Visual Appearance of Matte Surfaces shree K

!"#$%
&('*)+,+"-. /"021304)5046879;:=<'804+?>A@)+?6
BC+,D*0E)GFGHI+,6JFLK4MNLKJHD8OPFG+?)Q&R<$:S+,6*<$+
NLKT>SO*HU*:S0VC6*:XW3+?)YZ:XF[1
/"+$\^]KT)_`/C]
ikj4l#mRnolqpsrklutSt=vxwSy2lqz|{Gvxz|rkvAw=nlq}~{€2vƒ‚u{{Zt=vxwSw=v„{$…
a,bTbdcJe3` Vf.X& .hg
"!#%$&'("(")"+*,-./!101324*5+6$/!1270189!1/"701:;&<='>*5/10<@?BADC'+
*//E01C7F%GH>*501(@=!I5J/*50K*%;LM'!LN:*5/EOP1*%'.01Q:!1<SRT01CVU./)"'324*/01:?VW!1X
J/*%0#*5PU;-DLY:!.U.0I01P'!LN:*5/=+;-/I*5!1(&/-Z01C/0[*\'0I'!1>=01C'P%GH>*50;LMU.:*5!1]1*5:\'*
7!LN"*%E'-'+0I""P(U.):^&7!1):C0I'/I5?ADC'EU;-0#/_@/019"*`*5"'0*5:U;\'(a=\7C<7+*
\'C'`'"U;`b*cC9"U."_(')'$@C"-RT(')d-=01!I!15J/*501("&0RD`E\e:0#";0IC'b'!LN:*5@$
-=C7RT901E:**5'!K0I<E\'!I/-+*50f01C7b/\'\/!K*5gLh^RT+-8!#7)"b/L/01'!K'!LN:*5/%?ADC'
U9\'+*0I"iLj01C'/!1/'0KkLY:!C'U./F:$'U."*#C'('b("$/-l*%"U;\'701!T):!#\7C'*8!I
-U9"01!#/01/-E')M&e:01C.!1>4-d!1-!1/-EUm)">j/LB01C'!IXN-U9("/:&'n/*50K5?o6=\!10I*5X
'+!$4a0I!1U9p'!LN:*5E!1:')"C7'/1*/Q*E"&'n>*50#0I.\'!1-*5d(C':'010Ip(U.):/-@"+-lL
C"-(')'$\'!1>*5-')M+/\e`!#*5\701:.Lh"&'n/*508C\@?
(0I!#B-d1*%'\'0I"!K /!1T_'/RTE01ba\'("00IC'(! (0I*50LY"!h01C' 01!K"*50I"M&0RD
()"C0T/-FU./01!I/$0Id*5"@<9*5"U9\e`(')MC/\E*5'>i01d01C7^:&`!1@!
N? %J/*50I"9L
()"C0T&<.U./01!I/iUm><9&eM(RD>-F:01C7^2!K0TLY'-'/U;0#\7!1*5/I (lB\!#*5`\'01("l&<
C'U.:! U.:*cC7'@?4("!1%J/*50K*5U;>*cC/'U;*/p&D&7!1@:-<M*5+"I 2/-b01T0RDg*0I)":!1(/ 7!LN"*%-d&e-<@?Do6.'!LN:*5b!I5J/*50I:$@):C0!K><7D/!1b!I5J/*%01/-d0 01C'b(0I!LN:*5T&0RD`=0IC'
7!LN"*%=U;>-'U -Q(!? '"!@!I<[U;@:01CS'!LN"*5/%$01C'+!1/'0KS\/*%'/!b"!U;(!1!1:!1XY(_@
\7\e>!#/*5@$01C7^`RD/-.7!LN"*%^\7!1-*%')9=*%//!T(!101Um)"gL(0#T7!1!1:'-(')@801C/0+
)"`"U;0I!1+*(<M-01:!101>-=RTC';0IC''!LN:*5b'"0 \'/! N?fb01C''!LN:*5b):0#!1"7)"C'!`$0IC'
!10I(U.):=&):01P&'('!$h0I!1(')['!LN"*5m\'\//!#*5;LY!1"U C7<P01P)"(@I<@$/- @
-3GHbLY"!8C'):C.!1"7)"C''>1:('/%? @'!LN:*5!15J/*501(";+T*5"U9U;"$"LY:!(0K*5]$.U;`0#+5?
o E&-<E!I5J/*%01:$"(*5-0():C0B!#<7 \'0I!#0IT01C'8'!LN:*58-=/!181*`010I!1>-E!1:'-'901l!I5J/*%01:-Q!15LY!K"*50I"p*//-P&< ('C'"U9")"`'0I/TRT0IC'S01C'9'!LN"*59U;/-('Ul?
@:U;L0IC'T()"C0T'!I)"<.U.<;&E/&:!1&/-l&<F0IC'E'!LN:*5p:!0I!#/U;(010I/-;01C'!I"'):CP0?kADC'
!1`U.('')b2-' (0#RT<;&:*c_d01d01C'g01!LN"*5b0IE!1XYU;`!1)"g"D&-<.!I5J/*50I:?ADC'b!K-:U
/01'!ITL,'&7X6'!LN:*5bI*0I01!I') */ U9!1):')T()"C0f!K><701&8-01!1(&''0I/-^(dRT- !#/')"
Lh-!1>*501("%$")"((')01C'g'!LN"*5g^Um010I8\'\//!#/*5@? D-<E!I5J/*%01:=\7<'-:U;/0h!1"(
SU.0I!1+b(_@9*5<@$\'+"0I!$*%"*5!I01]$- \/\e`!?Qo6 U.<P/01'!KTU./01!I+bC'/RD@!`$
&"0IC.'!LN"*58/-=&-<dU;/*#C7U9*5@a0 -E01:)"0IC'! -0I!1U;('f2/e4/\'\/!K*5]?
0IC'U./01+*BU;-+LY"!&"01CS!15J>*501("QU;/*#C'+U95$&"/- : \'C<'*/-Q)":U;01!I*/
"\701*`5$'C@b&[01-(/-;a01@(<@?
:!&e-<E!15J>*501("$"'U;`!1"U;-C@D&97)")">01>- LY:!f01C'8I*0I01!I')g\'!1*5>1
$ $ 6?8U;"')0IC'/]$ Ud&!1!0 "
R #6$\7!1"\]/-.$ ##%$e!IU./f01C7^U9@0RT+-<d/S+/T\<7*cC7"\'C<'*& '#6$*5:U;\''0K01("/D"()N$f!1U9"01m'*) %#6$- *%"U;\'701!
)"!K\'C7*+ ,-6?ho60\'!1/-*50KH01C/0 0IC'&'!1()"C01'/I5$":! !K"-+*%@$ .0/`$/L4M-//@U.0I01'!LN:*5D\:0
2 31 *5@456$RTC'!I 6'$01C' (&e>-;"!g!15J>*501((0<]$ !I\'!I/0#T01C7^LY!#:*501("[L 01C'M01:0#h*5+-0
()"C0!15J>*501/-E&<=0IC'7!LN"*%@$2- 45H+i01C7b*%-*58'):b&0R d01C''!LN:*5b':!1U./401C7F(('U;01("S-!I/*50I",? ADC'.\"\'7!I0<VLUd&!1!0 pU;-`T*/ &[0I01!I&''0I/- 0IP0K
&7(0<p01M\'!1>-*50RT(01C.bLN! -`)"!1`/L:**5'!K"*5<E0IC'b/\'\/!K*%^/Lh^+!1):\/*%01!17U LB!1>X
RD:!1+- U./01!I/5?B7"01C7!f!1>":;f'-"'&701/-(<E0KiU;\7U.0IC'U./01+*"LY:!1UP$"RTC7*#CE-7
0K3Lb0I 'U;!I"p(0I!1/01(')Q\'\//!#/*5P\'!I"\!10I/ LY:!=0IC'"!I01+*5/d-V\'!#:*501(01:'!K
(_@@$401C';dL Ud&!10! +R F0IU;\'0K01("Q- .*%'0b0Il!I/+0?&D"0IC !1/::^C@d/01d0KDRT->\'!I/"-..'-!#0#/-7);/-FUd'+01(')p\!K*5\'0I:F/LU9\e:!10K0DB*5'>
*cC["8C"-(')'?
ADC'pU;]0k\'\//7);:\/*50T/L+Ud&!1!0 i+R +D0#D\7!1/-+*501(";0IC0801C7^&7!1):C0I'/IDL
d1*57^\:0+D-`\e`-0TL0IC'"&!1@`! D`RT\e:0?ADC'+ (.01'!IP*/l&a\7"(01/-;0I
/0#&7C01C/0f81*5`'\e:0 (('U;01>- &<`@!#/"()"C0B:'!#*5> */p&(RD>-^:(('U;01>&<;E'):"'!K*5RTC'@^(0I0<d-.-(!1/*%01:.!Ib)"(@.U;\'(<p&<=0IC'M*501!I"-ELj(H0IC'
:'!#*%/5? ''!I01C'`!1U;:!1@$f0IC'['!LN"*5['"!IU.8/-Z/&/- /LMQ1*57F\:0;*/Z&.'' '`<
-0I!1U9'/-=LY!I"U 0K&'!I)"C017/1b:('/bU;/:'!I/-F').0IC'!1E_'/RTQ('U;(0# 6? ADC'
(U;\'(*5(06<.LUd&e`!10 bR \!1U;(0#b@Q01C7;/(<'pLg*%"U;\'(alC7)"C7X :!#-!E\7C'':U;
*cC["D(0I!1!I5J/*%01: ,!
'$ N$0IC'&e:'*5(')ELj):C0 !#<7D&e`0R ;Ud'0I(<p&'(b\"(0K
" *%"*@[7!LN"*%@? o6V01C'[\'!1/*5./L01!I!15J/*501("%$ '!LN:*5P*%"01'/p0I &C>@
a7"*50I<.(_@M /U=&!I01+l:'ERT0IC'"70^(0I!1!I5J/*%01:D&''0RT(01CP.-3G4!10g0b/LT':!1U./
-l(&/-d"/'> ,#6?
:5$"'!M+/RD"!I-P(U;0KD01C'91*5:\;L Ud&e`!10 U;-`6? C'(E0M-@/RD( (
-/I*5!1(&'7) '&'XN'!LN"*5QI*0I01!I') ( +!I)"P:!I0<VLMU./01!I+5$0ELN(E01V->1*5!I&l0IC'
'&' 701:T01!I\'<d&e`0R '!LN"*5M'-'+0I"/-lU./)"!1>"('01(" ()"'!I #? b
\'!I*5/1')E&<dC'Um-mUm"*#C''>jUd0i!I<E:;2'0IXY!1/"701:.`:!#5? C':01:!1/*5`\'01:!#
L 01C'Q!1`01 /- \'ad -O*U;`!# /!1Q&e:01C&<Z7/*5/I0<V2'0IXN!1> -01/*%01"!K
()"C0f01`(0<M*/=&8!1/*%"!#-/- :'<M&<d*%"'01(')\'C'"0I" *5"(/*%01/-E&'*#_@0K L,U;/"'!#/&'
@?BADC'+h2'0IT!1/"701:$@/"7)pRT0ICE01C'T:\'01+*\"(0j\'!I/"- ,!'('C'!I0h01M<p(U.):')
<70IUP$/*/T>"*#C^!I/*5\701"!B01g!1/*5`@f()"C0':0 LY!1:U g7)" \"0B&''0f!K01C7!LY!I"U b'!LN:*5
!I/D0IC' 1*57@$01C'+!I/D*%!1/:7)8"H01C7D !1/L'0IC' -0#*5L701C' 7!LN"*%jLY!I"U0IC'f<@
"!801C7E*/U;!# ):'!1 %& #? LY0I$'&0K01+BU."*5!I@I*5"\'+* Rk>@`'):01C.Lj01C'M*5+-0
()"C0 '!LN"*5[!1:')"C'7/1;E\'!I"n/*50I/- :0IV (')"(P-`01/*50I"!`$DRTC'*#CZ( 01'!IZ\'!I-*5>F/
):)"!I)@/01&'!1()"C01'>1i:/'@? C7!1/: /U=&!I0 f+>R Um><MC'"+-=RD`RTC';:&`!1') E7)"
\'+/!iLN"*%0 '//!T)"C0 K$'M*5"(/*50I:ELh*cCELN"*5`0#iRT(01C9- G4!I0i:!1(0K0I" LN/!T)"C0 B+
)"!#/0I/-;01E:/01 /U=&!I0 R?ADC'\'!IU./!1<E!1>":.D01C7b:!1+0I".(mLY:!1/C'"!I017/
LN"*%0b/!1/:b'-!8U;:01:l/LD0IC'E"&!I@! ):'!1 " #?/<7+L 01C7T\'C'':U;':lC:
:')EC'+01:!1<./-.*.&01!K"*5/-;&:*c_9(U;@08E*501'!I<@? "0TR "!I_;C"D!I/701>-=.U;\7!1+*
U;-` ,$ ' -/()"'>- 0I 20;a\e`!1U90K8-'/0#V";R g";01C7"!I01+*8!1/'0K.-!1(@/LY!1:U 2!K0T\'!I*5(\'> )'$ %'$ 6? *cC./Lf0IC'RD"!I_;RT:DU;"0I:0I/-=&<=0IC''"7X /U=&!I01/
!1%J/*50K*5P/LE0IC' U9@""-'$ '$ #6? LY"!10I'/01(<@$0IC'/PU9-9!1S`@!1(<VU901> 1*5:\e90IC'!&<Q01C7.\/*5324*d'!LN"*5.)"`"U;0I!1< "1'U;/-Q"!p&<Q01C'(!/&'(0<l0IP\'!1/-*50
&'!I)"C017/1iLY:!0IC'0I!IbC'U;+\'C7!18Lj:'!#*5M/-l:!b-!1>*501("%?
7RW!1%J/*50K*59U;- C"=&`Z-@:\/- 01C/0;->1*5!I&/p01C7F!I/01("V&0RD
U.:*5!1]1*5:\'*E'!LN:*5;!1:')"C7'/1M-V:!p!I/:'0I",?.ADC';'!LN:*5;\/0#*#C (U.):/-l&< /:*cC
`:!p-01/*%01"!gbU;-(/-l:F*%"(/*50I"P/LT'U;!I"T:')[<U;U;0I!1+* bXNC/\e>- *(01(/
B)"7!1&
& i/:*cC *(0<[C"0RDl\7! Ud&!10I/ LN:*50#bRT(01C :\'\@(')Q'"!IU.+5$HLN"*5`0
':!1U./!ImLY!Id01Q-/01ELY!1:U 0IC';U;// '!LN:*5;':!1U./6$h-V(fLN"*50K^: 0IC'.'!LN:*5
C@;0IC'[1U9.(&e>- 6'?Vo60E+p"I'U9/- 01C/0E01C' bXN*(01(/p/!1.''3LY"!1U9<Q-+01!I&'701/- (
"!I0#/01(" 6 Ud'0ICV'): M"O01C' '!LN"*5[\'/'@$RTC'!I/" LN:*50E0I0 4 Y\"/!.7)"
E':!1U./<S-+01!I&'701/- RT0IC `!1QU;/ - 0#-'!K- -0I:f$ 01C'./010I!;!17)Q"
;!1:')"C'7/1p\/!#/U;01`! 5 ?;ADC'+b:01!I"\'+*='!LN:*5=U9-fC:b&e` \7!1:(<l/- 0IP01-<
7!LN"*%F!I5J/*%01: LY!1:U !I"'):C '!LN:*5/2 -6$/- p@"_@>- C'`!1;0IQ"*#C'@dU./01C'Um01+*
01!K"*50K&'((0<
#? C'` %$(LN"*5`0 ':!1U./f/()"ERT0ICp0IC'TU;//E7!LN"*%T'"!IU.N$\'!I-*5(')
\'+/!f\/0#*#Cp01C0f:&e`<' Ud&!1!0 R?/RD@!`$/"d*5!I/"/5$/01C7 bXN*(01(/H)"0h-`\e`!
"[01C'M@!K)"]$'-F01C7p-+0I";LY!I"U /U=&!I0 U;-4*%!1/:/%?
iR
lu}q nozvxwSw, ‚[w{Zv| zv„{%nv tSv w ‚y}t=vx~ p ‚urktSluw rkluy rytSluy|v tZ …! w zol z|{" r ‚#u$ vl#%&= nvAp' rkt=lqwkrklqy r
w= tS}|rS }t=v#l(%
S novwS}t)% ‚qr vm*S n' w8‚ wSwS}opv„{+S lrx‚ }wSv!= nvw=}t% ‚urkvS lA€2v~ lrx‚[~ ~-?
, ‚[pA€2vxt. ‚[z,…
/80 ‚(S }tk‚[~wS}ot% ‚urkvxwrk~ v„‚[t=~ yotSl#h% vxwSw‚m* {Zv%wSy2v„r1= tS}p l##% p ‚qrkt=lqwkrklqy r w=}tX% ‚qrkv2q vxlupv= t vxw …4o3 lqt{Zv t$5 z6
tSv|
7 v„r1k ‚[z|rkv8| ‚Rw=y|v r19 rRw=}t% ‚urkvdpl{Zvx~ZpA}w., €2v(‚ wSwS}opv„{$…Xz:S nvdy|‚[w.;u wSvu$ vxt ‚ ~wS}ot% ‚urkvRpl{Zvx~ w=<?>@5#ABC n|‚u$ v3€2vxvxz
% lu}z|{DS lA€2v{59E rk}~*S lAp ‚[z y}~‚(S v8{Z}t. zA tSv127 v„r1 ‚ z|rkvpl{Zvx~,{Gvxtq$ ‚#. lqz,…FXzGS nov#rklqz5= v1H8 l#4% €|l{5 tSv127 v„r1 luzI
t ‚u{5 ‚[z|r vJ zK= nv {" t=v„r1. luzl#%= nvAlq€w=vxtu$ vxtApA}w. €2vvLq$ ‚[~ }|‚#= v„{%‚[wA‚[zK z5S vu t ‚[~Jl#q$ vxt#‚ ~ ~M$5 w. €~ v#y2l z5S wluzKS nv
wS}ot% ‚urkv3y2‚# r=nyotSl;kN v r1 z
lqz5= l8‚Rw zu ~ vEw=vxzw=lqt3{ZvLS v„r1= lqt …MO5 z|rkv= z5= vq tk‚# luz n2‚[wI= nvTv1$P v„r1J l#% m3vL?u n5S v„{‚q$ vxtk‚#8 z6Q
&= }tSzow8lq}6&= n|‚#R w=vq$ vxtk‚[~?wS}t)% ‚qrkv pl{Zvx~ w3‚ tSvrx‚[y2‚[€~ vl#T% rx‚[y= }t zJ= nvyt p ‚[t tSv|7 v„r1k ‚[z|rkvAr=n|‚[tk‚qr1= vxt w. rkwl#%
S novwS}t)% ‚qr vq…TjRnvRTS rx‚$5
pl{Zvx~F< A6>.,C m(‚ w8r=nlqw=vxzL‚[w*=% ‚ur1 ~?k ‚#= vxw&= nv#‚ z|‚[~Z w wdl#E% y2vxt. zvxz58 tk‚q{5 lupv= t r8‚ z|{
q v lqpvLS t rPynvxzlupvxz2‚‚[z|{nv z|rkvtSvxw=}~S wU z ‚t=v1|
7 v„r ‚[z2rkv#pl{Zvx~VS n|‚(3 y2vxth% lqtSpwMX% ‚# tS~ m3vx~ ~V% lut(‚ ~‚[t.q vq$ ‚[t. vL
l#4
% tSv„‚ ~,w=}t% ‚urkvxw …
DA C'D!I5J/*50I:bU;-*`\'0I'!1/H7"0B"'(<b01C'fLY:!1/C'"!I01'(')8L(--/LN"*50K ):'!1
" #$/&''0h+8U."_(')'$`C:-/RT')7$@-01!I!15J/*501(" Y'\p0IT0R T&"'*%/ 4&0RD "-nI:*50
LN"*%0# -N?fADC'8&'!1()"C01'>1fL^'!LN:*58\0K*cCdfa\'!1>1>-E"i0IC'T01`)"!#/'LLN:*50f&7!1):C0I'/I
/@!gBLN"*50g'"!IU.+5?MADC'b01`)"!#/ +b*5'Ud&!#"U;0IF`"//01d/- Ud0&E&'!I"_@P(0I
*5:U;\"'0#!1\7!1/0I').LN"*5`0#p01C09!1.U.:_@/-4$fC"-/RD>-H$iUm"_@>- -VC"-/R /-H$ '(01C'`!U.:_@/-;':!MC:-/RD/-H?ADC7d*5"U;\7a0<dL 01C'E(0I)"!KBT/"(<lP&<.U./)"7')
01C7d- G4!I0gU."_(').- C"-/RT(')P*5:-(01:0IC0M!I;:^.'): bXN*(0<F+b!1"0K0I/V0IC'['!LN"*5.\'+'@?S "('01("O01P01C7F(0I)"!K RT"d!I!1(@/- 0d&< 2!K09-!I') l&"
LY'*%01: LY:!;/"*#CO*5"U9\e:'0=/L01C7l01`)"!#/6$T/- 0IC'V2-(')V*5@ m*5(0K^LY"!d01C'[&"/
01C7!1"7)"C a01`(@^'U;`!1*`B(U=70I: #6?EADC'd:**5'!K"*5<[Lk01C'EU;-fRT:b@!132/-F&<
U./0#*#C'')U;-H\'!I/-+*501("fRT0IC.!15J>*50#/*5bU;>"7!1U;`@0#LY!I"UW/01'!KB'!LN:*5/5$7*#C["%$
\'+"0I!$I-H$/-;*5+< ()"'!I #?o6;/4*:/%$\'!I/-*%01/-E/-;U;/"'!1>-E-'0KpRD!IDLY"'-;0I
&Td01!1:')M):!1U90`? <70IU./01*f(*5!1>"T(p&'!I):C0I'/1B :&!I@/-E"f0IC'T:!U;/@/
01/Rk!#-7p01C';(('U;0 01C'+^&:*c_71*`010I!1(')l+^(V*5"01!K"0E01 Ud&!10I/ &C:!pRTC'!I
&'!I)"C017/1TT*5:0K0b/-l-\-`0 L :!-(!1/*50I:$'/-l/9[*5"01!K"00I;'!LN:*5
!1%J/*50I"PRTC7!1d.\e>_PP&7!1):C0I'/I +a\/*501>-lQ01C'E*5('0<.Lk01C'd\/*5'+!M-!I/*50I"
-N
? '"!8/\'\'(*/01:DRTC'!IEU;\'(*530<p+T-/!1>-m/@! C'):Cl\'!I/*5+:$'/\'\'!IaUm01("DR !1
U.:-b019!I!1(@0T0IC' (0#/01@8U;-` . 4/ 45/ 5 6# 6 *5]45 ,%#*5@ / 5 h p0#/ % % * % -
% * % %)
RTC'!I ! i0IC'b(0I(0<pLh01C7:'!#*5]$ 4/8/ - 45"5 j!Ib01C'g"&!1@!k-;(7U;/0
-(!1/*50I: (P;*%@"!#-/01pLY!#/U;RT0ICl0K$ #"XNag()"'>-FRT0ICP01C' '!LN"*5M'"!IU.N$H/%- 4/& 45 '
- ( )"* 4/+ 45 K?
ADC'M-@("\/-=U;-HU.<d&^`RD/-;:T ):'!K( //01:;L Ud&!1!0 R$'RTC'*#C;+
(U;\'(<Ea01!IU;*`" RT0IC ( %?fADC7TU;-C"h-!I/*50BU;\'(*/01("'LY"!C\8!1/*5/@!I<(
U.:*cC'('B+: -@/- LY:!!1//01+* !1-!1(')D(M*5"U;\7'01!):!#\7C'*+ -'N? ''!I01C'`!$0\7!1/+-/
^2!IUW&"DLY"!801-<7)E+/\e`!#*5\701:.Lh01C'!IXN-U;`("/e:&'n/*50K5?A=(01!K0Ib01C'+5$
`@!#/e:&'n/*50KjR !1g*5:0I!1*50I/-pLY!1"U U./01!I+f*cC9"\e:!#*5`(.-;0I"'Rk!I@$'/-=01C7!
-()"0K4U./)"/ C'/RT.01d*5(@<dU.0K*cC9<01C'0I*T"'>D!1-!1/-d(')E01C'U;- ()"'!I K?
D"0ICV!1//8- !1`-!I/- C"-(')@d!IlV01P:/!1<V<*#C'!I"':(<@$D/-Z):' 24*`01<]$ RT0IC
U.:*5!1]1*5:\'*!I"'):C''/I5?
ADC'/da\!1(U;0#DC@p(/-l01[.*5'!I:"&!I"/01(" ADC'dU;-` \'!I/-+*50#0IC0bLY:!
@!I<lC'()"C U.:*5!1]1*5:\'*p!I"'):C''/I5$fRTC'` 01C'd"&!I@!M- 0IC';(7U;/08/!1.*%@=0Il:'
7"01C7!$74'!LN:*5b':!1U./fRT(e):'!K0Ib/\'\'!1/aU./01(<p0IC'bIU;8&'!I)"C017/1%?ADC'U;\'(/
01C0$]01C'!IXN-U9("/@"&'n/*%0$/!1!I/\/*%01@/LH(0#BC/\@$@RT\'!I-*5T':01C'(')bU;:!101C9
(C':'0I01TRT0IC;*%"0#0D(0I0<pRT(01C'(?fo6E01C7b*:b/L\"(<C7/-!#$/-)"/f&0RD`d"-nI:*50
LN"*%/iRT(H7E"7)"!T&-+1*5`!1'(&' ()"'!I @ #$/-.U;@:01C'(<;*57!1@/-E"&'n/*%0#DRT(&eM-`@"LhC"-') ()"'!I ` #?ADC7i4/U=&'()"'(0<^Um><M&R /-E" ^\!K*5\'0I4(')"7!I0<p(
RTC'+*cC01`!1\'!I0#/01:bL701C7i0IC'!1`X6-U;::C\TLM"&'n/*%0HLY!1"U 0#H(U.):fH(U;\@I&7
LY"!M&"01CVC'U./- Um"*#C''>5?;ADC7^\7C'':U;': /GH`!#EF\7&7da\701(" LY:!p0IC'
J4/01XN-I*p\7\e>!#/*5MLh01C'bLY'(U;@" B)"7!1 : #?
‚
Eye
Surface
Camera
€
()"'!I$ ‚ U?8 ‚[~ p ‚#uvxwl#%XmdlwS}t)% ‚qr v y2‚# r=nv wJ ~ ~ }pD z2‚#Sv {D% tSlup Snvw ‚[pv{5 tSv„r lqz,…%jRnvw=tSlqz6
wSn2‚q{5 z%
l#%Snvt.qn5#y2‚# r=nQ~ v„‚q{GwJSnv lq€owSvxt.$qvxtDSly2vxt rkvL?$uvL‚%r1Z~? z|{Gtrx‚[~Rw=}t%X‚qrkvm*=n ‚ $qvxt.rx‚[~‚H w„… Xz
rkluz = t ‚ w;F= nvA~ v1% y2‚# r=nn|‚ w% ‚( t=~}z9% lutSp€t.?un5Szvxw=w ‚ z|{2SnovA~ ‚ur Ll(%(w=n|‚q{5 z w=vxvxpw:Sl w=}uvxwA‚ y~‚[z2‚[t
wS}ot% ‚urkvq…jRnov ‚ur1S }|‚ ~4wSn|‚ y|vxw l#%&= nv#w=}tX% ‚qrkvxw‚[tSv {Gvxz5 rx‚[~X… Jl=ny|‚#kr=nvxw#‚ tSvArk~ yoy|v„{ % t=lqp p ‚(qvxw
>;AH B
y9H vx~ w l#% r1Z ~ z|{Zt. r ‚[~=q$ ‚[wSv w„… *zS nov ~ v1% ! w ‚ tSv„‚ ~(r ~ ‚K$q‚ wSvm*?=nK$qvxt.tSlu}qnv1HSvxt. lutJSn|‚(!$uvxw A‚D7 ‚(
‚[yoy|v„‚ t ‚ z|rkvq…4jRnvJtq n5 q$ ‚[w=v4n|‚[w {Gvxz5 rx‚[~[w=n|‚[y2vd€} w,t=vxz|{Zvxt=v„{ }w z?
, ‚[pA€2vxt w$pl{Zvx~< C% lut$€|l{5* tSv172v„r1 luz,…
, ‚ pA€|v t wT~‚ mQyt=v„{5 r1S w*w= tSlqz6# w=n|‚q{5 zA ‚[z2{{Zt.?u$ vxwR€t.?u n5S zvxw=w8‚#=S nvlrxrk~ }|{" z6# €2lq}z2{‚[t. v w&= l xv tSl|… Cn ~ v*
,
yt=v„{5 r1S w*= nvtSv12
7 v„r1 ‚ z|rkvl#,% w=vq$ vxtk‚[~?z|‚#= }t ‚ ~$wS}t)% ‚qrkv wRm*?= n ‚u{Zv u}|‚#= v‚qrxrk}ot ‚qr 5 % ‚# ~ wMS lArx‚ yS }t=vS nv z5S vxt=y~‚
€2vX m3v vxzp ‚urktSluw rkluy rRw=}t% ‚urkvtSlu}q nzovxwSw‚[z|{ wSvxzw=lqt*tSvxw=lq~ } luz,… € *R
vL z|‚ l#%
= nvnZ}p ‚ zAvq vJ<> LEC ‚ z|{Aw=lq~ {8S
wk ‚#= v#w=vxzwSlutSw z $5 {Zvxlrx‚ pvxtk‚[w8n2‚q$ vU|
zS vS w. v#t=v„rkvxy= lqt=w!S n|‚( ‚(q t=v ‚(S v€otq n5S zovxwSwU% t=lqp‚[tSv ‚[w8tk‚#= nvxtS n|‚ z
y2l z5S w* z'= nvw rkvxzovq…djRnv‚[tSv ‚ytSl;N v„r1S v {luz = l ‚ w zu ~ v t=v„rkvxy6S lqtU z|rktSv ‚[wSv wƒ‚ wRw u}|‚ tSvl#4
% wS}t)% ‚qrkv{5 w ‚ z|rkvh% tSlqp
Snov#w=vxzwSlut„… XzL‚D y6 r ‚[~ rx‚ pvxtk‚A}w=v„{ m*?= nL‚GA pp~ vxzw$ v„‚urSn%y9H vx~F p ‚#u vxw8‚:h% lqtSv wSnlutS v zv„{‚[t=v„‚l#%
@ pp:/ ‚#8 ‚A{5 w. ‚[z2rkvl#% p u lqt!> ppJ/ ‚(AB p%… d~ v„‚ tS~ Z ~‚ tq v‚ plq}oz = wTl#T% p ‚qrkt=lqw r lqy rR}oz|{Z}~‚#. lqzw8rx‚ z
yt=l;kN v„r1*
lqz5S lA‚w zu ~ v8y9H vx~X…
Source
Bright
Dark
Observer
Observer
Bright
Dark
Bright
Dark
‚
^
n
^
a
da
θa
dA
€
( )"'!I ‚ w. zq~ vJR*SSrx‚$5}w=v„{K=l ~ ~ }w=t ‚(SvAmRn5L‚rklu~ ~ v r1 lqz%l#% ,?‚[pA€2vxt.‚[zG% ‚urkv=w#m*Sn{59P$vxtSvxz5
lqt. vxz5 ‚#. lqzwA{ZlZvxwAzl8Alq€2v ,?‚[pA€2vxt w ~ ‚ m… Cnvxz Snov r ‚$ K w: ~ ~ }pD z2‚#Sv {G% t=lqp =nv tqn5FSnvw=p ‚ ~ ~ vxt
z|r1{Zvxz2rkv ‚ zq~ v:% lut!Snv~ v1% % ‚urkvp ‚ uvxw? €tqn5=vxt =n|‚[zK=nvt.qn5lqzovq… 3lut#‚[zlu€wSv t$qv t#luzKSnv~ v% ;Snv
% lutSvxw=nlqt.S vxz z l#%&= nv~ v1% T% ‚qr v wu tSv„‚(Svxt=n|‚[z l#%=Snvt.qn5Rlqzv‚[z|{‚ ~‚[tuvxt=% tk‚qr1. luzl#%M=nv r ‚$ D w8{o‚[t $…
8w S nvAlu€wSvxt.q$ vxt pl#q$ v w t.q n5; = l[m(‚ t {Zw=nvJ ~ ~ }pD z|‚ z5;=nv:% tk‚qr1. luzLl(% =nvA€t.?un5Svxt‚[t=v„‚G z|rkt=v„‚[w=vxw;Tr ‚[}w. z6
S nov ‚#8q t=v ‚(S vR€t.?u n5S zvxw=wTl#%I= nv*R*SS rx‚$5!S l t wSvq… € Ct=v1|
7 v„r ‚[z2rkv% }z2r1 lqzJ wT{Zvxt.q$ v„{ € pl{Zv ~? z8 ‚ƒwS}t)% ‚qrkv
y|‚( r=n‚[w8‚Arklu~ ~ v„r lqzl#%
RTS r ‚$ . v w Tm*= n {" $
P vxt=vxz5*% ‚urkvR zlutSp ‚ ~ w x…
L
r
+"01!
θ = 30
i
θ = 45
0.25
i
θ = 60
i
0.2
0.15
0.1
0.05
θr
-90
-75
-60
-45
-30
-15
15
30
45
75
60
90
()"'!I v ‚[wS}otSv„{ tSv172v„r1 ‚ z|rkv {GlSw w4rklqpy|‚[t=v„{m*Sn tSv17|v r1 ‚ z|rkv8yotSv„{5r1=v„{€5!Snov3plG{Gvx~ wSlq~{~ zvxw V% lut
y~‚[w.S vxt …MOZ}t)% ‚qrkv*t ‚u{5‚[z|rkv Zrklqpy}=v„{#‚ w(‚ z‚$qvxtk‚#uvRl#$qvxtM=nv8v z . tSv8w=}t%X‚qrkv*y|‚#krSn wTy~ l8Sv {A‚[w3‚U%h}z|r1. luz
l#T
% w=vxzwSlut{5 tSv„r1. lqz% lutS notSvxvA‚[zu ~ vxwRl#%M z|r1 {Zvxz2rkv
k… 8~ €2v„{Zl ‚[z|{t=lq}u nzvxw=w%mdvxt=v#w=vx~ v„r1S v { = l ‚qr=n vu$ v
SnovR€|vxw.FQ …IXz:S nv wSv8pv„‚[w=}tSv pvxz5S wS nvRw=lq}tkrkv {5 t=v„r1 luzI[ wSv zwSlut3{5 tSv„r lqzIZ ‚[z2{!= nv3pv„‚[z wS}t)% ‚qrkv*zlqt=p ‚ ~ ‚[t=v
rkluy~‚[z|‚ t B … ZO }ot% ‚urkv#€otq n5S zovxwSw! z|r tSv„‚ wSvxw‚[w= nv#w=vxzw=lqt‚[yyotSl ‚ur=nvxwwSlu}t rkv{" t=v„r1. luzIV$5 lu~‚# z
, ‚ pA€|v t w*~ ‚ m S n|‚( ytSv„{" rS w€tq n5= zvxwSw S l €|vJ z|{Gvxy|v z|{Zvxz5 l#%*$ vxm* z {5 tSv„r lqz,… jRn w €otq n5S zovxwSw: z|rktSv ‚[wSv
,
w ‚ ~ w=lJ zLrklqz5= t ‚[w.S lAwS}ot% ‚urkv#t=v1|7 v„r lqzpv„r=n|‚[z w=pw=S n|‚(8 yt=lG{G}|rkvy|v„‚ Zwƒ‚ tSlu}z|{G= nvwSy2v„rk}o~ ‚ t{5 tSv„r1. lqz,…UXz
SnovxwSv‚ z|{ l= nvxtv1H y2vxt pv z = wJ< A LCQ= nvytSluy|luwSv„{ pl{Zvx~ w*% lu}z|{G= l€2v zw.S tSluz ‚#u tSvxvxpvxz58 m*S n pv„‚ wS}t=v„{
{‚( ‚… jRnvAz|‚ tStSl[my|v ‚ lu€wSvxt.q$ v„{2 z2S nvAw=lq}tkrkv{5 tSv r1 lqzK w‚#.S t. €o}S v„{ S lG= nvAlqyy2lqw. lqzvP v„r < A LSC … jRn w
ynv zlqpvxzlqzG w8l(3
% tSv ~ ‚(q$ v ~? ~ vxwSw py2lqt.&= l'$5 wS}|‚ ~,y2vxt rkv y lqz‚[wU8 tSv q}6 t=vxwS nvlq€owSvxt.q$ vxt‚[z2{GS nvwSlu}t r v = l
€2vm*S n z‚Dh% vxm{Zvq t=vxvxw+% tSlup v„‚urSnl= nvxt;d
‚ w= }|‚#. luz{59E rk}~S l%vxpA}~‚#= v zytk‚qr1. rkvm*S nolq} vL?= nvxtAluzv
lq€owS t=}|r1. z6JS nvl= nvxt …4jRnvw rkluy|vl#%I= nvytSluy|luwSv„{plG{Gvx~Q wd€tSlZ‚q{Zv zv„{€5
rklqpA€ z z< A LC m*= nyt=v$5 lu}wS~
wS}6q v wS v {luzvxw % lqtJwS}t)% ‚qrkvt=v1|
7 v„r1. lqzK< A C S n|‚(( ‚ tSv8€2‚[wSv {AlqzAw. p' ~‚[t,t=lq}u nzvxw=w8‚[w=wS}py lqzow„…3R ‚[~ {5 l#,% wS}2rSn
‚ArklupA€ zv„{pl{Zv ~$m(‚ w&u$ vxt9|
v„{ }w z w ‚ py~ vxwdwS}|r=nL‚ wRw ‚ z|{ | r ~ l8S nI8h% l ‚[p2[ w ‚ z|{Zy|‚ y|v t;| ‚ z|{m3lZl{$…
'
‚
€
r {
v
()"'!I !"#$%&
')(*
+,)-./0$#1!2&3(4+44$&,5'$%-%&
$$67%&4
8,)
55/!$# 5 :9 ;=<>!2&?"@+2&A42B<(41(8C6&426&2&3!2&%D02&1$'E8%&1(!6$0%&1%GF&H43-55-)%&?3,;
I #%B!2&!8#$%&
(+!2J(!7$>
K'%&(0-%&(L)'%&
76&(!%&7!2&M!2&!-$&K
$$'EN3OQPSR 9 L*42BN3OTPVUR 9 '?
=W+')XC30+D6;(8
,)-Y(4H-%&+)L$$67%&4
XZ55/44$# 5[ 9 4D02&C$'E13!2&7')?D
&
I #%B!2&!86;(A$'EN3OJP]\ 9 L&42N8OTPV^ 9 ?C_%`;02G)$a%&
`(4#%02&08(L$b(H58)-6&2%&(4(
!2&$"'6;+(!6$H(c%%&-H$#dC;')!%55%&L+2&(a<#A22M6&2%&(H(a!2&42a6;6&(4(+$$&!2)+E(+H
5
K6&"$(Ha!2&(4+;H-2B!%&(4(+02'$"
(c%&1$%&'c<(!;$?@+2&K
$%&
M/54%0((06&(402&eE-"<#122
')(4-536&2%&(H(L+2&%f(46C%&
`(4%&(4>
K0-%&(3M'$(4M4D%&M-%&02&'=L$$+(064E%&-H$(8%&')H1!2&M(4
g;H2!%&(4(?3h$H'H%&H'$#L%#;iHLKH(!5!<34(102'j0
K4%&(0%&$(!2&5LK5)K
K6&(i06&(4>k(0$2&-6&4H8lK%&
75(H(!;$1HX5'<1(02&-5?C= I 52&(+$$67%&4
7-%&
`<"
km02&C(H-
K)!%a?3h8(1)-6&2%&(4(+%&(4(1,$1H
42BNOnP 9o OnP 5 R 9=o OnPb^ 9o +(02&
K%&8;-(F&44?p3/!+6&2%&(4(+42)'L!2&3(!52&355($l1AF&"
K(4L
)
(;&(4<
C%n!2&>(43a!2&3,6$$&K%a?
$%%
f?-' b*56$
"$7p? ? * C7"$A!1%? '(@!#0< !1/I5$ !1(*50I"$
)-) #?
p?
? @/:$ !#" $% !1`0I*5 b(B- p?'&M?'&'!KU.%$'&`R)("!I_H$ )-) K?
+*p
? ? ]01!1:')'-$ ,/.!01!2 #3g!I- '&'(*/01:5$&R4("!1_4$ ) #) #?
b5
? 380$ 6/798:;=<61>;798? @A8B+.C./DEF p? &p?7&'!#/U.5$ &4R ("!1_4$ !) #?
+'?Mp? Ud&e`!105
$ GH /1/.JIK?LM= % #?
? Nb'&(_:=/2
- D? ''_4P$ ORQST71Q-U19;V/$ a4c $ )-
!)
#?
5
? WC/-!K"`_C/!-$ X6.
YFC/" A*8@`! 7&'+*0I"5$ !)-% #?
' E
? ? 8Um"*#C-!#,P$ Z
A8B#$ [[ a $ ! )'-' K?
)b
? NE? ?M"!IP- ? '? D!I@"_75$ \-'%5? ]'1 @";/^_]'1.
oA !1>15$ !)'-) #?
,!%+'?8p? @U;(01C$8Ab? f? HK
$ NE6? '? /:`$ R1
%/^!^a%7bGcEP%
d.eX>^!
T
]-;
!)'% #?
,- ? D
? W:C'Sf- '? ^? S(:*5@g$ Xh.F;LAC.bX>
?i7`j^!9BJ]k
Bl1/; Nb*:-U;+*
!1/I !ILY/I:N$ D@01",$ !))
#?
,!
? '? @-CUPR$ mg@7%
?-GcEP%
"$ aBn $ !)'-% #?
,!
+''
? '? Nb@-!1('_9-.p? '?:o *@:!1S$ p'8B'
?k#"Kl1qmg@7%
?5]k79=%a#"$^a 7%"$ e [$
)-'
#?
, +*p? '"!#<0ICP/-lp5
? r+1!1U./$(s c7FQ5j/GRGRGutR"QvwtR^x@k8#oyg;s.
z# X>7%%LA !)'-) #?
,!? NEk? &b<!`5$ NE?4o _@`*cC76$Abk? N^/"-@g$ jB#'
'
?Rp'8B'
?#"tR^x@k8#syg;|$ {$ !)) #?
%
M? Q/01C'(U;!`$5w.7%
?R1 ;
?i% E?#b? "70K*"01]$
\-H? #W8? E? @&<!W:U;\<@$
@0`?H"'+5$/-H? '$ )-'% K$e@:6? "$4*cC/\?!?
,#+\T? 8\'(_H'
$ 8H?i7%
A+.c, mcH% Y;
A=$6A'^!7%
?k.c,v'YF/;LTK. '%8 $ c {$ !)# #?
,!' ? 7!I0
$ x/ @'19;7%
?Pp8B '
? $ n [ !) #?
,!)b5
? 3M? @U;(01C$ p8'
?-#"> @'1 ;7%
?'X$//71$ eTc $ !) #?
-%+*p
? D'C76$ ? '? Q+*cC$ *p5? 3M? >-$ p8'
?-#"
@'19;7%
?PX$//71$ e [$ !)' #?
? 3p?8!1(')8-Ab-? D? ]U;0IC$ 6j /%Q: 6A'8A7'.$$/'87%$ c [ ) #% #?
-+&p
? ? 8!I/:$ 6/PQ5ORQ !)- #?
-
? @()"4/- '? ?F8R N
$ 51^!
?'X6.
+
>/2" U;+\'C'`!1 '&7C'7)
W"!I\"!#/01("0$ !)- #?
#b?
?Mb/\'_@- p?"/ :!1-$ p8B '
?|#"> @'1 ;7%
?X>/71B$ {$ ! )-
K?
-+NE'
? \T?A:!1!K*5M/C- \T? @\!1!I/R-$ p'8B ?5#"$1!mg@7%
?P]k79=MA!#"$^a 7%"$ e )- #?
- ? 8!I.- '
? NE'? &b</!P$ jT A'
?-p8B '
?|#"!tR^x@k8T yg;$;\7!1/I )-) #?
b?
?Mb/\'_@@$ ^? ? &8"$ ? *p? @Ud<0IC'@'$ ]k79=7 #$ c { b $ !))
#?
-' ? 8!1[/- ? NE? &b<!$s /7FQ +t ]j X$6R !)) #?
,!!3
"!#"D
ADC'R "!I_lRT:b7\'\"!10I/-l&<l/Q ):!#/0/-PC*b-[- H*5( "*#_:!K-$`X
/R8C'\O01 BNK& -Z o 38!#"-0I `/R8C'\V01 M? [01C/'_ E? &b(RTlL D(
&:!#0I"!I/E/- M?)")]!IRTN$ ? - ? T/_@!bL$W"('U=&7 '@`!#(0<=LY"!:(&'(
7)")">01("%?DADC'_701 ? &'b/LcW"('Ud&' '@`!#(0<^LY"!g"I+0#/*5MRT01C.0IC'U./)"/%?