Display Reflectance Model Based on the BRDF

Transcription

1 CITATION: E. F. Kelley, G. R. Jones, and T. A. Germer, "Dsplay Reflectance Model Based on the BRDF." Dsplays, Vol. 19, No. 1, June 30, 1998, pp (June 1998). Dsplay Reflectance Model Based on the BRDF Edward F. Kelley, George R. Jones, and Thomas A. Germer NIST, Gathersburg, MD 20899, USA ABSTRACT: Many flat panel dsplays (FPDs) have ant-reflecton surface treatments that dffer n character from those of tradtonal cathode-ray-tube dsplays. Specular reflecton models (mrror-lke, producng a dstnct mage) combned wth dffuse (Lambertan) reflecton models can be entrely nadequate to characterze the reflecton propertes of such dsplays. A thrd reflecton component, called haze, exsts between specular and dffuse. Dsplay metrology should account for the haze component of reflecton. That s best done usng the bdrectonal reflectance dstrbuton functon (BRDF). The effects of usng oversmplfed reflectance models are dscussed n contrast wth a parameterzed BRDF. INTRODUCTION: Flat panel dsplays (FPDs) can have reflecton propertes that dffer substantally from ther cathode-raytube (CRT) counterparts. In the case of the CRT, the necessty of the thck front glass prevents strongly dffusng surface treatments from beng used on the front surface. Such treatments, dstant from the pxel surface, would compromse readablty. Wth FPDs the front surface can be very close to the pxel surface, permttng surfaces that substantally dffuse ncdent lght wthout serously compromsng the dsplay s resoluton. (Ths s easy to see: Take wax paper and hold t about 1 cm above some text; compare the readablty for that confguraton wth the readablty when the wax paper s placed drectly upon the text.) Therefore, CRTs are often made wth very mld surface treatments to dffuse the specular lght, but ther surfaces cannot be as dffusng as those that can be used wth some FPDs. Because strongly dffusng surfaces can be used n connecton wth FPDs, conventonal reflecton measurement technques used to characterze dsplay reflecton for CRTs may well prove to be nadequate or, at the very least, rreproducble when appled to all FPDs. In ths paper, when we refer to dffuse reflectance, we refer to an deal Lambertan reflector that obeys the relaton: L = qe = E d /, (1) where L s the lumnance, E s the llumnance, q = d / s the lumnance coeffcent, and d s the dffuse (Lambertan) reflectance. That s, the lumnance s ndependent of drecton. When we refer to specular reflecton, we mean mrror-lke reflecton that produces a dstnct vrtual mage of the source where the reflected lumnance L s related to the source lumnance L s by: L = s L s, (2) where s s the specular reflectance. A more general way to descrbe reflecton s through the bdrectonal reflectance dstrbuton functon (BRDF). It s the dfferental form of Eq. 1 and wll be developed n the next secton. Usng the BRDF, we can account for the above specular and dffuse (Lambertan) propertes, but also understand a thrd type of reflecton that exsts between the two extremes of specular and dffuse (Lambertan) reflecton. Ths thrd component of reflecton s quckly dentfed by the eye when t vews electronc dsplays. For want of a better term we wll call t haze (see ASTM E284 1 and D ). Haze reflecton s smlar to dffuse (Lambertan) reflecton n that t depends upon the llumnance (source-dsplay dstance), whereas t s smlar to specular reflecton n that the lumnance s peaked n the specular drecton. In Fg. 1 we show drawngs of the three types of reflecton and ther combnatons. Usng a bare bulb of a flashlght placed 200 mm or more n front of the screen, the sgnfcant components of the reflecton are easly observed and appear dstnct from one another. The dffuse (Lambertan) component s seen as an overall gray, as f t were a dark-gray matte pant, slghtly brghter where the screen s nearest the source and gradually darker near the edges of the dsplay because of the 1/r 2 falloff n llumnance. The specular (mrror-lke) component s the vrtual mage of the pont source seen n the dsplay surface. The haze component s the dstnct fuzzy ball of lght that surrounds the specular mage. Sometmes the 1

2 haze component can be very slght (as wth televson pcture tubes), other tmes the haze component can be the domnant reflecton component (as wth many FPDs found n laptop computers). It s mportant to realze that not all components of reflecton need to be observable. In practce, at least one of the three components must exst (Fg. 1a, b, c). Further, any combnaton of all three components s possble. There are dsplays that have almost entrely dffuse (Lambertan) surfaces (e.g., whte copy paper Fg. 1a). There are dsplays that have no specular component and have only a haze component wth the dffuse (Lambertan) component beng neglgble (10-4 or less than the sze of the haze reflecton peak n the specular drecton Fg. 1c). When the reflecton of a pont lght source s observed n screens havng only a haze component, only a fuzzy patch of lght s seen n the specular drecton, and no dstnct mage of the source s observed. There are dsplays that do not have a substantal haze component and exhbt only specular and dffuse (Lambertan) reflectons (Fg. 1d). Many televson CRT pcture tubes are of ths nature. In all these cases, a thn-flm antreflecton coatng can be added to further reduce the reflectons from the front surface of the screen, makng the surface of the dsplay appear qute dark. Ths s especally true n the case of 1b, 1c, or 1f where the dffuse (Lambertan) component s ether absent or neglgble. One way to vew the BRDF s to drect a narrow laser beam at the screen and vew the reflected lght aganst a large whte card n a dark room. The dstrbuton of the lght on the whte card s the projecton of the BRDF upon a plane. The specular and dffuse (Lambertan) components obey the above Eqs. 1 and 2. A more elaborate formalsm s requred to descrbe the haze component. When haze s present, the reflecton measurement becomes dependent upon vrtually every confguraton parameter of the apparatus and measurement nstrumentaton (the dstance, orentaton, sze, and unformty of the lght source; the dstance, entrance pupl, feld of vew, and focus of the lght measurng devce; etc. 3 ) BIDIRECTIONAL REFLECTANCE DISTRIBUTION FUNCTION FORMALISM: The reflecton model offered here s based on the mathematcal formalsm for the bdrectonal reflectance dstrbuton functon (BRDF). 4 Only comparatvely recently has an effort been made to examne the BRDFs assocated wth electronc dsplay surfaces n order to better characterze dsplay reflecton. 5,6 Neglectng any wavelength and polarzaton dependence, the BRDF s a functon of two drectons, the drecton of the ncdent lght (, n sphercal coordnates) and the drecton from whch the reflecton s observed ( r, r n sphercal coordnates). Snce not all screens exhbt a wavelength ndependent reflecton and because many lqud crystal dsplays (LCDs) and glare-reducng cover screens for CRTs exhbt polarzng propertes, care must be exercsed n applyng these assumptons. The BRDF relates how any dfferental element of ncdent llumnance, de from drecton (, ), contrbutes to a reflected lumnance dl r observed from drecton ( r, r ): dl, ) B(,,, ) de (, ), (3) r( r r r r where B(,, r, r ) s the BRDF. (In the lterature the BRDF s often denoted by f r. We use B to avod complcated subscrpts and confuson wth other uses of f wthn the dsplay ndustry.) By ntegratng Eq. 3 over all ncdent drectons n space, the lumnance L r ( r, r ) observed from any drecton ( r, r ) can be calculated. The llumnance contrbutons de can be related to lumnance sources n the room. For each element of sold angle da /r 2 = d = sn d d there s a source lumnance L (, ) at a dstance r from the screen producng llumnance de L (, )cos d L (, )cos sn d d, (4) where the cosne term accounts for the spreadng of the llumnance over a larger area as the nclnaton angle from the normal ncreases. Methods for obtanng the BRDF are well documented. 7,8 Most often, a collmated beam of lght of radant flux s allowed to be ncdent upon the sample from drecton (, ). The radant flux r scattered nto a drecton ( r, r ) and nto a sold angle (the detector) s measured. The BRDF s then approxmately B = r /( cos r ). Generally, both the source and detector cannot be along the normal at the same tme snce one obscures the other. In practce, the detector s placed a few degrees s off normal, and the peak reflecton s observed when the source s s on the other sde of normal. We can capture these three types of reflecton explctly wth the BRDF formalsm n terms of three addtve components B D S H, (5) where the components are defned 6 as: 2

3 D q /, 2 S 2 (sn sn ) ( ), (6) s d r H H (,, r, r ). In the specular term the delta functons provde for a mrror-lke dstnct vrtual mage of the source n the vewed reflecton. 4 When we ntegrate ths three-component BRDF over all ncdent llumnaton drectons by combnng Eqs. 3-6, the reflected lumnance s gven by Lr ( r, r ) qe s Ls ( r, r ) H(,, r, r ) L (, ) cos( ) d. 2 2 / 2 0 The frst term on the rght hand sde of Eq. 7 s the famlar Lambertan reflecton where E s the total llumnance from all drectons. The second term s the famlar specular reflecton where the specfcaton of ( r, r ±) smply selects the lght from the vewng drecton ( r, r ) reflected about the normal (z-axs),.e., the specular drecton assocated wth the vewng drecton. The last term s the haze contrbuton. See Fg. 2 for an example of a BRDF taken for the case of Fg. 1g. 9 The ultmate goal of ths research s to provde smple methods to obtan a parameterzaton for the BRDF. Two of those parameters are already famlar the dffuse (Lambertan) reflectance d and the specular reflectance s. We would expect the haze component to be specfed by a peak h, a wdth w at some level, and perhaps several shape parameters a, b,, etc. The realzaton of ths goal wll provde a means to calculate the reflected lumnance observed for a dsplay placed n any ambent-lght envronment. Dsplay reflectons allow us to take advantage of some smplfcatons: Most dsplays are vewed from the normal or nearly normal drecton, and the range of angles to observe the entre screen from the normal poston s usually less than ±30. It wll often be found that the shape of the BRDF does not change dramatcally over ths vewng-angle range. Thus, a reduced BRDF B(, ) B(,,, ) s adequate for most reflecton characterzatons, and we can drop the subscrpt n the followng, so we can wrte: B(, ) B(,,, ). If the BRDF s seen to be axally symmetrcal about the specular drecton then the BRDF s ndependent of, and B(, ) B( ). An example of such an n-plane BRDF s shown n Fg. 2. In Fg. 3 we show a comparson of dfferent observaton drectons for n-plane BRDFs obtaned usng a dsplay for whch there s only a non-trval haze component of reflecton. An llustraton of the nvarablty of the BRDF over the entre vewng surface of the dsplay s found n Fg. 4. The axal symmetry of the BRDF s one smplfcaton that we are not always able to make for all dsplays. Because of the pxel matrx structure beneath the front surface, spkes may be observed extendng out of the central BRDF profle (see Fg. 5). Such measurements are hghly non-trval. Fgure 5 suggests a method to obtan the BRDF by takng a pcture of the reflectance of a pont lght source usng a calbrated electronc camera, and determnng the needed profles from an analyss of the pcture. However, wth ths procedure, the measurement mght be corrupted by velng glare from the camera-lens-detector system. In Fg. 6 we show a comparson between several dfferent types of CRT and FPD dsplays. (AR refers to a mult-layer ant-reflecton coatng.) You wll note that the CRTs have a specular component that s roughly a factor of ten greater than the maxmum haze peak observed for the FPDs. The wdth of the specular component s ndcatve of the resoluton of the apparatus used (<0.5 ). Observe that there are two BRDFs shown for FPD2 for the horzontal and the vertcal plane. The pattern observed s very much lke that shown n Fg. 5. The vertcal BRDF for FPD2 ndcates that ths dsplay s almost a factor of ten lower n reflectance than the other dsplays for sources at large angles from the drecton of the observer. Indeed, the blackness of ths dsplay s mpressve even n a brght room. Note also that for the FPDs, the haze peaks appear relatvely flat over a ±0.5 or larger regon about the specular drecton, or so t would seem. Ths s on a log scale. However, on a lnear scale a substantal change s observed over ±0.5 from the specular drecton (see Fg. 7). CONVENTIONAL REFLECTION MEASUREMENTS: There are three types of reflecton measurements commonly employed for electronc dsplays: large-source dffuse measurements, large-source specular measurements, and small-source specular measurements see Fg. 8. Let s calculate the lumnance measured for each apparatus usng the form n Eq. 7. In dong ths we wll often take advantage of the fact that for small angles, the sne and tangent are approxmately equal to the angle n radans. LARGE-SOURCE DIFFUSE MEASUREMENT: Here we have two unform lamps each havng an ext port of dameter a (radus r = a/2 havng a subtense of a from the screen, typcally 15 ) placed at ± s (typcally 30 or more) on each sde of the normal. The detector vews the center of the screen from the normal drecton. From 0 r (7) 3

4 Eq. 7 the lumnance arses from two factors, the llumnance E = 2L s = 2L s r 2 /d 2 from the lamps, and an ntegraton of the haze over the surface of the lamps: 2 r L 2Ls d H( )cos sn d. (8) 2 d ExtPort The frst term s the lumnance from the dffuse (Lambertan) component. The second term s the contrbuton from the haze. Note, n Fg. 9 how much the haze can vary over the surface of the lamp (± a /2) for our two FPDs. To obtan an order of magntude estmate of the haze term we can use H( s )cos( s )r 2 /d 2. The approxmate expresson for the lumnance then becomes L 2L s r 2 [ d + H( s )cos( s )]. Ths expresson s dentcal to the expresson for the lumnance f we permt the dameter of the ext ports of lamps to decrease to 1 so that they can be consdered as sngle sources wth sold angle = r 2 /d 2 each; then we obtan: r 2 L 2L s ( )cos d H s s 2, (small sources) (9) d whch s very senstve to the angle assocated wth the haze contrbuton. In Fg. 9 we see that at 30 the haze contrbutes on the order of to the dffuse (Lambertan) term that may be from 0.01 to for CRTs and much less (0.001) for many FPDs. The rapd change n the haze reflectance wth angle shows why ths measurement s senstve to the angular algnment of the lamps. LARGE-SOURCE SPECULAR MEASUREMENT: In ths case we look n the specular drecton at one of the large-dameter sources used n the large-source dffuse measurement (agan, typcally a = 15 and s s often set at 15 ). Equaton 7 becomes: 2 r a / 2r / d L Ls d s 2 H( ) cos sn d 2. (10) d Here, the man contrbuton for dsplays s from the specular component and the haze component (where we are ntegratng around the peak of the haze). If we were to examne only the haze profles, such as n Fg. 7, we mght thnk that snce the haze functons are very small at 7.5 and beyond (the typcal half angle of the lamp subtense from the screen), that ths ntegral would be relatvely nsenstve to the sze and poston of the lght source. However, when we look at the ntegrand, we see the effect of the ncrease n sold angle wth ncreasng for any ncrement d see Fg. 10. Sgnfcant errors can be ntroduced by a change n poston, dstance, and unformty of the lamp used because of the haze contrbuton. For example, f the subtense of the lamp were to change from 14 to 16 (half angle 7 to 8 n Fg. 10), the haze contrbuton n Eq. 10 would change by 6 %. SMALL-SOURCE SPECULAR MEASUREMENT: Ths s the same confguraton as the large-source specular measurement wth the dameter of the source subtendng approxmately 1 or less as vewed from the screen. The source has a sold angle = r 2 /d 2, and the lumnance s: 2 r L qe s Ls he ( q h) E s Ls Ls ( q h) s Ls ( d h) 2 s, (11) d where h s the peak of the haze profle. Note that as h s on the order of 10 sr -1 and the dffuse (Lambertan) reflectance s rarely hgher than 0.05, the dffuse term s neglgble n both the large-source and small-source specular measurements. Note also how the contrbuton of the haze depends upon the llumnance as does the dffuse (Lambertan) term. The dfference between the large-source and small-source measurements s prmarly the extent of the contrbuton of haze. It s because the dffuse (Lambertan) component s generally not an mportant factor n Eqs. 10 and 11 that these three measurements can gve smlar results for dsplays that look very dfferent to the eye. Consder Eqs. 10 and 11. Ther dfference les n how much of the wdth of the haze peak s used. If the haze were not present, they would gve the same result. We have essentally three varables (at least) and two specular measurements. The three varables (the mnmum number) are the haze peak h, the haze wdth w, and the specular reflectance s. The large-source specular measurement s senstve to all three varables, whereas the smallsource specular measurement s senstve only to the specular and the haze peak. We can, therefore, get the same measurements for dfferent lookng dsplays dependng upon how these components mx. Addng the large-source dffuse measurement does not allevate the problem snce t adds another varable, the dffuse (Lambertan) reflectance, d. We then have a total of four varables (at a mnmum) and three measurements. Ths results n the undesrable stuaton that reflecton propertes are not suffcently defned by these measurements to dstngush 4

5 dsplays that can appear very dfferent to the eye. Fgure 11 shows two hypothetcal dsplays that would appear very dfferent to the eye n how they reflect lght. However, the measured reflected lumnance would be the same usng the above three technques. The specular term shown here s related to the specular reflectance by s = s /, where s the sold angle of the entrance pupl of the detector as vewed from the screen. POSSIBLE ALTERNATIVES: Alternatve procedures are currently under nvestgaton. These alternatve methods are suggested prematurely n order to promote ther nvestgaton rather than to defntvely prescrbe a fully tested metrology for dsplay reflecton. Ther weaknesses need to be characterzed, and ther sources of error need to be understood. These procedures are ntended to extract the parameters assocated wth the BRDF model. The dffuse (Lambertan) parameter would be consdered to be the asymptotc lower level the BRDF reaches as the lght source s rotated away from the normal as n Fg. 13. Ths would most lkely result from a nonlnear curve ft to the BRDF profle n the cases where a clearly defned plateau s not dentfable at large angles. The haze peak and specular reflectance mght be obtaned by observng the reflectance of a dstant llumnated annulus subtendng 1 or less from the dsplay see Fg. 13. The specular reflectance mght be obtaned by subtractng the value of the center of the annulus from the average of the value of the lghted porton and compare the result to the lumnance of the source annulus. Unfortunately, glare n the lens system wll need to be corrected for an accurate haze-peak measurement. It may be possble to do ths by drectly vewng the annulus where t subtends the same angular sze as that observed n the reflecton. Wth FPDs that can be acheved smply by usng a mrror or black glass (approprately calbrated) at the surface of the dsplay. The shape of the haze profle may be obtaned ether from a two-dmensonal pcture (wth correctons for glare), or sngle measurements of the reflectance at wde angles. For example, once the haze peak s obtaned from the annulus apparatus, t may be only necessary to obtan the angle at whch the reflectance s 1/10 the value of the haze peak, or at a few other ponts, n order to characterze the shape of the haze profle adequately. Exactly what wll be requred remans to be determned. Currently the functons that we have been usng to ft the haze profles are of two forms: h 1 b b H( ), or H( ) h. (12) n m n n 1 w b u 1 w 1 u The wdths w and u are often very narrow n ths formulaton. The profles shown n Fg. 7 have been ft wth the frst functon (see Table 1). (Note that these fttng parameters are for llustraton purposes only and do not consttute an accurate measurement of reflecton.) It s hoped that more useful functons can be developed that wll provde precse assgnment of the parameters. As t s wth these functons, there s great lattude n determnng the best values for the parameters assocated wth the b-factor. Table 1. Reflectance Parameters for FPDs Parameter FPD1 FPD2H h (measured) w n b u m q (measured) CONCLUSION: When we consder the standard measurement technques n lght of the mathematcal formulaton of the BRDF, we fnd that those measurements fal to dentfy the parameters necessary to descrbe the BRDF. Rather, they tend to be measurements that mx the three components together n ways that do not readly permt the extracton of the functonal form of the reflecton. We desre to develop smple measurement technques that wll obtan the parameters assocated wth a mathematcal specfcaton of the BRDF. The realzaton of ths goal wll provde a means to calculate the reflected lumnance observed for a dsplay placed n any ambent-lght envronment. Also, when we consder an ergonomc study of the reflecton of dsplay surfaces, we want to have a metrology at our dsposal that relates to what we see and provdes dscrmnatng detal at a reasonably fundamental level. Only when we can specfy the mathematcally relevant reflecton parameters the dffuse (Lambertan) reflectance d, the specular (mrror-lke) reflectance s, the haze peak h, haze wdth w, and any haze shape parameters (a, b, ) can we say that we have unambguously descrbed reflecton n a meanngful and predcable manner. Then the ergonomst can make dstngushng evaluatons that are reproducble and relevant to what the eye sees, and then we wll have a fully meanngful metrology wth whch to evaluate dsplay reflecton qualty. 5

6 a) B = D b) B = S c) B = H d) B = D + S e) B = D + H f) B = S + H g) B = D + S + H Fg. 1. Illustraton of the three types of reflecton found n modern electronc dsplays. B refers to the BRDF that can have a dffuse (Lambertan) component, D, a mrror-lke specular component that produces a dstnct mage, S, and a haze component, H. At least one component must exst. There are four combnatons of the three components. Any or all of the three components can exst nontrvally, or one component can domnate whle the other two components make a trval contrbuton to the reflecton (as n the case of the frst three llustratons). 6

7 BRDF for 3 Specular Confguraton (sr ) -1 BRDF for 3 Specular Confguraton (sr ) Specular Component Value at zero s plotted at angle 0.01 for vsblty purposes on a log-log plot. Specular Component 1 Haze Component 1 Haze Component Dffuse Component Lght Source Angle (degrees) 0.01 Dffuse Component Lght Source Angle (degrees) Fg. 2. An n-plane BRDF of a sample materal havng all three components of reflecton contrbutng nontrvally. The graph on the rght s the same data usng a log scale on the abscssa. We plot the q = 0 values at q = 0.01 so that they are vsble on the graph. The negatve q values are plotted as postve values. The data were collected wth the detector at 3 usng a pont lght source. The angle specfes the poston of the lght source as measured from the specular drecton (at 3 from the normal) for whch the angle s set to = 0. 7

8 BRDF (1/sr) E-3 FPD1 Haze Component Domnant Specular Confguraton Angle Angle from Specular Drecton (degrees) Fg. 3. Comparson of BRDFs taken at dfferent specular angles on the same dsplay. Detector at 3, 10, 20, and 30 from normal. 8

9 Fg. 4. For many dsplays, the mage of the source appears to have approxmately the same shape as vewed at postons all over the screen from a sngle observaton pont near the normal. 9

10 Fg. 5. A dsplay BRDF that s not symmetrcal about the normal. 10

11 BRDF (1/sr) E-3 1E-4 CRT1 CRT: specular, dffuse, haze CRT2 CRT: specular, dffuse, haze, and AR FPD1 FPD: trval specular, haze (no AR) FPD2H FPD: only haze wth AR (worst case horzontal) FPD2V FPD: only haze wth AR (vertcal plane) Specular Orentaton of Source and LMD: ±3 to ±5 (Values at zero are plotted at 0.01 for vsblty on log scale.) Angle of Source from Specular Drecton n Degrees Fg. 6. Comparsons of n-plane BRDFs for CRTs and FPDs. The data for the FPDs employed an apparatus wth a 0.2 detector aperture. Both FPDs are LCDs. 11

12 BRDF (1/sr) Specular Orentaton of Source and LMD: ±3 Values at zero are plotted at 0.01 for vsblty on log scale. FPD1 FPD2H Angle of Source from Specular Drecton n Degrees Fg. 7. BRDF of FPD1 and FPD2H showng that the value of the BRDF can change substantally over even

13 Small-Source Specular L s a a L s d a L d z a s s L s d L s a d a s s Large-Source Dffuse L z Large-Source Specular Fg. 8. Common reflecton measurement confguratons. 13

14 BRDF (sr ) Specular Orentaton of Source and LMD: ±3 of normal FPD FPD2H Angle of Source from Specular Drecton n Degrees Fg. 9. BRDFs off normal for two FPD surfaces. 14

15 H( ) cos sn Angle from Normal n Radans, Angle from Normal n Degrees, Fg. 10. Integrand for large-source specular contrbuton from haze usng the data for FPD1. 15

16 BRDF (sr ) DISPLAY 1 DISPLAY 2 s 1 s 2 1 h h q 1 a s s q 2 90 Fg. 11. Two BRDFs that could produce the same measurement results usng conventonal technques. However, the dsplays would appear very dfferent to the eye f a pont source were observed n the reflecton as n the above mages. 16

17 Source Detector Fg. 12. The dffuse (Lambertan) term, f non-trval, wll be ndcated by the haze asymptotcally reachng a constant as the angle of the lght source from the normal ncreases toward 90. Note that the detector would have to measure the entrety of the elongated llumnated area. Otherwse, the detector would have to measure wthn the llumnated area, correct the readng wth 1/cos, and the llumnaton would have to be very unform over ts crosssecton. 17

18 Center Cross-Secton D+S+H S D+H < 1 POSITION Fg. 13. The haze peak added to the dffuse component may be observable at the center of an annulus that s suffcently small. The specular component would be obtaned wth the same apparatus by subtractng off the haze peak and the dffuse component makng approprate correctons for glare. 18

19 FIGURE CAPTIONS: Fg. 1. Illustraton of the three types of reflecton found n modern electronc dsplays. B refers to the BRDF that can have a dffuse (Lambertan) component, D, a mrror-lke specular component that produces a dstnct mage, S, and a haze component, H. At least one component must exst. There are four combnatons of the three components. Any or all of the three components can exst nontrvally, or one component can domnate whle the other two components make a trval contrbuton to the reflecton (as n the case of the frst three llustratons). Fg. 2. An n-plane BRDF of a sample materal havng all three components of reflecton contrbutng non-trvally. The graph on the rght s the same data usng a log scale on the abscssa. We plot the q = 0 values at q = 0.01 so that they are vsble on the graph. The negatve q values are plotted as postve values. The data were collected wth the detector at 3 usng a pont lght source. The angle specfes the poston of the lght source as measured from the specular drecton (at 3 from the normal) for whch the angle s set to = 0. Fg. 3. Comparson of BRDFs taken at dfferent specular angles on the same dsplay. Detector at 3, 10, 20, and 30 from normal. Fg. 4. For many dsplays, the mage of the source appears to have approxmately the same shape as vewed at postons all over the screen from a sngle observaton pont near the normal. Fg. 5. A dsplay BRDF that s not symmetrcal about the normal. Fg. 6. Comparsons of n-plane BRDFs for CRTs and FPDs. The data for the FPDs employed an apparatus wth a 0.2 detector aperture. Both FPDs are LCDs. Fg. 7. BRDF of FPD1 and FPD2H showng that the value of the BRDF can change substantally over even 0.5. Fg. 8. Common reflecton measurement confguratons. Fg. 9. BRDFs off normal for two FPD surfaces. Fg. 10. Integrand for large-source specular contrbuton from haze usng the data for FPD1. Fg. 11. Two BRDFs that could produce the same measurement results usng conventonal technques. However, the dsplays would appear very dfferent to the eye f a pont source were observed n the reflecton as n the above mages. Fg. 12. The dffuse (Lambertan) term, f non-trval, wll be ndcated by the haze asymptotcally reachng a constant as the angle of the lght source from the normal ncreases toward 90. Note that the detector would have to measure the entrety of the elongated llumnated area. Otherwse, the detector would have to measure wthn the llumnated area, correct the readng wth 1/cos, and the llumnaton would have to be very unform over ts crosssecton. Fg. 13. The haze peak added to the dffuse component may be observable at the center of an annulus that s suffcently small. The specular component would be obtaned wth the same apparatus by subtractng off the haze peak and the dffuse component makng approprate correctons for glare. 19

20 REFERENCES: 1 ASTM Standards on Color and Appearance Measurement, 5 th edton, E a, Standard Termnology of Appearance, defnton of haze, p. 243, ASTM Standards on Color and Appearance Measurement, 5 th edton, D (Reapproved 1995), Standard Test Method for Vsual Evaluaton of Gloss Dfferences Between Surfaces of Smlar Appearance, pp , Ths dscusses dstnctness-of-mage gloss and reflecton haze. 3 To be publshed. 4 F. E. Ncodemus, J. C. Rchmond, J. J. Hsa, I. W. Gnsberg, and T. Lmpers, Geometrcal Consderatons and Nomenclature for Reflectance, NBS Monograph 160, Natonal Bureau of Standards, Gathersburg October M. E. Becker, Evaluaton and Characterzaton of Dsplay Reflectance, Socety for Informaton Dsplay Internatonal Symposum, Boston Massachusetts, May 12-15, 1997, pp Dr. Becker also makes reference here to the work by J. C. Stover, Optcal Scatterng, Measurement and Analyss, SPIE Optcal Engneerng Press, Bellngham, Wash., USA, E. F. Kelley and G. R. Jones, "Utlzng the Bdrectonal Reflecton [should be Reflectance] Dstrbuton Functon to Predct Reflectons from FPDs," Socety for Informaton Dsplay Internatonal Symposum, Boston Massachusetts, May 12-15, 1997, pp ASTM Standards on Color and Appearance Measurement, 5 th edton, E , Standard Practce for Angle Resolved Optcal Scatter Measurements on Specular or Dffuse Surfaces, pp , Ths refers also to reference 8. 8 ASTM Standards on Color and Appearance Measurement, 5 th edton, E , Standard Practce for Gonophotometry of Objects and Materals, pp , Note that the data presented n ths paper are for llustraton purposes only. The combned standard uncertanty n all the present measurements s estmated to be ±10% of the measurand usng a coverage factor of two. 20