Entropy, color, and color rendering

Luke L. A. Price

doi:10.1364/JOSAA.29.002557

Journal of the Optical Society of America A
Vol. 29,
Issue 12,
pp. 2557-2565
(2012)
•https://doi.org/10.1364/JOSAA.29.002557

Entropy, color, and color rendering

Luke L. A. Price

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Luke L. A. Price, "Entropy, color, and color rendering," J. Opt. Soc. Am. A 29, 2557-2565 (2012)

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Related Topics
Table of Contents Category
- Vision, Color, and Visual Optics
Optics & Photonics Topics
?

The topics in this list come from the Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Color (330.1690)
- Color vision (330.1720)
- Color, rendering and metamerism (330.1715)

About this Article
History
- Original Manuscript: June 27, 2012
- Revised Manuscript: August 21, 2012
- Manuscript Accepted: October 9, 2012
- Published: November 20, 2012
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 8, Iss. 1

Abstract

The Shannon entropy [Bell Syst. Tech J. 27, 379 (1948)] of spectral distributions is applied to the problem of color rendering. With this novel approach, calculations for visual white entropy, spectral entropy, and color rendering are proposed, indices that are unreliant on the subjectivity inherent in reference spectra and color samples. The indices are tested against real lamp spectra, showing a simple and robust system for color rendering assessment. The discussion considers potential roles for white entropy in several areas of color theory and psychophysics and nonextensive entropy generalizations of the entropy indices in mathematical color spaces.

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Illuminant	CE	$C E_{Wh}$	$C E_{Sp}$	$x$	$y$
1. $x y z$ -bar at 555 nm	0.0%	62.6%	0.0%	0.409	0.590
2. Green LED	48.2%	77.2%	62.3%	0.128	0.675
3. Compact fluorescent	69.7%	93.7%	74.3%	0.417	0.414
4. RGB LED	76.6%	99.8%	76.7%	0.367	0.313
5. 17 000 K fluorescent	78.0%	96.0%	81.2%	0.263	0.260
6. White LED	84.2%	98.9%	85.2%	0.296	0.295
7. 2856 K blackbody	85.4%	90.1%	94.7%	0.458	0.410
8. Tungsten halogen	85.6%	90.2%	95.0%	0.457	0.411
9. Extreme T blackbody	85.7%	92.9%	92.2%	0.240	0.235
10. Indirect daylight	96.4%	98.3%	98.1%	0.283	0.291
11. Equal quanta	99.0%	99.5%	99.5%	0.307	0.311
12. 6504 K blackbody	99.2%	99.8%	99.4%	0.313	0.323
13. Equi-energy	100.0%	100.0%	100.0%	0.333	0.333

Illuminant	CE ( $n = 81$ )	$C E_{Wh}$ ( $n = 81$ )	$C E_{Sp}$ ( $n = 81$ )	CRI $R_{a}$	CQS $Q_{a}$ 7.1	CCT (K)
32: Ideal prime color	24.2%	98.8%	24.5%	69.1%	68.8%	4236
9: HPS	64.5%	79.5%	81.2%	37.4%	20.1%	2071
72: RGB model CRI opti	72.9%	95.1%	76.7%	81.6%	89.8%	3300
45: CIE F12	73.1%	92.9%	78.7%	79.0%	83.1%	3000
6: Tri-phosphor FL	74.9%	95.4%	78.5%	79.5%	82.2%	3380
29: Illum. A (400–700 nm)	82.3%	91.6%	89.9%	98.2%	99.5%	2864
11: Incandescent	86.7%	91.2%	95.1%	98.0%	99.8%	2812
5: Daylight FL	92.3%	99.9%	92.4%	76.5%	77.4%	6484
30: $D_{65}$ (400–700 nm)	93.7%	99.9%	93.9%	99.8%	99.7%	6504
33: Blackbody 6504 K	99.4%	99.8%	99.6%	98.4%	98.0%	6502

Illuminant	CE	$C E_{Wh}$	$C E_{Sp}$	$x$	$y$
1. $x y z$ -bar at 555 nm	0.0%	62.6%	0.0%	0.409	0.590
2. Green LED	48.2%	77.2%	62.3%	0.128	0.675
3. Compact fluorescent	69.7%	93.7%	74.3%	0.417	0.414
4. RGB LED	76.6%	99.8%	76.7%	0.367	0.313
5. 17 000 K fluorescent	78.0%	96.0%	81.2%	0.263	0.260
6. White LED	84.2%	98.9%	85.2%	0.296	0.295
7. 2856 K blackbody	85.4%	90.1%	94.7%	0.458	0.410
8. Tungsten halogen	85.6%	90.2%	95.0%	0.457	0.411
9. Extreme T blackbody	85.7%	92.9%	92.2%	0.240	0.235
10. Indirect daylight	96.4%	98.3%	98.1%	0.283	0.291
11. Equal quanta	99.0%	99.5%	99.5%	0.307	0.311
12. 6504 K blackbody	99.2%	99.8%	99.4%	0.313	0.323
13. Equi-energy	100.0%	100.0%	100.0%	0.333	0.333

Illuminant	CE ( $n = 81$ )	$C E_{Wh}$ ( $n = 81$ )	$C E_{Sp}$ ( $n = 81$ )	CRI $R_{a}$	CQS $Q_{a}$ 7.1	CCT (K)
32: Ideal prime color	24.2%	98.8%	24.5%	69.1%	68.8%	4236
9: HPS	64.5%	79.5%	81.2%	37.4%	20.1%	2071
72: RGB model CRI opti	72.9%	95.1%	76.7%	81.6%	89.8%	3300
45: CIE F12	73.1%	92.9%	78.7%	79.0%	83.1%	3000
6: Tri-phosphor FL	74.9%	95.4%	78.5%	79.5%	82.2%	3380
29: Illum. A (400–700 nm)	82.3%	91.6%	89.9%	98.2%	99.5%	2864
11: Incandescent	86.7%	91.2%	95.1%	98.0%	99.8%	2812
5: Daylight FL	92.3%	99.9%	92.4%	76.5%	77.4%	6484
30: $D_{65}$ (400–700 nm)	93.7%	99.9%	93.9%	99.8%	99.7%	6504
33: Blackbody 6504 K	99.4%	99.8%	99.6%	98.4%	98.0%	6502

Abstract

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Figures (4)

Tables (2)

Equations (5)

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Journal of the Optical Society of America A

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