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October 27, 2020 05:09
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CIE color matching functions approximation
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import numpy as np | |
from scipy.optimize import curve_fit | |
from matplotlib import pyplot as plt | |
t = np.arange(380.0, 781.0, 5.0) | |
s = np.asarray([ | |
[0.0014, 0.0000, 0.0065], [0.0022, 0.0001, 0.0105], [0.0042, 0.0001, 0.0201], | |
[0.0076, 0.0002, 0.0362], [0.0143, 0.0004, 0.0679], [0.0232, 0.0006, 0.1102], | |
[0.0435, 0.0012, 0.2074], [0.0776, 0.0022, 0.3713], [0.1344, 0.0040, 0.6456], | |
[0.2148, 0.0073, 1.0391], [0.2839, 0.0116, 1.3856], [0.3285, 0.0168, 1.6230], | |
[0.3483, 0.0230, 1.7471], [0.3481, 0.0298, 1.7826], [0.3362, 0.0380, 1.7721], | |
[0.3187, 0.0480, 1.7441], [0.2908, 0.0600, 1.6692], [0.2511, 0.0739, 1.5281], | |
[0.1954, 0.0910, 1.2876], [0.1421, 0.1126, 1.0419], [0.0956, 0.1390, 0.8130], | |
[0.0580, 0.1693, 0.6162], [0.0320, 0.2080, 0.4652], [0.0147, 0.2586, 0.3533], | |
[0.0049, 0.3230, 0.2720], [0.0024, 0.4073, 0.2123], [0.0093, 0.5030, 0.1582], | |
[0.0291, 0.6082, 0.1117], [0.0633, 0.7100, 0.0782], [0.1096, 0.7932, 0.0573], | |
[0.1655, 0.8620, 0.0422], [0.2257, 0.9149, 0.0298], [0.2904, 0.9540, 0.0203], | |
[0.3597, 0.9803, 0.0134], [0.4334, 0.9950, 0.0087], [0.5121, 1.0000, 0.0057], | |
[0.5945, 0.9950, 0.0039], [0.6784, 0.9786, 0.0027], [0.7621, 0.9520, 0.0021], | |
[0.8425, 0.9154, 0.0018], [0.9163, 0.8700, 0.0017], [0.9786, 0.8163, 0.0014], | |
[1.0263, 0.7570, 0.0011], [1.0567, 0.6949, 0.0010], [1.0622, 0.6310, 0.0008], | |
[1.0456, 0.5668, 0.0006], [1.0026, 0.5030, 0.0003], [0.9384, 0.4412, 0.0002], | |
[0.8544, 0.3810, 0.0002], [0.7514, 0.3210, 0.0001], [0.6424, 0.2650, 0.0000], | |
[0.5419, 0.2170, 0.0000], [0.4479, 0.1750, 0.0000], [0.3608, 0.1382, 0.0000], | |
[0.2835, 0.1070, 0.0000], [0.2187, 0.0816, 0.0000], [0.1649, 0.0610, 0.0000], | |
[0.1212, 0.0446, 0.0000], [0.0874, 0.0320, 0.0000], [0.0636, 0.0232, 0.0000], | |
[0.0468, 0.0170, 0.0000], [0.0329, 0.0119, 0.0000], [0.0227, 0.0082, 0.0000], | |
[0.0158, 0.0057, 0.0000], [0.0114, 0.0041, 0.0000], [0.0081, 0.0029, 0.0000], | |
[0.0058, 0.0021, 0.0000], [0.0041, 0.0015, 0.0000], [0.0029, 0.0010, 0.0000], | |
[0.0020, 0.0007, 0.0000], [0.0014, 0.0005, 0.0000], [0.0010, 0.0004, 0.0000], | |
[0.0007, 0.0002, 0.0000], [0.0005, 0.0002, 0.0000], [0.0003, 0.0001, 0.0000], | |
[0.0002, 0.0001, 0.0000], [0.0002, 0.0001, 0.0000], [0.0001, 0.0000, 0.0000], | |
[0.0001, 0.0000, 0.0000], [0.0001, 0.0000, 0.0000], [0.0000, 0.0000, 0.0000]]) | |
D65 = { | |
380: 49.428921, | |
385: 51.759850, | |
390: 54.090779, | |
395: 68.025953, | |
400: 81.961127, | |
405: 86.313504, | |
410: 90.665880, | |
415: 91.655559, | |
420: 92.645238, | |
425: 89.319349, | |
430: 85.993460, | |
435: 95.060474, | |
440: 104.127488, | |
445: 110.199807, | |
450: 116.272126, | |
455: 116.704928, | |
460: 117.137730, | |
465: 115.706664, | |
470: 114.275597, | |
475: 114.837711, | |
480: 115.399824, | |
485: 111.895876, | |
490: 108.391928, | |
495: 108.703479, | |
500: 109.015030, | |
505: 108.268521, | |
510: 107.522013, | |
515: 106.057800, | |
520: 104.593588, | |
525: 106.069007, | |
530: 107.544427, | |
535: 105.928756, | |
540: 104.313086, | |
545: 104.157277, | |
550: 104.001468, | |
555: 102.000734, | |
560: 100.000000, | |
565: 98.184891, | |
570: 96.369783, | |
575: 96.119049, | |
580: 95.868315, | |
585: 92.348821, | |
590: 88.829328, | |
595: 89.531304, | |
600: 90.233281, | |
605: 90.059665, | |
610: 89.886050, | |
615: 88.959839, | |
620: 88.033629, | |
625: 85.844284, | |
630: 83.654939, | |
635: 83.904045, | |
640: 84.153151, | |
645: 82.327113, | |
650: 80.501074, | |
655: 80.631971, | |
660: 80.762868, | |
665: 81.835533, | |
670: 82.908199, | |
675: 80.915868, | |
680: 78.923538, | |
685: 74.590608, | |
690: 70.257678, | |
695: 71.238575, | |
700: 72.219472, | |
705: 73.564167, | |
710: 74.908862, | |
715: 68.486759, | |
720: 62.064656, | |
725: 66.225988, | |
730: 70.387321, | |
735: 73.001133, | |
740: 75.614945, | |
745: 69.824749, | |
750: 64.034552, | |
755: 55.396835, | |
760: 46.759117, | |
765: 57.025699, | |
770: 67.292280, | |
775: 65.562176, | |
780: 63.832072 | |
} | |
def gauss(x, *p): | |
A, mu, sigma = p | |
return A * 1.0 / sigma / np.sqrt(2.0 * np.pi) * np.exp(-(x-mu)**2/(2.*sigma**2)) | |
def gauss_mix(x, *p): | |
A1, mu1, sigma1, A2, mu2, sigma2 = p | |
return gauss(x, A1, mu1, sigma1) + gauss(x, A2, mu2, sigma2) | |
fig, ax = plt.subplots() | |
for i in range(3): | |
p0 = [1., 450., 50., 1., 600., 50.] if i == 0 else [1., 450., 50.] | |
d65s = [D65[x] * y for x, y in zip(t, s[:, i])] | |
coeff, var_matrix = curve_fit(gauss_mix if i == 0 else gauss, t, d65s, p0=p0) | |
print(*coeff) | |
r = (gauss_mix if i == 0 else gauss)(t, *coeff) | |
c = ['red', 'green', 'blue'][i] | |
ax.plot(t, r, c=c) | |
ax.scatter(t, d65s, c=c, label=c, alpha=0.9, edgecolors='none') | |
ax.set(xlabel='wave length[nm]', ylabel='Intensity', | |
title='CIE Color matching functions') | |
ax.legend() | |
ax.grid(True) | |
fig.savefig("test.png") | |
plt.show() |
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