appendix C To save the requested output in a file the Save results in file option must be selected see figure 1 If it is not selected
18. ex The azimuthal components of the intensity at the user defined polar angle cosines and azimuthal angles at depths defined by depth depth_index beam_ depth_index Remainder of the incident beam at depths defined by depth depth_index Table 5 The fields in the result struct FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 25 25 References 1 2 P Edstr m Fast and Stable Solution Method for Angle Resolved Light Scattering Simulation FSCN Report ISSN 1650 5387 2002 12 Internal FSCN Report Number R 02 35 Mid Sweden University 2002 P Edstr m and M Lehto Fast and Stable Solution Method for Angle Resolved Light Scattering Simulation II Model Enhancements FSCN Report ISSN 1650 5387 2003 17 Internal FSCN Report Number R 03 42 Mid Sweden University 2003
19. fscn Page 11 25 3 2 Save Results in File If the Save results in file option is selected the Save output file s dialog window is opened see figure 6 Save output file s F a oj x Hame of simulation Matlab CMATI result file a Bronge Texti TAT result file PO Browse OK Cancel Figure 6 The window for saving output files It is there possible to choose whether to save the results in a formatted text file in a binary MATLAB file or both The target directory and filename of the result file s are defined using the Browse button s Leaving any of the fields Matlab MAT result file and Text TXT result file empty results in no file saving of that file type 3 2 8 Clear Pressing the Clear button or choosing Clear from the File menu erases all fields in the main window This makes it easy to start from scratch If a parameter file is opened the fields are cleared but the parameter file is unchanged 3 2 9 Exit Pressing the Exit button or choosing Exit from the File menu exits the DORT2002 Graphical User Interface 3 2 10 Interaction with the MATLAB Command Window There are two ways to retrieve the output from a calculation done in the Graphical User Interface into the current MATLAB workspace One way 1s to load a MATLAB result file MAT from a previous calculation However it is also possible to retrieve the DORT2002 output in the MATLAB Command Window without at all saving
20. ldnames defining the phase function moments included in the opened file will be shown in the Phase function moments pop up menu and the wanted field can be selected See section 3 3 4 for more information about phase function library files The parameter field Number of phase moments specifies the number of phase moments to be used in the intensity correction procedures If left empty the number of phase moments will be set automatically for a high accuracy See section 5 1 for more information on the intensity correction procedures When all parameter fields are filled in press OK to return to the main window or press More layers to define properties for the next layer The layer properties are displayed in the Layer Properties list box see figure 3 and are updated for every new layer defined Layer Properties 1 thickness 0 00500 sigma_s 100 000 sigma_a 10 0000 g 0 70000 N mom 41 2 thickness 0 00100 sigma_s 90 0000 sigma_a 20 0000 Phase function henyey_gree 4 thickness 0 00100 Figure 3 The Layer Properties list box The defined layer properties can be edited by selecting the layer to edit and pressing the Edit button The Add Layer s dialog window then appears with the chosen layer properties filled in After editing press OK and the updated layer properties will be displayed in the Layer Properties list box Any layer can be deleted by selecting the specific layer and pressing Delete More layers can
21. le Vector of reals in 0 1 size cosine s Ne Amir ero oleh phi interpol Output azimuthal angle s Vector of reals in 0 27 azimuthal pbreak Use azimuthal break 0 Do not use algorithm 1 Use azimuthal break algorithm aore Vie Convergence criterion Positive real in 0 0 2 Max relative error in intensity calculations parameter_check Internal parameter check 0 do not check parameters in DORT2002 1 check parameters Table 2 Parameters for controlling the calculation settings Should be used with caution See section 5 2 FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 21 25 o i Fieldname si Description o o Output options 0 no calculation calculation intensity at desired depth s results I a Azimuthal distribution of the intensity at desired depth s results _beam Remainder of the incident beam at desired depth s Plot options Plot of azimuthally averaged BSDF 2D curve 0 no plot Figure number s 1 plot BSDF plot 3D plot graphs_BSDF_fig Figure number s Figure numbers graphs_I_ftc_mesh Fourier components of the intensity visualized in mesh plot Range Vector of graphs_I_fc_mesh_fig Figure number s R graphs_I_ac_ mesh Azimuthal components of the intensity S ze IN_aepthsx 1 visualized in mesh plot graphs_I_ac_mesh_fig Figure number s graphs_I_ac_3d Azimuthal components of the intensity visualized in 3D plot
22. rameters if the user states nothing else This means that the maximum number of Fourier components of the intensity will be calculated at all times limited only by the number of channels specified by the user These calculations can be very time consuming and often unnecessary since the intensity often converges far earlier Therefore the user has the opportunity to specify a maximum relative error allowed for the intensity as a convergence criterion for the azimuthal loop over Fourier components 1 e the calculations will continue until the convergence criterion is met or until the maximum possible precision is reached dependent of the specified number of channels Since the azimuthal loop is the outermost loop in the calculations much 1s gained if it can be terminated earlier The method is based on an ad hoc assumption that the Fourier components of the intensity are approximately exponentially decreasing It is an engineering method based on experimental numerical studies of the Fourier components that makes DORT2002 far more efficient The method does not stand on a solid scientific ground The FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 17 25 algorithm has been carefully tested under a wide range of conditions and has proven to be valid for all tested single layer cases However there is no guarantee that it will be valid for all possible single layer simulations There is no way to as
23. results already are fully accurate within the DORT model geometry but the calculation time would still increase The choice of N thus affects the accuracy and calculation time but it has nothing to do with the angular resolution of the results The parameters Output depth s Output polar angle cosine s and Output azimuthal angle s specify for which depths and for which polar and azimuthal angles the results are to be calculated Depending on the chosen plot and output options some or all of these properties do not need to be defined Output depth s only affects intensity and beam Output azimuthal angle s only affects BSDF and intensity and Output polar angle cosine s affects mean BSDF BSDF and intensity The parameter fields needed for the chosen plot and output options are therefore marked with an asterisk see figure 4 This only applies to these three parameter fields and no other parameter fields in the Graphical User Interface Note that the user supplied output depths polar and azimuthal angles are entirely decoupled from the predefined channels in the core calculations and a high angular resolution does not require a large number of channels In fact it is one of the main features of DORT2002 to offer high accuracy and resolution at a small number of channels thus giving a large decrease in computation time The parameter field Maximum relative error specifies the convergence criterion of a given calculation If left blank or s
24. s and azimuthal angles I azimuthal 3D 3D plot of the angular distribution of the intensity in Cartesian coordinates Table 4 Description of the plot options R 03 43 Page 23 25 Figure No 4 ls xj File Edit view Insert Tools Window Help Densa raans AES Fourier components of the intensity Intensity 20 Fourier component number Cosine of polar angle LS lx File Edit Yiew Insert Tools Window Help D na taar PH Azimuthal components of the intensity E EEE a N Sr a Age Ga oO Cc w c ENN Hh Hh Ay re bY ee er i Hi Mi 9 i ONN Ne Me Me Ht i i i af 0 R Mj f Azimuthal angle Cosine of polar angle Figure No 5 File Edit view Insert Tools Window Help JOSH S KAAS PER Angular distribution of the intensity LOK ae th Hi S fF SO 5 tr lige HER UEA P fii fj tit A Gilt FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 24 25 Appendix C The DORT2002 Result Struct The following table describes the fields of the result struct _ Fieldname Description __ S Output Variables the medium through the medium medium Azimuthally averaged BSDF Bidirectional Scattering Distribution Function Te VAS OE nex The Fourier components of the intensity at the user defined polar angle cosines at depths defined by depth depth_index Lac depinuind
25. sure that the assumption of exponentially decreasing terms is valid or even reasonable in the infinity of combinations of optical properties that are possible to create Some multi layer cases give bad results The user should be aware of this and it is also possible to turn off this feature if there is any doubt that it yields bad results in a particular case FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 18 25 6 Acknowledgements This report was supported by T2F TryckTeknisk Forskning a Swedish printing research program which 1s gratefully acknowledged FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 19 25 Appendix A The DORT2002 Parameter Struct The following tables show the fields in the DORT2002 parameter struct by category Fieldname Description Range _ _ _ Upper Iin Diffuse intensity Vector of positive reals size Boundary Nx Conditions Positive real Lower TSR_type Bottom surface type 1 Diffuse surface Boundary 2 No surface Conditions Bottom surface reflectance Real in 0 1 bOLTOM_ depth Depth at lower boundary Positive real gt top_depth Layer Number of layers Positive integer Properties Sigma_s Scattering coefficient s Vector of non negative reals size 1xN_layers IxN_layers phase type Phase function type Vector of 1 or 2 size 1x N_layers 1 Henyey Greenstein 2 User defined phas
26. the core calculations The field N_ phase_moments in the parameter struct sets the number of phase moments to be used in the intensity correction procedures In the Graphical User Interface it is set through the Number of phase moments field in the Add Layer s dialog window If the Number of phase moments field is left empty in the Graphical User Interface or if the field phase_moments_check is set to 1 in the input struct the number of phase moments will be set automatically for a high accuracy It is possible to set it to a lower number to get faster computations when a lower accuracy is acceptable An unnecessary large number will give slower computations without higher accuracy The user who chooses to set this parameter should be aware of how many phase function moments are needed for different phase functions for desired accuracy since this number is strongly varying for different types of phase functions and asymmetry factors The N method combined with the TMS IMS methods gives maintained accuracy for cases with strongly forward peaked phase functions for considerably lower number of channels than would have been the case without these features This of course gives rise to a significant performance improvement See 2 for a detailed description of the 6 N method and the intensity correction procedures 9 2 Breaking the Azimuthal Loop The DORT2002 calculations are always made using highest possible accuracy for any given input pa
27. the results to a file The results of each DORT2002 simulation carried out using the Graphical User Interface are stored in the global variable dort 2002 output To get access to that variable the variable must be declared as global in the current workspace This is done using the following expression global dort2002_output The struct dort 2002_output containing the chosen output can then be used inside the current MATLAB workspace Note that the variable dort 2002 output is FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 12 25 renewed for every calculation e g only the results of the latest simulation are found in the variable If DORT2002 is used without the graphical user interface the output is returned in a variable as from any MATLAB function result dort2002 parameters 3 3 Managing Parameter Files Filling in all parameter fields manually for every simulation to be performed using the Graphical User Interface is quite time consuming Therefore there is a possibility for the user to save parameter files for later use The parameters saved in a parameter MAT file can later be opened in the interface and can for example be used as a template for new simulations or when redoing a specific simulation It is always possible to save any changed parameters to a new parameter file 3 3 1 Saving Parameter Files When saving a parameter file all parameters fields must be fill
28. use underlying surface is selected the total surface reflectance of that surface must be defined 3 2 2 Layer Properties Adding new layers and setting their properties 1s carried out by pressing the Add button in the main window This activates the Add Layer s dialog window shown in figure 2 x Layer Properties Layer thickness Scattering coefficient Absorption coefficient Phase Function Type Iw Henyey Greenstein Predefined phase moments Henyey Greenstein asymmetry factor jar Phase Tunction moment trom tiles Hone Phase tinction libram tile Bronse Number of phase function moments Cancel hore layers Figure 2 The window for defining layer properties FSCN Systems Analysis and Mathematical Modeling R 03 43 Internet http www mh se fscn Page 8 25 The first three fields in figure 2 define thickness scattering coefficient and absorption coefficient of the given layer The DORT2002 software handles all types of phase functions but only Henyey Greenstein phase function moments are generated internally Therefore the phase function moments have to be supplied for any other phase functions to be used while only the asymmetry factor needs to be supplied for the Henyey Greenstein case If other phase functions than Henyey Greenstein are to be used choose the Predefined phase moments alternative and open the phase function library file containing the desired phase function moments The fie
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