Print By Number::光譜值到 Lab值的計算
光譜值到 Lab值的計算
色彩的起始狀態是光譜分佈， 但是光譜分佈值對於人機界面過於複雜，目前在系統平台與應用軟體間基本上用 Lab標示會比較好操作。這裏我們來說明一下光譜值到Lab的轉換。
我們實際取得一個印機油墨C100的光譜分佈: 
|
380nm |
0.134776 |
|
390 |
0.216068 |
|
400 |
0.307452 |
|
410 |
0.412823 |
|
420 |
0.505658 |
|
430 |
0.577052 |
|
440 |
0.647535 |
|
450 |
0.694771 |
|
460 |
0.712983 |
|
470 |
0.718428 |
|
480 |
0.712655 |
|
490 |
0.695992 |
|
500 |
0.665136 |
|
510 |
0.614834 |
|
520 |
0.542581 |
|
530 |
0.458487 |
|
540 |
0.373013 |
|
550 |
0.284983 |
|
560 |
0.200927 |
|
570 |
0.140309 |
|
580 |
0.105894 |
|
590 |
0.087318 |
|
600 |
0.073749 |
|
610 |
0.065351 |
|
620 |
0.06392 |
|
630 |
0.066473 |
|
640 |
0.072996 |
|
650 |
0.085311 |
|
660 |
0.100071 |
|
670 |
0.107459 |
|
680 |
0.103985 |
|
690 |
0.095292 |
|
700 |
0.083791 |
|
710 |
0.078098 |
|
720 |
0.088365 |
|
730 |
0.116629 |
CIE標示來自於光源，感受器 (人眼)，及物體三組光譜組合積分得來，上述油墨光譜分佈必須再積分光源與人眼感應的光譜分佈才能取得CIE 三刺激值(Tristimulus Value, XYZ)：
D50 光源光譜分佈如下：
.
|
380 |
17.92359 |
|
390 |
20.97985 |
|
400 |
23.91156 |
|
410 |
25.88722 |
|
420 |
24.44787 |
|
430 |
29.82885 |
|
440 |
49.24662 |
|
450 |
56.44974 |
|
460 |
59.97316 |
|
470 |
57.76397 |
|
480 |
74.76665 |
|
490 |
87.18889 |
|
500 |
90.55862 |
|
510 |
91.32148 |
|
520 |
95.06664 |
|
530 |
91.92939 |
|
540 |
95.69667 |
|
550 |
96.59098 |
|
560 |
97.11314 |
|
570 |
102.0873 |
|
580 |
100.7473 |
|
590 |
102.3134 |
|
600 |
100 |
|
610 |
97.73786 |
|
620 |
98.9245 |
|
630 |
93.5113 |
|
640 |
97.70746 |
|
650 |
99.29399 |
|
660 |
99.07049 |
|
670 |
95.75347 |
|
680 |
98.89672 |
|
690 |
95.70871 |
|
700 |
98.2379 |
|
710 |
103.0586 |
|
720 |
99.18921 |
|
730 |
87.42788 |
人眼感應光譜分佈如下(2⁰觀察者)：
|
x |
y |
z |
|
|
380 |
0.001368 |
0.000039 |
0.00645 |
|
390 |
0.004243 |
0.00012 |
0.02005 |
|
400 |
0.01431 |
0.000396 |
0.06785 |
|
410 |
0.04351 |
0.00121 |
0.2074 |
|
420 |
0.13438 |
0.004 |
0.6456 |
|
430 |
0.2839 |
0.0116 |
1.3856 |
|
440 |
0.34828 |
0.023 |
1.74706 |
|
450 |
0.3362 |
0.038 |
1.77211 |
|
460 |
0.2908 |
0.06 |
1.6692 |
|
470 |
0.19536 |
0.09098 |
1.28764 |
|
480 |
0.09564 |
0.13902 |
0.81295 |
|
490 |
0.03201 |
0.20802 |
0.46518 |
|
500 |
0.0049 |
0.323 |
0.272 |
|
510 |
0.0093 |
0.503 |
0.1582 |
|
520 |
0.06327 |
0.71 |
0.07825 |
|
530 |
0.1655 |
0.862 |
0.04216 |
|
540 |
0.2904 |
0.954 |
0.0203 |
|
550 |
0.43345 |
0.99495 |
0.00875 |
|
560 |
0.5945 |
0.995 |
0.0039 |
|
570 |
0.7621 |
0.952 |
0.0021 |
|
580 |
0.9163 |
0.87 |
0.00165 |
|
590 |
1.0263 |
0.757 |
0.0011 |
|
600 |
1.0622 |
0.631 |
0.0008 |
|
610 |
1.0026 |
0.503 |
0.00034 |
|
620 |
0.85445 |
0.381 |
0.00019 |
|
630 |
0.6424 |
0.265 |
5.00E-05 |
|
640 |
0.4479 |
0.175 |
0.00002 |
|
650 |
0.2835 |
0.107 |
0 |
|
660 |
0.1649 |
0.061 |
0 |
|
670 |
0.0874 |
0.032 |
0 |
|
680 |
0.04677 |
0.017 |
0 |
|
690 |
0.0227 |
0.00821 |
0 |
|
700 |
0.011359 |
0.004102 |
0 |
|
710 |
0.00579 |
0.002091 |
0 |
|
720 |
0.002899 |
0.001047 |
0 |
|
730 |
0.00144 |
0.00052 |
0 |
先取得三刺激值，其計算如下
X=SUMPRODUCT(油墨光譜, 人眼光譜感應x, D50光源光譜)/ SUMPRODUCT(人眼光譜感應y, D50光源光譜)
Y=SUMPRODUCT(油墨光譜, 人眼光譜感應y, D50光源光譜)/ SUMPRODUCT(人眼光譜感應y, D50光源光譜)
Z=SUMPRODUCT(油墨光譜, 人眼光譜感應z, D50光源光譜)/ SUMPRODUCT(人眼光譜感應y, D50光源光譜)
|
D50光譜(P) |
光譜nm |
油墨光譜(R) |
人眼x |
人眼y |
人眼z |
P*R*x |
P*R*y |
P*R*z |
P*y |
|
24.44787 |
380 |
0.135 |
0.00137 |
0.000039 |
0.00645 |
0.004508 |
0.0001285 |
0.021253 |
5.26E-06 |
|
29.82885 |
390 |
0.216 |
0.00424 |
0.00012 |
0.02005 |
0.027346 |
0.00077341 |
0.129224 |
0.002518 |
|
49.24662 |
400 |
0.307 |
0.01431 |
0.000396 |
0.06785 |
0.216667 |
0.00599583 |
1.027315 |
0.009469 |
|
56.44974 |
410 |
0.413 |
0.04351 |
0.00121 |
0.2074 |
1.013946 |
0.02819754 |
4.833198 |
0.031324 |
|
59.97316 |
420 |
0.506 |
0.13438 |
0.004 |
0.6456 |
4.075196 |
0.12130364 |
19.57841 |
0.097791 |
|
57.76397 |
430 |
0.577 |
0.2839 |
0.0116 |
1.3856 |
9.463187 |
0.38666068 |
46.18595 |
0.346015 |
|
74.76665 |
440 |
0.648 |
0.34828 |
0.023 |
1.74706 |
16.86164 |
1.11352259 |
84.58221 |
1.132672 |
|
87.18889 |
450 |
0.695 |
0.3362 |
0.038 |
1.77211 |
20.36576 |
2.30189978 |
107.3479 |
2.14509 |
|
90.55862 |
460 |
0.713 |
0.2908 |
0.06 |
1.6692 |
18.77601 |
3.8740055 |
107.7748 |
3.59839 |
|
91.32148 |
470 |
0.718 |
0.19536 |
0.09098 |
1.28764 |
12.81716 |
5.9690077 |
84.47937 |
5.255366 |
|
95.06664 |
480 |
0.713 |
0.09564 |
0.13902 |
0.81295 |
6.479583 |
9.41856561 |
55.07714 |
10.39406 |
|
91.92939 |
490 |
0.696 |
0.03201 |
0.20802 |
0.46518 |
2.048068 |
13.3095606 |
29.7632 |
18.13703 |
|
95.69667 |
500 |
0.665 |
0.0049 |
0.323 |
0.272 |
0.311891 |
20.5593697 |
17.31315 |
29.25044 |
|
96.59098 |
510 |
0.615 |
0.0093 |
0.503 |
0.1582 |
0.552303 |
29.8718724 |
9.39509 |
45.93471 |
|
97.11314 |
520 |
0.543 |
0.06327 |
0.71 |
0.07825 |
3.333807 |
37.4111373 |
4.123128 |
67.49731 |
|
102.0873 |
530 |
0.458 |
0.1655 |
0.862 |
0.04216 |
7.746343 |
40.3465093 |
1.973328 |
79.24313 |
|
100.7473 |
540 |
0.373 |
0.2904 |
0.954 |
0.0203 |
10.91324 |
35.8513614 |
0.762875 |
91.29462 |
|
102.3134 |
550 |
0.285 |
0.43345 |
0.99495 |
0.00875 |
12.63835 |
29.0103267 |
0.255129 |
96.10321 |
|
100 |
560 |
0.201 |
0.5945 |
0.995 |
0.0039 |
11.94511 |
19.9922365 |
0.078362 |
96.62757 |
|
97.73786 |
570 |
0.14 |
0.7621 |
0.952 |
0.0021 |
10.45106 |
13.0552539 |
0.028798 |
97.1871 |
|
98.9245 |
580 |
0.106 |
0.9163 |
0.87 |
0.00165 |
9.598711 |
9.11369455 |
0.017285 |
87.65013 |
|
93.5113 |
590 |
0.087 |
1.0263 |
0.757 |
0.0011 |
8.379965 |
6.18107121 |
0.008982 |
77.45122 |
|
97.70746 |
600 |
0.074 |
1.0622 |
0.631 |
0.0008 |
7.65403 |
4.54687723 |
0.005765 |
63.1 |
|
99.29399 |
610 |
0.065 |
1.0026 |
0.503 |
0.00034 |
6.505833 |
3.26394754 |
0.002206 |
49.16215 |
|
99.07049 |
620 |
0.064 |
0.85445 |
0.381 |
0.00019 |
5.410877 |
2.41271506 |
0.001203 |
37.69023 |
|
95.75347 |
630 |
0.066 |
0.6424 |
0.265 |
5E-05 |
4.088889 |
1.6867305 |
0.000318 |
24.78049 |
|
98.89672 |
640 |
0.073 |
0.4479 |
0.175 |
0.00002 |
3.233419 |
1.26333642 |
0.000144 |
17.09881 |
|
95.70871 |
650 |
0.085 |
0.2835 |
0.107 |
0 |
2.314779 |
0.87365561 |
0 |
10.62446 |
|
98.2379 |
660 |
0.1 |
0.1649 |
0.061 |
0 |
1.621093 |
0.59967666 |
0 |
6.0433 |
|
103.0586 |
670 |
0.107 |
0.0874 |
0.032 |
0 |
0.967918 |
0.35438652 |
0 |
3.064111 |
|
99.18921 |
680 |
0.104 |
0.04677 |
0.017 |
0 |
0.482395 |
0.17534124 |
0 |
1.681244 |
|
87.42788 |
690 |
0.095 |
0.0227 |
0.00821 |
0 |
0.189118 |
0.06839896 |
0 |
0.785769 |
|
91.65707 |
700 |
0.084 |
0.01136 |
0.004102 |
0 |
0.087239 |
0.03150351 |
0 |
0.402972 |
|
92.93752 |
710 |
0.078 |
0.00579 |
0.002091 |
0 |
0.042028 |
0.01517697 |
0 |
0.215496 |
|
76.89465 |
720 |
0.088 |
0.0029 |
0.001047 |
0 |
0.0197 |
0.00711415 |
0 |
0.103851 |
|
86.55502 |
730 |
0.117 |
0.00144 |
0.00052 |
0 |
0.014536 |
0.00524931 |
0 |
0.045462 |
|
SUM: |
200.6517 |
293.226564 |
574.7658 |
1050.526 |
取得三刺激值如下：
X=200.6517/1050.526=0.191001
Y=293.226564/1050.526=0.279123
Z=574.7658/1050.526= 0.547122
取得三刺激值XYZ後，依下列公式取得Lab
Where
L=116*fy-16
fy須根據yr的數值來決定函式，當yr >0.008856(Ԑ) 時，fy=
，當yr 
0.008856(Ԑ) 時，fy=
由於fy 函式的不連續性(discontinuity)，Ԑ代表函式的分歧點。
yr=Y/Yr
Y=上述取得的 Y刺激值 0.279123
Yr =SUMPRODUCT(人眼光譜感應y, D50光源光譜)/SUMPRODUCT(人眼光譜感應y, D50光源光譜)
|
D50(P) |
nm |
x |
y |
z |
Px |
Py |
Pz |
|
24.44787 |
380 |
0.001368 |
0.000039 |
0.00645 |
0.033445 |
0.000953 |
0.157689 |
|
29.82885 |
390 |
0.004243 |
0.00012 |
0.02005 |
0.126564 |
0.003579 |
0.598069 |
|
49.24662 |
400 |
0.01431 |
0.000396 |
0.06785 |
0.704719 |
0.019502 |
3.341384 |
|
56.44974 |
410 |
0.04351 |
0.00121 |
0.2074 |
2.456128 |
0.068304 |
11.70768 |
|
59.97316 |
420 |
0.13438 |
0.004 |
0.6456 |
8.059194 |
0.239893 |
38.71867 |
|
57.76397 |
430 |
0.2839 |
0.0116 |
1.3856 |
16.39919 |
0.670062 |
80.03776 |
|
74.76665 |
440 |
0.34828 |
0.023 |
1.74706 |
26.03973 |
1.719633 |
130.6218 |
|
87.18889 |
450 |
0.3362 |
0.038 |
1.77211 |
29.3129 |
3.313178 |
154.5083 |
|
90.55862 |
460 |
0.2908 |
0.06 |
1.6692 |
26.33445 |
5.433517 |
151.1605 |
|
91.32148 |
470 |
0.19536 |
0.09098 |
1.28764 |
17.84056 |
8.308429 |
117.5892 |
|
95.06664 |
480 |
0.09564 |
0.13902 |
0.81295 |
9.092173 |
13.21616 |
77.28443 |
|
91.92939 |
490 |
0.03201 |
0.20802 |
0.46518 |
2.94266 |
19.12315 |
42.76371 |
|
95.69667 |
500 |
0.0049 |
0.323 |
0.272 |
0.468914 |
30.91002 |
26.02949 |
|
96.59098 |
510 |
0.0093 |
0.503 |
0.1582 |
0.898296 |
48.58526 |
15.28069 |
|
97.11314 |
520 |
0.06327 |
0.71 |
0.07825 |
6.144348 |
68.95033 |
7.599102 |
|
102.0873 |
530 |
0.1655 |
0.862 |
0.04216 |
16.89545 |
87.99924 |
4.304 |
|
100.7473 |
540 |
0.2904 |
0.954 |
0.0203 |
29.25701 |
96.1129 |
2.04517 |
|
102.3134 |
550 |
0.43345 |
0.99495 |
0.00875 |
44.34772 |
101.7967 |
0.895242 |
|
100 |
560 |
0.5945 |
0.995 |
0.0039 |
59.45 |
99.5 |
0.39 |
|
97.73786 |
570 |
0.7621 |
0.952 |
0.0021 |
74.48603 |
93.04645 |
0.20525 |
|
98.9245 |
580 |
0.9163 |
0.87 |
0.00165 |
90.64452 |
86.06431 |
0.163226 |
|
93.5113 |
590 |
1.0263 |
0.757 |
0.0011 |
95.97065 |
70.78805 |
0.102862 |
|
97.70746 |
600 |
1.0622 |
0.631 |
0.0008 |
103.7849 |
61.65341 |
0.078166 |
|
99.29399 |
610 |
1.0026 |
0.503 |
0.00034 |
99.55215 |
49.94488 |
0.03376 |
|
99.07049 |
620 |
0.85445 |
0.381 |
0.00019 |
84.65077 |
37.74586 |
0.018823 |
|
95.75347 |
630 |
0.6424 |
0.265 |
5E-05 |
61.51203 |
25.37467 |
0.004788 |
|
98.89672 |
640 |
0.4479 |
0.175 |
0.00002 |
44.29584 |
17.30693 |
0.001978 |
|
95.70871 |
650 |
0.2835 |
0.107 |
0 |
27.13342 |
10.24083 |
0 |
|
98.2379 |
660 |
0.1649 |
0.061 |
0 |
16.19943 |
5.992512 |
0 |
|
103.0586 |
670 |
0.0874 |
0.032 |
0 |
9.007325 |
3.297877 |
0 |
|
99.18921 |
680 |
0.04677 |
0.017 |
0 |
4.63908 |
1.686217 |
0 |
|
87.42788 |
690 |
0.0227 |
0.00821 |
0 |
1.984613 |
0.717783 |
0 |
|
91.65707 |
700 |
0.011359 |
0.004102 |
0 |
1.041147 |
0.375977 |
0 |
|
92.93752 |
710 |
0.00579 |
0.002091 |
0 |
0.53814 |
0.194332 |
0 |
|
76.89465 |
720 |
0.002899 |
0.001047 |
0 |
0.222943 |
0.080509 |
0 |
|
86.55502 |
730 |
0.00144 |
0.00052 |
0 |
0.124637 |
0.045009 |
0 |
|
Sum |
1012.591 |
1050.526 |
865.6417 |
Yr =1050.526/1050.526=1
yr=Y/Yr=0.279123/1=0.279123
yr > 0.008856
fy=![clip_image018[1]](http://www.fredkuo.idv.tw/wordpress/wp-content/uploads/2017/05/clip_image0181.gif "clip_image018[1]"){kind=small}
=
=0.6535
L=116*0.6535-16=59.806
a=500(fx-fy)
xr=X/Xr
X=上述取得的 X刺激值 0.191001
Xr =SUMPRODUCT(人眼光譜感應x, D50光源光譜)/SUMPRODUCT(人眼光譜感應y, D50光源光譜)
Xr = 1012.591/1050.526=0.963889
xr=X/Xr=0.191001/0.963889=0.198157
xr> 0.008856
fx=
=
=0.5829
a=500(0.5829-0.6535)=-35.3
b=200(fy-fz)
zr=Z/Zr
Z=上述取得的 Z刺激值 0.547122
Zr =SUMPRODUCT(人眼光譜感應z, D50光源光譜)/SUMPRODUCT(人眼光譜感應y, D50光源光譜)
Zr = 856.6714/1050.526=0.824008
zr=Z/Zr=0.547122/0.824008=0.664
zr> 0.008856
fz=
=
=0.8724
b=200(0.6535-0.8724)=-43.78
由以上算式，取得油墨 Lab 值：59.8、-35.3、-43.78
再由 Lab 值取得這個顏色的三個屬性表現:亮度，色角度與飽和度。
亮度(L*): 59.8
色角度=IF(DEGREES(ATAN2(a*+0.00001,b*+0.000001))<0,DEGREES(ATAN2(a*+0.00001,b*+0.000001))+360,DEGREES(ATAN2(a*+0.00001,b*+0.000001)))=231
飽和度=SQRT(a*^2+b*^2)=56
無迴響
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