Evaluation of the Suitability of Polarimetric Scattering and Emissivity Models with Scene Generation Software

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1 Evaluation of the Suitability of Polaimetic Scatteing and Emissivity Models with Scene Geneation Softwae Michael G. Gatley Cheste F Calson Cente fo Imaging Science, Rocheste Institute of Technology 54 Lomb Memoial D, Rocheste, NY ABSTRACT Softwae based polaimetic image geneation models and hadwae based infaed scene pojectos commonly utilize analytical foms of polaized bi-diectional eflectance distibution function and emission models. Many of these models ae based in fist pinciples physical concepts, but in pactice ae configued as least eo fits to measued signatues. The esulting analytical model may well descibe the lab measued data points, but povide eoneous esults when integated into a wide anging adiometic simulation envionment. In this wok we pesent a methodology fo chaacteizing the suitability of incopoating limited ange lab measued data, usually though fitting to an analytical model, into a wide ange modeling envionment. We have found lab measued eflectance data can be fit to analytical models with paametes staying significantly fom the fist pinciples physical desciption of the suface. This effect may be due to ove paameteization o an unde sampled measuement space, esulting in adiometic anomalies when integated into a lage scale, multi-suface, multi-mateial, modeling envionment. Ou methodology consists of a seies of sanity tests that each scatteing and emission model configuation must pass befoe confidence is had in the polaimetic optical popety desciption. Keywods: Modeling, simulation, optical popeties, polaization. 1. INTRODUCTION The needs of the tactical emote sensing community ae quite dynamic, often equiing a vaiety of imaging modalities to adequately chaacteize aeas of inteest. One such modality that often aids in impoving contast between man-made tagets and natual backgound clutte is polaimetic imaging [1]. In many cases, polaimetic imaging sensos and payloads can benefit geatly fom polaization capable synthetic image geneation softwae [2] as well as polaization capable scene pojectos [3]. Howeve, at the coe of both image simulation models and scene pojection hadwae is the equiement of a solid undestanding of suface level polaimetic eflectance and emissivity popeties. The Digital Image and Remote Sensing Image Geneation (DIRSIG) softwae model [2] has been capable of fully spectal and polaimetic adiative tansfe and image geneation fo ove 10 yeas. Two example DIRSIG polaimetic image outputs ae shown below in Figue 1. Howeve, the weak link in the model has histoically been adequate polaimetic optical popety desciptions fo a wide ange of mateials. Existing mateial eflectance and emissivity databases ae commonly leveaged fo modeling of lage scale scenes, while smalle scale scenes might have objects attibuted with scene specific and locally (at the Rocheste institute of Technology) measued optical popeties. In eithe case, the challenge tends to be poviding an empiical desciption of lab measued data to the models. Woking inside the geometic and spectal bounds of lab measuements can povide the best esults, but is not a guaantee of adiometically accuate simulated esults due to a vaiety of issues to be discussed in this pape. Polaization: Measuement, Analysis, and Remote Sensing X edited by David B. Chenault, Dennis H. Goldstein, Poc. of SPIE Vol. 8364, 83640P 2012 SPIE CCC code: X/12/$18 doi: / Poc. of SPIE Vol P-1

2 Figue 1. Example polaimetic image simulations of a gound (top) and space (bottom) based taget using the DIRSIG model. 2. GENERALIZED, POLARIMETRIC SCATTERING AND EMISSION MODEL The common backbone of both polaized eflectance and emissivity models is the polaimetic bi-diectional distibution function (pbrdf). Geneally, thee ae two main classes of mateial scatteing models utilized in the polaimetic emote sensing community, namely man-made taget [1, 4, 5] and natual clutte models [1, 2, 3]. The man-made taget BRDF model (Eq. 1) typically takes the fom of a mico-facet eflectance function (Eq. 2) coupled with a vaiety of volume o bulk mateial scatteing tems (Eq. 3). A schematic showing the scatteing geomety elated to both tems is shown below in Figue 2. f ( λ, θ, φ, θ, φ, n, k,... ) = f1( λ, θ, φ, θ, φ, n, k,... ) + f ( λ, θ, θ, n k ) i i i i bulk i, The fist suface scatte tem, sometimes efeed to as the specula tem, is a function of an abitay gain value ρ s, a suface facet slope pobability distibution (which may be based on measued values o simply a closed fom distibution model such as a Gaussian o Cauchy) p, a 4x4 element Fesnel eflectance Muelle matix R fesnel taking wavelength dependent complex index of efaction values and the scatte half angle β as inputs, a potentially complex o absent shadowing and obscuation function SO( ), and the incident and eflected zenith angles θ i and θ espectively. (1) ( σ ( λ), θ ) R β, n( λ), k( λ) ( ) ρ s p mf fesnel f1( λ, θi, φi, θ, φ ) = SO 4 cosθ cosθ i (...) (2) Poc. of SPIE Vol P-2

3 The bulk mateial scatteing tem of the genealized polaimetic BRDF contains thee sub tems, one that is pefectly Lambetian ρ L, one that is a modified Lambetian fom containing the value ρ v, and one that is some potion ρ B of bulk, multiply scatteed light that induces polaization via the 4x4 element Muelle tansmission matix T fesnel. f bulk ( λ, θ, θ, n, k) = ρ T ( θ, n( λ), k( λ) ) i B fesnel ρv + ρ L + cosθ + cosθ i (3) This geneic fom the polaimetic BRDF can be configued to epesent the modified Bead-Maxwell BRDF model utilized by the Nonconventional Exploitation Factos (NEF) database, the Piest-Geme micofacet model, the Toance and Spaow BRDF, and a vaiety of othes with subtle diffeences. The Rocheste Institute of Technology has implemented this geneic BRDF into its DIRSIG adiative tansfe model in ode to suppot mateial popeties fom a vaiety of oigins. A quantity that is often deived fom the full fom of the BRDF is the Diectional Hemispheical Reflectance (DHR) function (sometimes efeed to as the diffuse hemispheical eflectance) which has the fom DHR ( θ ) = f ( θ θ, φ ) 0 0 i, cosθ dθ dφ (4) Figue 2. Schematic of scatteing geomety fo 1 st suface and bulk scatteed light utilized by a genealized polaimetic scatteing model. The hemispheically integated BRDF fo a given angle of incidence, o DHR( θ i ), is quite useful and employed commonly fo modeling diectional emissivity signatues in a polaimetic adiative tansfe famewok [9,10]. Moe specifically, the equation fo the Stoke s emissivity vecto (Eq. 5) fo a given mateial is expessed as Poc. of SPIE Vol P-3

4 ε ( θ ) 1 f 0 0 f = 0 0 f 0 0 f 0 0 0,0 1,0 2,0 3,0 ( θ, θ, φ ) ( θ, θ, φ ) ( θ, θ, φ ) cos cos cos θ dθ dφ θ dθ dφ θ dθ dφ ( θ, θ, φ ) cosθ dθ dφ (5) whee the subscipt on the BRDF function f in the integands coesponds to the ow and column of the full BRDF Muelle matix. 3. SPECTRAL INTERPOLATION OF POLARIMETRIC BRDF MODELS It is often the case, such as with the NEF mateials database, that the high angula fidelity BRDF measuements ae conducted at a small numbe of wavelengths (i.e. lase wavelengths aound 328 nm, 632nm, 1.06 micons, 3.39 micons and 10.6 micons). These lab based measuements ae typically augmented by high spectal esolution diectional hemispheical eflectance measuements at one specific angle of incidence. The esult is two somewhat dispaate pieces of infomation: (1) high angula fidelity, low spectal fidelity goniomete measuements fit to an empiical model and (2) low angula fidelity, high spectal fidelity integating sphee measuements. The job of spectally intepolating a BRDF model leveages both pieces of infomation to hopefully bidge the gaps fo accuate spectal, polaimetic image simulations and scene pojections. We have encounteed thee diffeent appoaches to spectal intepolation which ae summaized in Table 1. Table 1. Summay of Existing pbrdf Spectal Intepolation Appoaches Type Intepolation Desciption Suitability Requiement(s) I Linea intepolation of modeled BRDF between efeence wavelengths II Linea intepolation of 1 st suface scatte tem of BRDF between efeence wavelengths. Apply wavelength dependent gain to bulk scatte BRDF tem such that the esulting hemispheical integation of full BRDF matches the lab measued DHR spectum III Linea intepolation of both 1 st suface and bulk scatte tems of BRDF between efeence wavelengths with an additional wavelength dependent gain applied to model such that the esulting hemispheical integation of modeled BRDF matches the lab measued DHR spectum Fist suface dominated mateials that have well known complex index of efaction values that adequately esolve all spectal featues ove desied wavelength ange Examples: Solid metals, optically opaque and homogeneous liquids Mateials possessing a combination of 1 st suface and bulk scatteing behavios fo which the magnitude of the specula glint changes slowly in wavelength and the diffuse scatte changes quickly with wavelength Examples: ca paints and some vegetation in the visible to nea IR Mateials fo which 1 st suface scatte dominates, but is not the only contibuto to the full BRDF magnitude and complex index of efaction values ae not known adequately Examples: Painted sufaces in the mid and long wave infaed Paameteized BRDF at a small numbe of spasely spaced wavelengths Paameteized BRDF at a small numbe of spasely spaced wavelengths. High spectal esolution lab measuement of DHR Resulting DHR of model equals lab measued DHR Paameteized BRDF at a small numbe of spasely spaced wavelengths High spectal esolution lab measuement of DHR Resulting DHR of model equals lab measued DHR Poc. of SPIE Vol P-4

5 We have also found that no single spectal intepolation appoach is best fo all mateials. In contast, the optimal spectal intepolation appoach is typically both mateial and wavelength dependent fosteing the need fo flexibility in this aea. In esponse to these findings, RIT has chosen to suppot all thee vaiations of spectal intepolation fo its genealized micofacet based polaimetic BRDF model utilized in the DIRSIG softwae. To futhe demonstate the impotance of which spectal intepolation appoach is used, we show DIRSIG simulation esults fo thee spheical objects (see Figue 3 below). Each of the sphees is attibuted with exactly the same mateial pbrdf paametes at wavelengths of 350nm and 1060 nm. Additionally, each sphee is attibuted with the same exact high spectal esolution DHR cuve. Howeve the thee sphees diffe in the spectal intepolation appoach fo which they utilize fo detemining the shape of the BRDF between the two efeence wavelengths of 350 and 1060 nm. We have delibeately chosen to keep the BRDF paametes at the efeence wavelengths the same (implying use of the BRDF paametes without the DHR cuve esults in a spectally flat BRDF) in ode to demonstate how the high spectal esolution DHR lab measued cuve can significantly dive the objects colo independent (II) o depedent (III) on the shape of the BRDF measued at the efeence wavelengths. Also notable is the spectal colo of the glint (and hence the S1 signatue) of appoaches I and II ae spectally flat while the glint of the sphee utilizing appoach III follows the spectal shape of the lab measued DHR cuve egadless of the glint magnitude descibed in the BRDF model at the efeence wavelengths alone. Figue 3. DIRSIG endeings (Stoke s S0 and S1) of thee sphees having exactly the pbrdf paametes but using diffeent spectal intepolation appoaches. 4. SUITABILITY TESTS FOR SCATTERING AND EMISSION MODELS Fo use in ou DIRSIG adiative tansfe envionment, RIT commonly conducts thee sepaate testing methods fo evaluating the suitability of specific mateial popeties. In a nutshell, a well paameteized BRDF has the following qualities: (1) a calculated hemispheical integation of the modeled BRDF (befoe spectal intepolation) at the efeence wavelengths agees with the lab measued DHR cuve, (2) the hemispheical integation of the modeled BRDF afte spectal intepolation has values between 0 and 1.0, and (3) the total polaization of the Stoke s emissivity vecto is less than o equal to 100%. These thee equiements and example testing methods ae descibed below Inspection of BRDF Paametes Relative to DHR Spectum Ou man-in-the-loop type of mateial inspection involves hemispheical integation of the BRDF paametes at the efeence wavelengths (befoe spectal intepolation) and compaing the values to the lab measued DHR values. In many cases, we have found this to be the simplest way to disciminate which mateials ae moe likely to behave well and within the bounds of physics and which ae likely to violate them unde stessing geometic conditions (gazing angles). Additionally, we typically inspect the values of the complex index of efaction model paametes in hopes that they coespond to expected values fo one o moe of the mateial s constituents. This is staightfowad fo Poc. of SPIE Vol P-5

6 homogeneous sufaces such as metals whee these values ae commonly published in CRC handbooks, but can be quite challenging fo aggegate mateials such as concetes and asphalt. Figue 4. Examples of ageement (left) and disageement (ight) between goniomete deived DHR (points) and integating sphee measued DHR (cuve). The two sets of cuves in Figue 4 demonstate notional white paint DHR cuves measued using an integating sphee compaed with a hemispheical integation of the total amount of light eflected fom the same suface measued by a goniomete (used fo deiving the BRDF paametes at efeence wavelengths). Additionally, we can utilize this ageement o lack of ageement to help decide which spectal intepolation method to employ in the modeling envionment. We have not yet found a simple ule of thumb to follow, but the wok is ongoing Evaluation of Diectional Hemispheical Reflectance of Spectally Intepolated BRDF Model Next, we utilize the DIRSIG model to simulate the spectally intepolated DHR via the concept of ecipocity. Moe specifically, we illuminate the mateial suface in DIRSIG with a unifom hemisphee of adiance 1 W/cm2/s/um illumination and measue the DHR by evaluating the apetue eaching adiance as a function of view angle (epesenting the incidence angle of DHR since we ae leveaging BRDF ecipocity). This concept is illustated in Figue 5 below. Figue 5. Cut-away illustation showing light paths in integating sphee DHR measuement next to illustation of light paths used fo DIRSIG evaluation of a mateial s modeled DHR. Poc. of SPIE Vol P-6

7 In pactice, we find that pefoming this vitual DHR evaluation is most efficiently conducted by endeing a spheical object on a pefectly eflecting mio gound plane. Ideally, each suface of the sphee with a local nomal diection pointing towads the some potion of the sky (local zenith angle of nomal between 0 and 90 degees) will see unifom iadiance in the hemisphee above it due to the pefectly eflecting gound plane. To illustate this concept, we pesent a few vaiations on a DHR = 1.0 mateial, each vaiation having a diffeent set of BRDF paametes that nominally achieve a hemispheical integation value of 1.0. Figue 6. Examples of vitual DHR evaluation fo vaiations on a DHR = 1.0 (nominally) mateial. Left to ight, the mateials ae epesentative of a pefectly Lambetian mateial, two vaiations of a glossy white paint, and a nea pefect specula Fesnel eflecto (mio suface) whee the gound plane gay level coesponds to a vitual DHR measuement of 1.0, dak aeas less than 1.0 and white aeas geate than 1.0. In some cases, manual modification of the BRDF paametes at the efeence wavelengths is equied to keep the modeled DHR physically meaningful (less than o equal to 100%). Although the DIRSIG softwae model has checks in place to pevent negative valued spectally intepolated BRDF magnitudes, the model elies on the use to coectly configue mateials such that the esulting DHR at all angles is less than 100%. Fo the puposes of calculating emissivity Stoke s vectos fom calculated DHR, the DIRSIG model pevents >100% values (peventing negative emissivity magnitudes) Evaluation of Total Polaization of Stoke s Emissivity Vecto A final test of a specific mateial s set of BRDF paametes and associated lab measued diectional hemispheical eflectance is an evaluation of the deived polaization state of the spectal emissivity. RIT has found a significant numbe of mateials in community databases that tend to pedict a S1 and/o S2 component of the Stoke s emissivity vecto that is actually geate than the S0 component of the emissivity vecto. The esulting themally emitted adiance has a degee of linea polaization geate than 100%, which is quite non-physical. We have found that in many cases the oigin of the non-physical emission polaization signatue aises fom a nonphysical set of BRDF model paametes that might be pefectly valid fo many geometies of the BRDF evaluation, but when hemispheically integated to deive an emissivity vecto, the esult defies physical boundaies. In ode to detect poblems befoe they manifest themselves in a full adiometic, multi-bounce complex adiative tansfe scenaio (see bottom ow of Figue 7), we typically model the emitted polaimetic signatue of a simple shape such as a sphee to pobe fo poblematic signatues (see top ow of Figue 7 below). Poc. of SPIE Vol P-7

8 Figue 7. Illustation demonstating well behaved mateial popeties in the long wave infaed (top ow: degee of linea polaization less than o equal to 1.0) and pooly behaved mateial popeties (bottom ow, cicled egion has degee of linea polaization geate than 1.0 due to pooly configued BRDF paametes). 5. CONCLUSION In conclusion, we have pesented a genealized BRDF model that is flexible fo captuing the mateial eflectance and emissivity popeties of a vaiety of existing mateials databases. Additionally we have summaized a total of thee diffeent appoaches to pefoming spectal intepolation of this model and emphasized the pos and cons of each elative to what is known about the mateial and the wavelengths fo which the intepolation might occu. Additionally, we have pesented a seies of sanity tests RIT typically pefoms on mateial popeties befoe utilizing database and lab measued esults that ae to be used to dive BRDF and emission signatue modeling in the DIRSIG model. Futue wok equies not only defensive type testing of models afte the fact, but a deepe look to offensively undestand how to bette chaacteize mateial optical popeties in the lab envionment befoe extending them into the vitual modeling wold of polaimetic signatues. Thee ae wavelength egions and mateial types that ae well undestood and well modeled (see Figue 8 below) and many examples of the opposite case (see many of the peceding figues in this pape). Theefoe the impotant takeaway fo us is to continue to citically evaluate mateial BRDF and emission models well befoe implementing them into a complex adiative tansfe envionment whee any non-physical scatteing and emission mechanisms might not be as appaent. Figue 8. Examples of a DIRSIG simulations of a gound based polaimetic image (top ow) and aibone based polaimetic image ove a paking lot aea. Poc. of SPIE Vol P-8

9 REFERENCES [1] Chenault, D., Pezzaniti, L., Hanks, J., Polaimetic imaging fo ISR, Aibone Intelligence, Suveillance, Reconnaissance (ISR) Systems and Applications IX, Poceedings of SPIE v8360, Baltimoe MD, Apil [2] Pesna, M.D.; Keekes, J.P.; Pogozala, D.R., Dynamic Image Simulations fo Adaptive Senso Pefomance Pedictions, Poceedings of the Second Wokshop on Hypespectal Image and Signal Pocessing: Evolution in Remote Sensing, IEEE, Reykjavik, Iceland, June (2010). [3] Haiping Yu, Hong Wei, Lei Guo, Shenggang Wang, Le Li, Jack R. Lippet, Steve Seati, Neelam Gupta and Fank R. Calen, "Multispectal polaized scene pojecto (MPSP)", Poc. SPIE 8015, (2011). [4] Schott, J.R., Fundamentals of Polaimetic Remote Sensing, Chapte 10, SPIE Pess, Bellingham, WA, ISBN [5] Shell, J., Schott, J., A polaized clutte measuement technique based on the govening equation fo polaimetic emote sensing in the visible to nea infaed, Tagets and Backgounds XI: Chaacteization and Repesentation, Poceedings of SPIE Vol. 5811, [6] J.L Deuzé, F.M Béon, P.Y Deschamps, C Devaux, M Heman, A Podaie, J.L Roujean, Analysis of the POLDER (POLaization and diectionality of eath's eflectances) aibone instument obsevations ove land sufaces, Remote Sensing of Envionment, Volume 45, Issue 2, August 1993, Pages [7] M. W. Hyde, J. D. Schmidt, and M. J. Havilla, "A geometical optics polaimetic bidiectional eflectance distibution function fo dielectic and metallic sufaces," Opt. Expess 17, (2009). [8] Richad G. Piest and Steven R. Meie, "Polaimetic micofacet scatteing theoy with applications to absoptive and eflective sufaces", Opt. Eng. 41, 988 (2002). [9] Andew Resnick, Chis Pesons, and Geoge Lindquist, "Polaized Emissivity and Kichhoff s Law," Appl. Opt. 38, (1999). Poc. of SPIE Vol P-9