Scattering Analysis UsingBSDF Data andLightTools provides several waysofusing measured BSDF data andLightTools Scatter Modelsthe ability to direct the scatter fromNormal Incidencea particular surface towards anaperture.These options are0.9important when performing manytypes of scattering analysis,such0.80.7as stray-light analysis.This paper06-Lambertianwill describe the process of-CosNth (N=2)0.5performing a typical stray-light04Gaussian(Sigma =15)analysis in LightTools.User-Defined0.30.2Scatter Models0.1There are several models inLightTools that can be used to-90-60-300306090model the scattering characteristicsScatter Angle (degrees)of a surface.Scattering modelswill split an incident ray into oneFigure 1.Examples of scatter model profiles in LightToolsor more transmitted or reflected (orboth)rays,and assign thedirections and amplitudes of thepreserved when a scatterer is shiftwhere o is the standard deviationscattered rays according to aInvariant.of the gaussian energy distribution.mathematical formula.Mostscatter models can operate in shift-The choices of scattering modelsElliptical Gaussian:A general-invariant mode,which means theirin LightTools are:purpose scattering model whichscattered energy distributions are acan be used to model surfaces withfunction of the shift-invariantLambertian:A model of aanisotropic scattering distributions.scatter angle 0,which is definedperfectly diffuse surface.such as brushed metal surfaces andaslight shaping diffusers.BSDF()=constantBSDF()=CosNth:A general-purposescattering model.where 0,is the angle of incidencefrom the surface normal and 0,iswhere is the azimuthal scatteringthe scatter angle.Shift-invarianceangle,and ox and o,are theimplies that the shape of thestandard deviations of the gaussianscattered energy distribution doesGaussian:A general-purposeenergy distribution along thenot change in direction-cosinesurface x and y axes,respectively.space with angle of incidence,andis the result of treating theUser-defined:Uses measuredscattering surface as a linearBSDF(0,)=eBSDF data directly to define thesuperposition of diffraction22model.Linear interpolation isgratings[1].Reciprocity is alsoBSDF To Elliptical Gaussian Converterthe data to one of theis very general and can be fit wellto typical scatter distributions.Inmodels.The simplestaddition,the Elliptical GaussianBrowse..way to do this is to usemodel is anisotropic,so it can beCancelthe User-Definedused to model scattering from suchscatter model.Thesurfaces as a brushed-metalmeasured BSDF datasurface,which can have acan be used directly toscattering distribution function thatcreate the model,andvaries with both the elevationDffuse Component0.0000the program will thenscatter angle 0 and the azimuthinterpolate byscatter angle o.The Excel macro0.0000performing a linear fitis executed using the dialog box0.0000between adjacent datashown in Figure 2.This dialog boxpoints.This methodChi-squared error0.0000takes as input the name of the fileworks best when youthat contains the BSDF data.TheFigure 2.Dialog box interface for the Excel BSDFhave a lot of dataMacromacro accepts BSDF data files inpoints,and can only beASTM format,which is a standardused if the distributionformat used for reporting BSDFperformed between adjacent dataof scattered energy isdata [2].Once the data is read inpoints.isotropic;that is,if the energyfrom the file,Excel will fit the datadistribution does not vary as ato the Elliptical Gaussian function,Figure I shows the plotted profilesfunction of the azimuthaland the best-fit coefficients will beof some of the built-in scatteringscattering angle.displayed in the dialog box.Thesetypes in Light Tools.The Ellipticalcoefficients can then be used toGaussian is similar to the GaussianMeasured BSDF data can also bedefine a scattering surface inmodel,except that different ofit to any of the other scatterLightTools.A measure of the errorvalues can be specified along eachmodels.A macro has been writtenof the fit (Chi-squared)is alsoof the axes of the surface X-Yin Microsoft Excel to read in adisplayed,which is equal to thecoordinate systemBSDF data file and fit it to thesum of the squares of theLightTools Elliptical Gaussiandifferences between the BSDFModeling a scattering surface inscatter model.The macro isvalues of the input data and theLightTools based on measuredavailable on our website,BSDF values of the fitted model.BSDF data always involves fittingwww.opticalres.com.This modelStray-Light AnalysisRight Side ViewOnce the scattering surface hasbeen defined in LightTools usingthe measured BSDF data,a stray-light analysis of the system can beperformed using the LightToolsIllumination Module.Figure 3illustrates a Cassegrain imagingsystem with housing surrounding aprimary and secondary mirror.Aclassical stray-light problemoccurs when collimated light fromthe sun hits the inside of thehousing and scatters directly to thefocal plane.This light is unwanted,and may have a serious impact onthe performance of the system.We would like to quantify theFigure 3.Cassegrain imaging systems with housing.Paraxial rays are shown.amount and distribution of thisThe inside of the housing barrel and the inside of the hole in the primary mirrorlight,and,if possible,to design aare scattering surfaces.baffle to block it.To perform thisanalysis,we would first need tomeasure the BSDF of the housingsurface and define a LightToolsscatter model of it.Next,we wouldlike to efficiently quantify theamount of light in the scatter path.Since we already know the path wewish to investigate,we don't wantto trace rays from the source or thescatterer in all directions-wecal planewould like to illuminate only theinside of the housing,and traceonly those scattered rays which aredirected towards the focal plane.We can do this in LightTools usingaim areas,which are a form ofimportance sampling.Aim areasare circular or rectangular near-Figure 4.Light scattering from the inside of the housingfield apertures that can be definedto the focal plane.for sources and scattering surfacesand allow the user to directradiation.In this analysis,we use apoint source with an aim area toFocal planeFocal planesimulate off-axis solar radiation.The source is located a large0.0002distance away from the inputaperture,and has an aim area thatdirects light at an angle of 20 tothe z-axis into the input aperture of0.0001the housing.Because the source isfar away,it is not seen in Figure 3.The source output power is 878.6Watts,which is the amount ofwattage in the visible band (40000.0011nm-700 nm)for the solarX,incountblackbody (@6000 K).TheFigure 5.Magnitude and distribution of scattered energy on the focalscattering properties of the housingplane due to the scatterpath shown in Figure 4.are based on BSDF measurementsof anodized aluminum at 633 nm.amount and distribution of light onhousing around the primary,The housing also has an aim area,the focal plane due to this scatterincrease its diameter,add a bafflewhich coincides with the focalpath.Note that the magnitude ofvane to the inside of the housing,plane of the system.some of the scattered rays reachingor make the hole in the primarythe focal is very low-for thissmallerFigure 4 illustrates a ray coming inreason,it is important to lower thefrom the source and scattering offminimum power threshold of theSometimes,we may be interestedof the housing to the focal plane.raytrace to a suitable level to avoidin investigating a moreNote that some of the rays striketeminating rays prematurely.complicated scatter path,such as athe primary mirror and don'tFigure 5 illustrates the result ofdouble-bounce path.Such a pathpropagate to the focal plane.Sincethis simulation.occurs when incident light scatterswe are not interested in these raysoff one surface,then another,thenright now,we have chosen toWe can look at the magnitude ofhits the focal plane.Lightterminate them at the primary.the radiation in Figure 5 andundergoing scattering from moredecide if we need to block thesethan one surface is usually veryWe can run an illuminationrays.There are a variety of ways todim,but can be a problem forsimulation to determine thedo this-we could shorten thesensitive systems.For instance,in