{"group":{"id":1,"name":"Community","lockable":false,"created_at":"2012-01-18T18:02:15.000Z","updated_at":"2026-04-06T14:01:22.000Z","description":"Problems submitted by members of the MATLAB Central community.","is_default":true,"created_by":161519,"badge_id":null,"featured":false,"trending":false,"solution_count_in_trending_period":0,"trending_last_calculated":"2026-04-06T00:00:00.000Z","image_id":null,"published":true,"community_created":false,"status_id":2,"is_default_group_for_player":false,"deleted_by":null,"deleted_at":null,"restored_by":null,"restored_at":null,"description_opc":null,"description_html":null,"published_at":null},"problems":[{"id":685,"title":"Image Processing 2.1.1 Planck Integral","description":"Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\r\n\r\nPlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\r\n\r\nc1'=1.88365e23; % sec^-1 cm^-2 micron^3\r\n\r\nc2=1.43879e4;  % micron K\r\n\r\nMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\r\n\r\nRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\r\n\r\nInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\r\n\r\nOutput:  4.9612 E+018  : units ph/sec/m^2/ster\r\n\r\nPerformance Rqmts: \r\n\r\nAccuracy: \u003c0.001% error\r\n\r\nTime: \u003c100 msec (using cputime function)\r\n\r\n\r\nCorollary problem will include spectral transmission and emissivity.\r\n\r\n\r\nIR Calibration Reference:\r\n\r\n\u003chttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003e","description_html":"\u003cp\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/p\u003e\u003cp\u003ePlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/p\u003e\u003cp\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/p\u003e\u003cp\u003ec2=1.43879e4;  % micron K\u003c/p\u003e\u003cp\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/p\u003e\u003cp\u003eRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\u003c/p\u003e\u003cp\u003eInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\u003c/p\u003e\u003cp\u003eOutput:  4.9612 E+018  : units ph/sec/m^2/ster\u003c/p\u003e\u003cp\u003ePerformance Rqmts:\u003c/p\u003e\u003cp\u003eAccuracy: \u0026lt;0.001% error\u003c/p\u003e\u003cp\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/p\u003e\u003cp\u003eCorollary problem will include spectral transmission and emissivity.\u003c/p\u003e\u003cp\u003eIR Calibration Reference:\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\"\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function Radiance = Calc_Radiance(Lo,Hi,T)\r\n% Lo wavelength um\r\n% Hi wavelength um\r\n% T  Blackbody Temperature (K)\r\n\r\n  Radiance = T;\r\nend","test_suite":"%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=250.0;\r\n% Radiance = 4.96124998 e18 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.96124998e18; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=300.0;\r\n% Radiance = 4.1826971 e19 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.1826971e19; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=8.0;\r\nhi=12.0;\r\nT=280.0;\r\n% Radiance = 1.37122128 e21 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 1.37122128e21; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\n\r\n% Add random to block answer writers\r\nlo=3.0+rand\r\nhi=5.0+rand\r\nT=250.0;\r\n% Radiance = To be calculated ph/m2/sec/ster\r\n\r\nc1p=1.88365e23; % sec^-1cm^-2micron^3\r\nc2=1.43879e4;  % micron K\r\nsteps=1000;\r\n\r\nx=lo:(hi-lo)/steps:hi;\r\n\r\n% Planck Vectorized for Trapz\r\ny=1e8./(x.^4.*(exp(c2./(x.*T))-1));\r\n% Leading 1e8 is for numerical processing accuracy\r\n\r\nz=trapz(x,y);\r\nrad_correct=z*1e4*c1p/pi()/1e8 % 1e4 normalizes from cm-2 to m-2\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-14T04:31:21.000Z","updated_at":"2025-12-10T03:26:46.000Z","published_at":"2012-05-14T05:39:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec2=1.43879e4; % micron K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eRadiance : L = Me/pi in units of ph sec^-1 m^-2\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eInput: (3.0 5.0 250) : From 3um to 5um at 250K\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eOutput: 4.9612 E+018 : units ph/sec/m^2/ster\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePerformance Rqmts:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eAccuracy: \u0026lt;0.001% error\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eCorollary problem will include spectral transmission and emissivity.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIR Calibration Reference:\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:hyperlink w:docLocation=\\\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\\\"\u003e\u003cw:r\u003e\u003cw:t\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:hyperlink\u003e\u003c/w:p\u003e\u003c/w:body\u003e\u003c/w:document\u003e\"},{\"partUri\":\"/matlab/output.xml\",\"contentType\":\"text/xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\" standalone=\\\"no\\\" ?\u003e\u003cembeddedOutputs\u003e\u003cmetaData\u003e\u003cevaluationState\u003emanual\u003c/evaluationState\u003e\u003clayoutState\u003ecode\u003c/layoutState\u003e\u003coutputStatus\u003eready\u003c/outputStatus\u003e\u003c/metaData\u003e\u003coutputArray type=\\\"array\\\"/\u003e\u003cregionArray type=\\\"array\\\"/\u003e\u003c/embeddedOutputs\u003e\"}]}"}],"problem_search":{"errors":[],"problems":[{"id":685,"title":"Image Processing 2.1.1 Planck Integral","description":"Integrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\r\n\r\nPlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\r\n\r\nc1'=1.88365e23; % sec^-1 cm^-2 micron^3\r\n\r\nc2=1.43879e4;  % micron K\r\n\r\nMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\r\n\r\nRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\r\n\r\nInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\r\n\r\nOutput:  4.9612 E+018  : units ph/sec/m^2/ster\r\n\r\nPerformance Rqmts: \r\n\r\nAccuracy: \u003c0.001% error\r\n\r\nTime: \u003c100 msec (using cputime function)\r\n\r\n\r\nCorollary problem will include spectral transmission and emissivity.\r\n\r\n\r\nIR Calibration Reference:\r\n\r\n\u003chttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003e","description_html":"\u003cp\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/p\u003e\u003cp\u003ePlanck  Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/p\u003e\u003cp\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/p\u003e\u003cp\u003ec2=1.43879e4;  % micron K\u003c/p\u003e\u003cp\u003eMe = integral ( Me(Lambda,T) ) at T over a range of Lambda\u003c/p\u003e\u003cp\u003eRadiance  :    L = Me/pi in units of ph sec^-1 m^-2\u003c/p\u003e\u003cp\u003eInput:  (3.0 5.0 250)  : From 3um to 5um at 250K\u003c/p\u003e\u003cp\u003eOutput:  4.9612 E+018  : units ph/sec/m^2/ster\u003c/p\u003e\u003cp\u003ePerformance Rqmts:\u003c/p\u003e\u003cp\u003eAccuracy: \u0026lt;0.001% error\u003c/p\u003e\u003cp\u003eTime: \u0026lt;100 msec (using cputime function)\u003c/p\u003e\u003cp\u003eCorollary problem will include spectral transmission and emissivity.\u003c/p\u003e\u003cp\u003eIR Calibration Reference:\u003c/p\u003e\u003cp\u003e\u003ca href=\"http://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\"\u003ehttp://austin-speaks.com/FTP/Microchip%20C/Field%20Guide%20for%20IR%20Systems%20Design.pdf\u003c/a\u003e\u003c/p\u003e","function_template":"function Radiance = Calc_Radiance(Lo,Hi,T)\r\n% Lo wavelength um\r\n% Hi wavelength um\r\n% T  Blackbody Temperature (K)\r\n\r\n  Radiance = T;\r\nend","test_suite":"%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=250.0;\r\n% Radiance = 4.96124998 e18 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.96124998e18; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=3.0;\r\nhi=5.0;\r\nT=300.0;\r\n% Radiance = 4.1826971 e19 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 4.1826971e19; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\nlo=8.0;\r\nhi=12.0;\r\nT=280.0;\r\n% Radiance = 1.37122128 e21 ph/m2/sec/ster\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\nrad_correct = 1.37122128e21; % ph/m2/sec/ster\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))\r\n%%\r\n% Input: BB Temp, Lo Wavelength, Hi Wavelength, Integration steps\r\n% Output radiance in ph/m2/sec/ster\r\n% Nominal steps of 1000 yields accuracy and timeliness\r\n\r\n% Add random to block answer writers\r\nlo=3.0+rand\r\nhi=5.0+rand\r\nT=250.0;\r\n% Radiance = To be calculated ph/m2/sec/ster\r\n\r\nc1p=1.88365e23; % sec^-1cm^-2micron^3\r\nc2=1.43879e4;  % micron K\r\nsteps=1000;\r\n\r\nx=lo:(hi-lo)/steps:hi;\r\n\r\n% Planck Vectorized for Trapz\r\ny=1e8./(x.^4.*(exp(c2./(x.*T))-1));\r\n% Leading 1e8 is for numerical processing accuracy\r\n\r\nz=trapz(x,y);\r\nrad_correct=z*1e4*c1p/pi()/1e8 % 1e4 normalizes from cm-2 to m-2\r\n\r\nts=cputime;\r\nrad_entry=Calc_Radiance(lo,hi,T)\r\ntc=cputime;\r\ndt=1000*(tc-ts) % Processing Time in ms\r\n\r\ntol=.00001;\r\nPass=rad_entry\u003erad_correct*(1- tol) \u0026 rad_entry\u003crad_correct*(1+ tol) \u0026 dt\u003c100;\r\n\r\nassert(isequal(Pass,1))","published":true,"deleted":false,"likes_count":1,"comments_count":0,"created_by":3097,"edited_by":null,"edited_at":null,"deleted_by":null,"deleted_at":null,"solvers_count":11,"test_suite_updated_at":null,"rescore_all_solutions":false,"group_id":1,"created_at":"2012-05-14T04:31:21.000Z","updated_at":"2025-12-10T03:26:46.000Z","published_at":"2012-05-14T05:39:19.000Z","restored_at":null,"restored_by":null,"spam":false,"simulink":false,"admin_reviewed":false,"description_opc":"{\"relationships\":[{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/document\",\"targetMode\":\"\",\"relationshipId\":\"rId1\",\"target\":\"/matlab/document.xml\"},{\"relationshipType\":\"http://schemas.mathworks.com/matlab/code/2013/relationships/output\",\"targetMode\":\"\",\"relationshipId\":\"rId2\",\"target\":\"/matlab/output.xml\"}],\"parts\":[{\"partUri\":\"/matlab/document.xml\",\"relationship\":[],\"contentType\":\"application/vnd.mathworks.matlab.code.document+xml\",\"content\":\"\u003c?xml version=\\\"1.0\\\" encoding=\\\"UTF-8\\\"?\u003e\\n\u003cw:document xmlns:w=\\\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\\\"\u003e\u003cw:body\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003eIntegrate the Planck function in Lambda (um) at T (K) accurately and quickly to find Radiance for a Lambertian source.\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ePlanck Me(Lambda,T) =c1'/Lambda^4/(e^(c2/(Lambda*T))-1) ph sec^-1 cm^-2 um^-1\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle w:val=\\\"text\\\"/\u003e\u003c/w:pPr\u003e\u003cw:r\u003e\u003cw:t\u003ec1'=1.88365e23; % sec^-1 cm^-2 micron^3\u003c/w:t\u003e\u003c/w:r\u003e\u003c/w:p\u003e\u003cw:p\u003e\u003cw:pPr\u003e\u003cw:pStyle 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