Automated three-axis gonioreflectometer for computer graphics applications

Transcription

1 Automated thee-axis gonioeflectomete fo compute gaphics applications Hongsong Li, Sing Choong Foo, Kenneth E. Toance, and Stephen H. Westin Pogam of Compute Gaphics, Rhodes Hall, Conell Univesity, Ithaca, NY ABSTRACT We descibe an automated thee-axis BRDF measuement instument that can help incease the physical ealism of compute gaphics images by poviding light scatteing data fo the sufaces within a synthetic scene that is to be endeed. To ou knowledge, the instument is unique in combining wide angula coveage (beyond 85 fom the suface nomal), dense sampling of the visible wavelength spectum (124 samples), and apid opeation (less than ten hous fo complete measuement of an isotopic sample). The gonioeflectomete employs a boadband light souce and a detecto with a diffaction gating and linea diode aay. Validation was achieved by compaisons against efeence sufaces and othe instuments. The accuacy and spectal and angula anges of the BRDFs ae appopiate fo compute gaphics imagey, while ecipocity and enegy consevation ae peseved. Measued BRDFs on ough aluminum, metallic silve automotive paint, and a glossy yellow paint ae epoted, and an example endeed automotive image is included. Keywods: Optics, optical devices, scatteing, eflectance, eflectometes, compute gaphics 1. INTRODUCTION Realistic endeing is that pat of compute gaphics that stives to simulate the appeaance of thee-dimensional scenes in the eal wold. Accuate physical simulation of light tanspot and scatteing is essential to achieve demonstably accuate ealism, as opposed to a convincing atistic epesentation. 1,2 Such simulation diffes fom most optical simulations in that the output is appeaance athe than quantitative data. Futhe, instead of dealing with a single wavelength and/o a single eflection configuation, we must epoduce the diectional and spectal dependence of the eflectance ove the entie angula domain and visible spectum. The pesent pape descibes a eflectomete to measue the bidiectional eflectance distibution function (BRDF) fo compute gaphics imagey. The instument povides Boad angula coveage High-esolution coveage of the visible spectum Rapid opeation Accuacy appopiate fo compute gaphics. 2. PREVIOUS WORK To ende sufaces at abitay oientations with abitay lighting, we wish to maximize the coveage of the incident and eflection hemisphees (with highest gazing angles >8 ). To ende colos accuately, moe than 3 spectal samples ae equied fo each angula configuation. 18 In ode to fully chaacteize the angula and spectal distibutions of the BRDF fo a suface, the total numbe of samples can easily be 1 4 ~1 5. Since we need to chaacteize many sufaces, the measuement opeations have to be easonably apid. The limitations of human vision, such as polaization insensitivity and limited dynamic ange, can be exploited to acceleate the pocess. We biefly eview pevious wok. A classic gonioeflectomete includes a light souce, a detecto, and some means of vaying thei angles elative to the sample A goniomete is often used to hold and otate the sample so that the angula configuation can be changed epeatedly to cove the incident and eflection hemisphees. Such instuments can achieve boad angula coveage 3,4 and boadband spectal coveage. 5,6 But none of these instuments combines these capabilities. Fo example, Geme et al. 4

2 have built an instument (GOSI) that achieves excellent angula coveage, but limited spectal coveage (3 wavelengths) and long measuement time (weeks fo a full angula coveage). To speed acquisition, multiple detectos can be used in paallel. An example of angula paallelism is using a camea, possibly with special optics, to captue thousands of angles at once, as did Wad et al., 13 Kane et al., 14 Castonguay, 15 Dana et al., 16 and Maschne et al. 17 The speed makes such an aangement popula in the compute gaphics community. 13,16,17 Wad et al. 13 intoduced an image gonioeflectomete that samples two dimensions of the BRDF (two eflection diections) simultaneously, educing the measuement time to minutes. On the othe hand, a camea is geneally unable to povide sufficient accuacy fo compute gaphics, because of its limited spectal coveage (3 channels) and limited dynamic ange (8/12 bits). To measue acoss a boad ange of wavelengths, we could use eithe a light souce o a detecto selective to wavelength. The fist option can be a boadband souce woking with a monochomato o a set of naow band filtes. With such an appoach, STARR of NIST 6 and the NASA Goddad scatteomete 1 povide high-quality BRDF measuements ove the UV-Vis-NIR spectum. But scanning such a boad spectum takes a long time (hous fo STARR). And these instuments usually cove only a potion of the incident and eflection hemisphees. The second option can be a spectoadiomete that measues the entie spectum at once, 5 o a naow-band detecto that can vay its wavelength. 13 Feng et al. 5 intoduced a gonioeflectomete equipped with a spectoadiomete detecto, which coves a boad ange of specta in one snapshot. Using a spectoadiomete is faste than the fist option, though the dynamic ange of the measued signals is geneally lowe. None of these instuments displays the combination of angula coveage, wavelength esolution, efficiency, and data quality that we desie. Theefoe, we designed and built a gonioeflectomete. 3. DESCRIPTION OF THE INSTRUMENT The gonioeflectomete measues the Bidiectional Reflectance Distibution Function (BRDF), the atio of the adiance eflected fom a suface in the diection (, ) to the iadiance onto the suface fom the diection ( i, i ) (see Figue 1): f( i, i;, ) = dl ( i, i;, ) / dei ( i, i ). Fo an isotopic suface only thee angles ae needed. The eflected adiance dl and iadiance de i have units of W/m 2 s and W/m 2 espectively. de i i n ^ dl Light souce Folding mio Polaize Focusing lens Spectoadiomete Moto 1 axis Sample holde i Souce am pivots aound sample (Moto 3) Moto 2 axis Figue 1. Coodinate system Figue 2. Oveview of the Gonioeflectomete An oveview of ou gonioeflectomete is shown in Figue 2. The instument consists of fou pats: a boadband light souce; a positioning mechanism with thee moto-contolled axes of otation; a fixed spectoadiomete detecto; and a compute system (not shown) to contol opeation, data acquisition, and data pocessing. The instument was designed in confomance with the ASTM standad; 19 instument paametes ae listed in Table 1. The laboatoy is maintained at 2 C and a elative humidity of 5% to aid sample and optical stability.

3 3.1 Light souce Opal glass diffuse GE lamp ELH 12V 3W Condense lens Vaiable apetue Lens mount Figue 3. Light souce optical components Nikon lens 135mm 1:2.8 The light souce (Figue 3) is a 3-watt MR16 tungsten halogen lamp with integal dichoic eflecto. The souce povides a continuous spectum while minimizing infaed emission, educing heating of the sample. The beam is depolaized with an opal glass diffuse, gatheed by an aspheic condense lens, passed though a small apetue to appoximate a point souce, and then collimated by a Nikon camea lens (f = 135mm) focused at infinity. The souce is poweed by a egulated, pogammable powe supply (stable to within.3% to give stable output) and cooled by a fan to avoid deteioation of the dichoic eflecto. We un the lamp at 1 volts athe than its ated 12 volts to polong its life beyond the ated 35 hous. The esulting beam is well collimated: it subtends a solid angle of appoximately s, with illumination unifom to within ± 5% ove a cicula egion of 25mm diamete. A scientific gade CCD camea is used to check the unifomity and symmety of the light spot on the sample suface. The entie souce assembly is mounted on a 1m optical ail (Figue 2), which is in tun attached to a motoized otation stage. A baffled, ventilated housing aound the entie souce assembly contols stay light. When needed, we mount a dichoic polaize on the optical ail to contol the polaization state of the souce; in nomal opeation we use a depolaized light souce. 3.2 Positioning mechanism The sample holde (Figue 2) is mounted on two moto-diven stages to povide two axes of otation; a thid stage, mentioned above, supplies a thid axis by moving the souce am in a hoizontal plane (paallel to the table). The thee axes of otation povide the thee otational degees of feedom needed to sample an isotopic BRDF. The configuation is simila to that descibed by Eb and Kystek. 12 All thee axes ae contolled by stepping motos unde compute contol. All otational axes intesect at the cente of the sample plane, so that measuements at all angles ae centeed on the same suface point. The sample holde pecisely locates the sample plane by means of fou suppoting lugs, with elastic bands holding the sample with slight pessue fom behind. The angula esolution is.1 fo the sample stage and.13 fo the souce am. The maximum angula eo is.34, mainly due to lash in the gea tains of the stages. In most cases, the eo is within.1. Fo BRDF measuements of smooth sufaces, special pocedues ae used to educe the eo. All sufaces of the sample holde ae painted flat black to minimize stay light scatte. 3.3 Detecto The detecto is designed to accept a boadband signal fom the sample, measuing many wavelengths at once fo faste opeation. The detecto unit consists of a folding mio, focusing optics, and a spectoadiomete (see Figue 2). The position of the entie unit is caefully aligned and fixed. The light scatteed by the sample suface is ediected by the folding mio and focused on the entance slit of the spectoadiomete though an achomatic doublet. The diffaction gating in the adiomete makes it sensitive to polaization. Fo this eason, we measue the BRDF twice with diffeent detecto polaizations, using a dichoic polaize in font of the folding mio to select a single linea polaization fo measuement. By aveaging the two measuements, and using a detecto-polaization calibation cuve, we obtain the polaization-aveaged eflectance. The spectoadiomete contains a spectogaph with a eflective intefeence gating of 6 lines/mm and a 124-pixel diode aay detecto, coveing the visible spectum (386nm-711nm). We decimate the esolution to 31 output samples (4nm-7nm with 1nm intevals), using a Gaussian kenel, to educe noise in the output data. The diode aay is themoelectically cooled to stabilize its output. The signal esolution is 16 bits. Fo a fixed exposue time, the dynamic ange of the detecto is appoximately 1:2,. We veified that the esponse of the detecto is linea ove the ange that we opeate the detecto, except at vey low signal levels (a few counts). Othe expeiments confimed the stability and epeatability of the detecto.

4 The detecto optics detemine the viewed sample suface aea, which is defined by the magnified image of the detecto slit on the sample. At = the viewed aea is 2mm 4mm; the 2mm dimension inceases as (cos ) -1. The minimum diamete of the illuminated spot at nomal incidence is 25mm, so the constaint on becomes,max = cos -1 (2/25) ~ 85. The latte epesents the fundamental limit on the angula coveage of the instument: when the pojection of the slit exceeds the illuminated spot size, the BRDF will be undeestimated. The angula limit compaes favoably with othe compute gaphics instuments such as that of Wad et al., which was limited to appoximately 6 fom the nomal. 22 A typical exposue time is 1 seconds at each angula configuation, esulting in measuement times of oughly 9-1 hous fo a easonably diffuse sample (using about 1 3 angula configuations). The contol softwae automatically senses satuation of the detecto and educes exposue time to obtain useful data in the bightest egions of the BRDF, notably nea specula peaks. 3.4 Contol softwae The gonioeflectomete is contolled by a C pogam that accepts an input file of angula configuations. The file specifies the position of each of the thee motos. The pogam powes up the light souce in a contolled, epeatable fashion, then leads the opeato though the steps of aligning the thee dive motos, measuing detecto dak cuent and the souce intensity, and making two sets of measuements, one fo each polaization diection. The opeato intevenes only at the stat to mount the sample, and midway to change the polaize oientation. The input file of moto positions is geneated offline. Fo a nomal measuement, we geneate sampling positions on a egula gid on the unit squae. These ae then mapped to the unit sphee with a tansfomation that poduces a unifom distibution in solid angle. 23 The tansfomation fom this space to the coodinates of the thee steppe motos is easonably staightfowad, and is developed both by Foo 2 and by Eb and Kystek. 12 Some sampling positions (within appoximately 7 of eto-eflection) ae not achievable, due to mechanical intefeence between the light souce and detecto. We omit such positions fom the command steam sent to the contolle, and depend on late intepolation to fill gaps as needed. Futhe details of the instument and opeating pocedues ae available in technical epots. 2,21 4. CALIBRATIONS AND NORMALIZATION 4.1 Absolute method - Spectalon test The instument allows both absolute and elative BRDF measuements, using the ASTM standad potocols. 19 The absolute method woks diectly fom the atio of eflected and incident adiant beams. To do this, we fist position the souce to illuminate the detecto diectly, captuing the entie souce iadiating flux that impinges on the sample. We then measue the eflected flux fom the sample at each angula configuation. The spectoadiometic signal fo each angula configuation is divided by the signal of the diect light souce measuement, the incident cosine, and the solid angle of the detecto. The last facto effectively becomes the scale facto. To veify the diectional and magnitude accuacy of ou instument, we compae in Figue 4 ou polaized BRDF measuements of Spectalon in the incidence plane with data published by Labsphee. 24 The incident light was p polaized by installing a hoizontal polaize at the light souce. The eflected light of both s and p polaizations was then measued, at a wavelength of 633nm. The incidence angle was 3 and the eflection angle vaied fom 86 to 86. Ou ps measuements (the depolaized component) ae essentially identical with the published esults; the pp measuements (which include suface scatte) diffe slightly (by.2s -1 ). We wee unable to veify that the suface oughness of ou sample matched that of the sample used in the published data, so diffeences in suface finish between ou sample and the sample measued by Labsphee may account fo the diffeences in the two sets of ps measuements. The absolute nomalization method can give good diectional and magnitude accuacy fo sufaces with stongly specula, o mio-like, eflection behavio. Fo sufaces with stongly-diffusing eflection behavio, o with vey low diffuse eflectance values (dak sufaces), the altenate elative method is pefeed. 4.2 Relative method The elative method of BRDF measuement woks by simply compaing the eflected signal fom a test sample to that fom a efeence suface with a known BRDF. To do this, the sample is mounted on the goniomete and the eflected signal is measued fo each angula configuation. Subsequently, we measue the eflected signal fom the efeence sample (Spectalon) at one paticula angula configuation, i = and = 1 (/1). The spectoadiometic signal

5 fom the test sample fo each angula configuation is then divided by the signal fom the Spectalon at /1 and a cosine facto, and multiplied by the absolute BRDF of the Spectalon at /1 to give the sample s BRDF. The absolute BRDF of Spectalon at /1 is deived fom measuements of both the angula distibution of the eflected signal by using the gonioeflectomete, and the diectional-hemispheical eflectance, the latte measued with an Optonic Labs OL-75 diffuse eflectomete. The diectional-hemispheical eflectance is the atio of the adiant powe eflected to the hemisphee to the adiant powe incident onto a suface, both in W/m 2. Thus, the absolute BRDF of Spectalon at /1 becomes the instument calibation facto. Ou elative method is most simila to the Relative Total Reflectance Method ecommended in the ASTM standad. 19 That method integates the measued elative BRDFs ove the eflection hemisphee and adjusts calibation factos to match a sepaately-measued diectional-hemispheical eflectance. We use a diectional-hemispheical eflectance at only one incidence angle (1 ) to obtain the calibation facto. This simplification is valid when the eflectance of the test sample is simila to that of the efeence sample in magnitude and diectionality. In the next two sections, esults obtained using the elative method ae pesented fo thee samples. 5. VALIDATION Physical laws constain the BRDF to satisfy two elations that can be checked easily: Helmholtz ecipocity equies that f ( i, i ;, ) = f (, ; i, i ), and enegy consevation limits the integal of all enegy scatteed fom the suface: f, ;, cos d 1 ( ) i i whee the integal is ove the eflection hemisphee. The left side of this inequality is defined as the diectional-hemispheical eflectance dh. Instuments ae commecially available to measue dh, giving an oppotunity to veify BRDF measuements by numeical integation. In this section, we use a ough aluminum suface to demonstate the elative method and veify the enegy consevation of measuements fo a non-tivial suface. We tested ecipocity with the Spectalon sample. Simila veification pocedues ae applied to the othe samples and the esults ae pesented in the next section. 5.1 Enegy consevation ough aluminum suface We tested enegy consevation by measuing a ough aluminum suface, which was pepaed by coating gound glass with pue aluminum. The esulting RMS oughness was.63µm. Figue 5 shows BRDF measuements in the plane of incidence fo vaious illumination angles i, using linea intepolation between the dense sample points. The measuements ae consistent with measuements by Toance and Spaow. 25 Off-specula peaks beyond the mio angle of eflection ( = i ) ae evident, as is a unifom diffuse (Lambetian) component (to the left in the gaph). The off-specula peak inceases with inceasing incidence angle. A second set of measuements coveed the whole incident and eflection hemisphees. Fo an incident diection of 1 and a wavelength of 55nm, the BRDF in the eflection hemisphee is shown in Figue 6. The vetical axis is the BRDF; the left and ight othogonal axes map the spheical coodinates above a suface. The plane of incidence coesponds to on the left axis. The sampling positions wee unifomly distibuted to captue the basically diffuse chaacte of this suface. The points ae plotted in a unifom paameteization of the hemisphee such that each gid in the plot epesents a egion of the hemisphee with the same solid angle. The mapping is esponsible fo the shap-edged atifacts along the diagonals; they do not exist in the data. We tested enegy consevation of these measuements by compaing with anothe instument. The BRDF data wee integated ove the eflection hemisphee to obtain the diectional-hemispheical eflectance. The same sample was also measued with the Optonics OL-75 diffuse eflectomete system, which obtains the diectional-hemispheical eflectance of a flat suface at an incidence angle of 1 with a ated eo of less than 1%. Figue 7 shows a compaison of the integated and diect measuements. The diectional-hemispheical eflectance obtained fom the gonioeflectomete BRDF measuements matches the diect measuements fom the OL-75 within 2% ove the entie visible spectum, except fo the shotest wavelengths, below 42nm. At these wavelengths, seveal factos contibute to inceased eo: the tungsten souce of the gonioeflectomete has elatively low output, the silicon-based detecto has

6 educed sensitivity, and the dichoic polaize is much less effective. The compaison suggests indiectly that the BRDF measuements ae accuate in both magnitude and spectum, with less than 2% integated eo. 5.2 Recipocity Spectalon suface The BRDF satisfies ecipocity: when the positions of the light souce and detecto ae intechanged, the measued esults should be the same. To veify ecipocity, the light eflection of Spectalon was measued in the plane of incidence, whee i = =. We compaed the signal eadings of two measuements, each satisfying i1 = 2 and i2 = 1. Repesentative data, in Table 2, show that ecipocity is satisfied to within 1% to angles as geat as 8 fom the suface nomal. 6. MEASUREMENTS In this section, we pesent measued BRDFs fo two additional mateials: a metallic silve automotive paint and a glossy yellow paint. In contast with Section 5, these sufaces epesent mateials that ae moe common in typical eal-wold envionments. The silve paint demonstates the captue of an inteesting diectional dependence of the BRDF. The silve paint is basically gay in colo, as wee the mateials pesented in the pevious section. The yellow paint shows ou instument's ability to captue the spectal dependence of the BRDF, esulting in billiant colo. 6.1 Metallic silve paint The metallic silve paint (dupont) scattes light though a moe complex mechanism than the ough aluminum suface consideed in section 5.1 above: thee is an ideal specula eflection fom the smooth, glossy suface of the paint, but most light penetates the suface and is scatteed moe diffusely fom flakes of metal beneath the suface. Figue 8 shows the measued BRDFs in the plane of incidence. The gaph is taken fom the full hemispheical data set, so shows coase sampling than that used fo Figue 5. We intepolated the spase data points with a cubic spline afte deleting samples nea the specula (mio) diection to bette isolate the subsuface scatteing fom the fist-suface eflection. The deleted mio peak essentially follows the Fesnel fomula fo mio eflection fom a smooth dielectic suface. In BRDF coodinates, the mio peaks would be off scale in Figue 8, and would be centeed on the mio eflection angle with a half angle of about.4 due to the small solid angle of the light souce. The paint sample shows a eflectance patten in Figue 8 that is vey diffeent fom the ough aluminum suface (Figue 5). Fist, thee is almost no Lambetian component to the left in the figue. Second, the diectional lobe is naowe and is centeed on the mio diection (except fo i = 8 ). Thid, the incease in BRDF magnitude with inceasing i is much smalle, and eveses as i exceeds 7. We suspect the thid effect is due to two factos: the unknown angula distibution of the subsuface metal flakes, and the fist-suface eflection (not shown) which tends to divet a lage popotion of the incident light nea gazing incidence. Figue 9 povides an example BRDF fo the paint ove the mapped eflection hemisphee, fo an incident diection of 1 and a wavelength of 55nm. Figue 1 displays a compaison of the integated and sepaately-measued diectionalhemispheical eflectances fo the paint, ove the visible wavelength spectum. Fo this figue, the Fesnel component has been excluded fom both cuves. Figues 9 and 1 espectively esemble thei countepats fo the ough aluminum suface, Figues 6 and Glossy yellow paint The glossy yellow paint (Kylon 7221 Canay) scattes light fom its suface and fom subsuface paint pigments. Reflection fom the nealy smooth suface is gloss-like, with Fesnel-like eflection at lage angles of incidence. The subsuface scatteing is wavelength dependent, giving the mateial its yellow colo, and is diffuse in chaacte. Figue 11displays the measued incidence-plane BRDF fo thee angles of incidence and two wavelengths. The full hemispheical BRDF data set has been intepolated to get the incidence-plane cuves. The Fesnel-like mio component fom the suface has been deleted; that component follows the Fesnel fomula fo mio eflection fom a smooth dielectic and is nealy independent of wavelength since the index of efaction of the paint binde is nealy independent of wavelength. The peaks appeaing nea the mio eflection angles of 1º, 4º and 6º ae due to a glosslike component of suface eflection. The gloss peaks vay slightly in magnitude with wavelength. Away fom the peaks, thee is a nealy constant (i.e., ideal diffuse) BRDF, which aises fom the subsuface eflection. Since the subsuface eflection is wavelength dependent, the diffuse component is wavelength dependent.

7 We obseve stiking diffeences between the incidence-plane BRDFs fo the aluminized gound glass, the metallic paint, and the yellow paint in Figues 5, 8, and 11, espectively. The eflection patten of the aluminum suface (Figue 5) is due to fist suface eflection fom the ough suface, accounting fo the eflection peaks, and multiple eflections among oughness elements on the suface, poducing a nealy constant diffuse patten. At lage angles of incidence, the BRDF peaks ae at eflection angles beyond the mio eflection angle. The two paints, howeve, show stong gloss-like peaks nea the mio eflection angle. Fo the metallic paint (Figue 8), the peaks aise fom metal flakes within the paint binde, wheeas fo the yellow paint (Figue 11), the peaks aise fom a suface glossiness. Futhe, the metallic paint shows only a weak o nonexistent diffuse eflection away fom the gloss-like peaks (Figue 8), wheeas the yellow paint shows a stong nealy ideal-diffuse eflection away fom the glossy peaks (Figue 11). Figue 12 povides a compaison of the integated and sepaately-measued diectional-hemispheical eflectances fo the yellow paint, ove the visible wavelength ange, and the ageement is to within a few pecent. Fo this figue, the Fesnel component has been excluded fom both cuves. 7. EXAMPLE IMAGE Finally, we demonstate the use of ou instument fo its designed pupose by endeing a ealistic image of a 3- dimensional scene. We adapted the BRDF measuements of silve paint pesented in Section 6.1 fo endeing by appoximating them with smooth basis functions. 26 This epesentation offes both poven accuacy and the computational efficiency needed fo endeing, whee each BRDF may be evaluated millions of times to geneate a single image. Figue 13 was then endeed using Blue Moon Rendeing Tools, a RendeMan TM -based pogam that implements high-quality ay tacing. 27 A custom RendeMan TM shade pogam (available at was witten to implement ou BRDF appoximation. The ca body uses ou measued eflectance, with an additional Fesnel tem to model eflection fom the smooth suface. The convincing appeaance of this image demonstates the usefulness of endeing fom actual physical measuements, and the capability of ou instument to povide these measuements. 8. CONCLUSION We have pesented an automated thee-axis gonioeflectomete designed to meet the needs of compute gaphics. The instument can cove almost the entie angula domain of an isotopic BRDF, coves the entie visible spectum with ample wavelength esolution, and is apid enough to measue eal mateials in a pactical time (less than ten hous.) The angula ange coves the entie incident and eflection hemisphees to an angle of at least 85, with the exception of a cone of appoximately 7 aound eto-eflection. We measue 31 wavelength samples coveing the visible spectum (4nm-7nm) in one snapshot. Ou initial measuements have validated the accuacy of the instument. Computegeneated images based on the measuements ae ealistic and physically plausible. ACKNOWLEDGEMENTS The authos would like to thank Donald Geenbeg, Huf Sheldon, and Eic P. F. Lafotune of the Conell Pogam of Compute Gaphics fo thei encouagement and technical suppot. Equipment was donated by the Imaging Science Division of Eastman Kodak (Lay Iwan) and the Hewlett-Packad Company; the silve paint sample was donated by Fod Moto Company. This eseach was suppoted by the NSF Science and Technology Cente fo Compute Gaphics and Scientific Visualization (ASC ), by the NSF Themal Systems Pogam (CTS ), and by the NSF Infomation Technology Reseach Pogam (ACI ).

8 REFERENCES 1. D. P. Geenbeg, K. E. Toance, F. X. Sillion, J. Avo, J. A. Feweda, S. Patanaik, E. P. F. Lafotune, B. Walte, S. C. Foo, and B. Tumboe, A famewok fo ealistic image synthesis, Comput. Gaph. Poc., Annual Confeence Seies (SIGGRAPH95), (1995). 2. X. D. He, K. E. Toance, F. X. Sillion, and D. P. Geenbeg, A compehensive physical model fo light eflection, Comput. Gaph. 25 (SIGGRAPH91), , L. Davis and J. G. Kepos, Impoved facility fo BRDF/BTDF optical scatte measuements, in Stay Radiation V, R. P. Beault, ed., Poc. SPIE 675, (1986). 4. T. A. Geme and C. C. Asmail, A goniometic optical scatte instument fo bi-diectional eflectance distibution function measuements with out-of-plane and polaimety capabilities, in Scatteing and Suface Roughness, A. A. M. Zu-Hun Gu, ed., Poc. SPIE 3141, (1997). 5. X. Feng, J. R. Schott, and T. Gallaghe, Compaison of methods fo geneation of absolute eflectance-facto alues fo bi-diectional eflectance-distibution function studies, Appl. Opt. 32, , J. E. Pocto and P. V. Banes, NIST high accuacy efeence eflectomete-spectophotomete, J. Res. Natl. Inst. Stand. Technol. 11, (1996). 7. J. J. Hsia and J. C. Richmond, Bidiectional Reflectomety Pat I. A high esolution lase bi-diectional eflectomete with esults on seveal optical coatings, J. Res. Natl. Inst. Stand. Technol. 8A, (1976). 8. S. Mainguy, M. Olivie, M. Josse, and M. Guidon, Desciption and calibation of a fully automated infaed scatteomete, in Optical Scatte: Application, Measuement, and Theoy, J. C. Stove, ed., Poc. SPIE 153, (1991). 9. B. T. McGuckin, D. A. Hane, R. T. Menzies, C. Espoles, and A. M. Bothes, Diectional eflectance chaacteization facility and measuement methodology, Appl. Opt. 35, , T. F. Schiff, M. W. Knighton, D. J. Wilson, F. M. Cady, J. C. Stove, and J. J. Butle, Design eview of a highaccuacy UV to nea-ir scatteomete, in Optical Scatteing: Application, Measuement, and Theoy II, J. C. Stove, ed., Poc. SPIE 1995, (1993). 11. D. R. White, P. Saundes, S. J. Bonsey, J. van de Ven, and H. Edga, Reflectomete fo measuing the bidiectional eflectance of ough sufaces, Appl. Opt. 37, , W. Eb and M. Kystek, Ein neuatiges 3D-Gonioeflektomete, Optik, 83, 51-54, G. J. Wad, Measuing and modeling anisotopic eflection, Comput. Gaph. 26 (SIGGRAPH92), , K. F. Kane, H. Maye, and M. Gevautz, Am image based measuement system fo anisotopic eflection, Compute Gaphics Foum (Euogaphics 96 Poceedings) 15, (1996). 15. R. J. Castonguay, New geneation high-speed high-esolution hemispheical scatteomete, in Optical Scatteing: Application, Measuement, and Theoy II, J. C. Stove, ed., Poc. SPIE 1995, (1993). 16. K. Dana, S. Naya, B. Ginneken, and J. J. Koendeink, Reflectance and textue of eal-wold sufaces, ACM Tans. Gaph. 18, 1-34 (1999). 17. S. R. Maschne, S. H. Westin, E. P. F. Lafotune, and K. E. Toance, Image-based bidiectional eflectance distibution function measuement, Appl. Opt. 39, , R. A. Hall, Compaing Spectal Colo Computation Methods, IEEE Comput. Gaph. Appl. 19, No.4, 36-45, (1999). 19. Ameican Society fo Testing and Mateials, Standad Pactice fo Angle Resolved Optical Scatte Measuements on Specula o Diffuse Sufaces (Ameican Society fo Testing and Mateials, West Conshohocken, PA, 1996), Standad E S. C. Foo, A gonioeflectomete fo measuing the bidiectional eflectance of mateial fo use in illumination computation, M.S. Thesis (Conell Univesity, Ithaca, NY, 1997). 21. H. Li and K. E. Toance, Validation of the Gonioeflectomete, Technical Repot PCG-3-2 (Pogam of Compute Gaphics, Conell Univesity, Ithaca, NY, 23). 22. A. Gynbeg and G. Wad, A new tool fo eflectomety, Monogaph 161, (Lawence Bekeley National Laboatoy, Bekeley, CA, 199). 23. P. Shiley and K. Chiu, Notes on adaptive quadatue on the hemisphee, Technical Repot 441 (Depatment of Compute Science, Indiana Univesity, Bloomington, IN, 1994). 24. A. W. Spingsteen, J. Leland and T. M. Ricke, A guide to eflectance mateials and coatings, Labsphee Copoation (Noth Sutton, NH, 199).

9 25. K. E. Toance and E. M. Spaow, Theoy fo off-specula eflection fom oughened sufaces, J. Opt. Soc. Am. 57, (1967). 26. E. P. F. Lafotune, S. C. Foo, K. E. Toance, and D. P. Geenbeg, Non-linea appoximation of eflectance functions, Comput. Gaph. Poc., Annual Confeence Seies (SIGGRAPH97), (1997). 27. L. Gitz and J. K. Hahn, BMRT: A global illumination implementation of RendeMan standad, Jounal of Gaphics Tools 1, No.3, (1996). Table 1: Technical Paametes of the Gonioeflectomete Light Souce: Souce Powe Dift:.3% + 5mA Solid Angle: s Detecto: Solid Angle:.128 s Signal Readout Resolution: 16 bit Detecto Dynamic Range: 1:22, Electon Sensitivity: 1,9 photoelectons/count Spectal Range: 386nm-711nm Spectal Resolution: 2.8nm Mechanical System: Rotation Stage 1 Range: ~36 Rotation Stage 1 Resolution:.1 Rotation Stage 2 Range: ~18 Rotation Stage 2 Resolution:.1 Rotation Stage 3 Range: 7 ~18 Rotation Stage 3 Resolution:.13 Test Sample: Dimension of Sample Suface: 13mm 13mm Illumination Spot: 25mm diamete Unifomity of Illumination: within ±5% Maximum Angle of Reflection: 85 Table 2 Recipocity assessment on Spectalon with the Gonioeflectomete i Reading Signal Relative Eo % % % % BRDF(s -1 ) Lines: Gonioeflectomete Points: Labsphee θ Figue 4. Compaison of measued and efeence BRDFs fo Spectalon in the plane of incidence fo i = 2, = 633nm, and ps and pp components of polaization } } ps pp

10 Absolute BRDF (s -1 ) θ = 6 i θ = 45 i θ = 3 i.4 θ i = 1.2 θ i = θ(degees) Figue 5. Incidence-plane BRDF of ough aluminum suface fo seveal incidence angles i ; = 55nm Absolute BRDF (s ) θ = 1 i θ = 3 i θ i = 7 θ i = 5 θ = 8 i θ (Degees) Figue 8. Incidence-plane BRDF of metallic silve paint fo seveal incidence angles i ; = 55nm BRDF (s -1 ) BRDF (s -1 ) Figue 6. BRDF of ough aluminum ove the mapped eflection hemisphee fo i = 1 and = 55nm Figue 9. BRDF of metallic silve paint ove the mapped eflection hemisphee fo i = 1 and = 55nm 1 Diectional Hemispheical Reflectance (%) OL75 Gonioeflectomete Wavelength (nm) Figue 7. Compaison of diectional-hemispheical eflectance of ough aluminum as measued by two instuments, i = 1 Figue 1. Compaison of diectional-hemispheical eflectance of metallic silve paint as measued by two instuments, i = 1

11 Diectional Hemispheical Reflectance (%) Gonioeflectomete Figue 11. Incidence-plane BRDF of glossy yellow paint fo seveal incidence angles i; = 45, 65nm OL Wavelength (nm) 65 Figue 12. Compaison of diectional-hemispheical eflectance of glossy yellow paint as measued by two instuments, i = 1 Figue 13. Compute-geneated image based on measued BRDF of the metallic silve paint 7