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Based on the cone cell sensitivity, a new metric defined as cone sensitivity difference (CSD) was proposed to describe the color discrimination property of a light source. We conducted experiments at mesopic condition to test the performance of the metric. A color temperature tunable poly-chromatic LED system consisted of 7 single-color LEDs was utilized in the experiments. The performance of the metric was assessed by computing the Spearman and Pearson correlation coefficients with the observers’ ratings of color discrimination obtained from the experiments. Several conventional color quality metrics, including Ra, color quality scale (Qa), gamut area scale (Qg) and color-discrimination index (CDI), were also evaluated with respect to color discrimination by correlation analyses. Among the selected metrics, Qg had the best Spearman and Pearson correlation coefficients with the observers’ ratings for most of the correlated color temperatures (CCTs). The newly proposed CSD was highly (p<0.01) correlated with Qg, and its correlation with the observers’ ratings increased at the higher CCTs. For CCT above 5000K, CSD had significant Pearson correlation coefficients with the observers’ ratings. There was a possibility that CSD would be qualified to describe color discrimination with further optimization.
© 2015 Optical Society of America
1. Introduction
“Color discrimination” is a capability of a light source which allows an observer to discriminate among various colors viewed simultaneously [1,2]. It is closely related to “feeling of contrast” of object colors under illumination [3], thus it has direct influence on visual clarity [4]. In a color vision process, the spectral content reflected from an object surface enters into the eyes, then elicits the retinal cones to generate color sensation [5]. The color discrimination is determined by the spectral effects on objects’ color appearance of the light source, as well as the cone cells responses to the stimulus [6].
For a light source, there are three commonly used parameters to characterized the chromaticity qualities, namely, luminous efficacy of optical radiation (LER), correlated color temperature (CCT) and color rendering metric (Ra) [7]. The factor that fundamentally determines the property of a light source is the spectral power distribution (SPD), which also determines the value of LER, CCT and Ra. For several decades, Ra has been recommended as the most common metric to evaluate color quality of light sources. But in recent years, numerous studies have claimed that Ra is not qualified for the light-emitting diodes (LEDs) [3,7–9], and several new metrics have been proposed to evaluate the color quality [8]. The new metrics include those focusing on the objective aspect of a light source, such as CDI and Qa [2,8], and those focusing on the subjective aspect, such as feeling of contrast index (FCI) [3], flattery metric [10], color preference metric and metric based on memory colors [9,11,12]. Most of the metrics have been validated with experimental verification. However, most of the verification experiments were conducted through visual physiological experiments under photopic condition [3,13], with little consideration for the mesopic condition. The Purkinje effect implies that spectral sensitivity of human eyes relies on the light intensity [14], and the color vision is a dynamic system from photopic vision to scotopic vision. At low illumination condition, colors are fading, and human eyes perceive colors different from those under photopic lighting condition. For example, a green color palette would turn out to be “blue” in mesopic vision [15]. As a result of Purkinje effect, the color quality of a light source will change in mesopic condition as well.
The color quality of a light source has various descriptors, such as fidelity, vividness, naturalness, attractiveness, contrast, etc [3,9,13]. Different descriptors have interdependence in between, so they can be classified into different groups based on factor analyses. For example, the color fidelity and color naturalness describe the same factor. However, one descriptor alone cannot describe the color quality comprehensively, for example, Ra and Qa are appropriate metrics for color fidelity and naturalness, and memory color similarity (Sa) is qualified to describe the preference and attractiveness of color appearance [9].
Color discrimination is one of the most important descriptor of color quality. The existing metric for the descriptor is the color discrimination index (CDI). It is complementary to the CRI. CDI is also an objective measure using the first eight test color samples for evaluating CRI. The area of the octagon defined by the chromaticities in CIE1964 coordinates of the test color samples illuminated by a illuminant C is set as 100 [2]. The percentage of the area of the octagon formed by a test source compared to the area formed by illuminant C is the CDI of the test light source. Similar to CDI, Qg is complementary to the CQS. The polygon formed by the 15 test color samples illuminated by a test light source in the CIELAB (a*,b*) coordinates is the gamut area. The value of the area normalized by the gamut area of illuminant D65 multiplied by 100 is the Qg [8].
In this paper, we proposed another metric, which was independent of color spaces, sample colors and standard illuminants, to represent the color discrimination capability of a light source. In order to obtain such metric, we studied the mechanism of cone cells that dominate chromatic vision and conducted experiments under mesopic condition to test color discrimination by utilizing a color temperature tunable LED system. The LED system is composed of blue, green, amber and red LEDs with narrow-band type SPDs. We defined the metric based on cone cell sensitivity and compared it with conventional color quality metrics in terms of color discrimination. The performance of each metrics in describing color discrimination was also analyzed.
2. Cone cell sensitivity
The raw color signals for vision are originated from cone cells in the retina [16]. There are three types of cone cells with different spectral sensitivity, which are the foundation of color vision [17]. According to the relative spectral positions of the peak sensitivity, they are referred to as long-, middle- and short-wavelength-sensitive cone cells, shortened as L, M and S cone cells. The spectral sensitivities of these three cone cells overlap with each other extensively. Thus, light is rarely perceived by only one type of cone cell [18].
As shown in Fig. 1, both M and L cone cell sensitivity curves cover the whole visible spectrum while the spectral sensitivity of S cone cell diminishes above 560nm. Because M and L cone sensitivity overlap the whole visible spectrum range, we presume that their sensitivity difference, as shown in Fig. 2, is the key factor to discern the wavelength. By integrating the cone sensitivity difference value with SPD value, we get a typical metric that reveal the spectral effects on the color stimulus intensity.
Fig. 1 The normalized cone sensitivity of L, M and S cone cells of 10°visual angle in logarithmic distribution [19].
The proposed metric is cone sensitivity difference (CSD), which is defined as:
S(λ) is the relative spectral power of the wavelength λ, L(λ) is the L cone cell spectral sensitivity and M(λ) is the M cone cell spectral sensitivity.
3. Experimental
In this section, visual physiological experiments were conducted to validate the correlation between the metrics and color discrimination property.
3.1 Apparatus
Two observation booths, adjacent to each other, were placed on a platform which was 1.50 m above the floor in a dark room. The booths were 0.55 m (width) × 0.41 m (length) × 0.33 m (height). The color of the inner booth surface was the neutral Munsell N8 gray.
As shown in Fig. 3, the identical object sets in the booth were: blue can, green can and red can, a green apple, a red apple, a mango, purple grapes, paper flowers of red, green, blue and yellow. The metal cans had glazed surface and always formed reflection points. The fruit had textured surface with mixed chroma. The colored paper flowers had the most uniform surface chroma. These three types of surface appeared different chroma shifts under the same light source. Furthermore, it has been summarized that the “feelings of contrast” or “visual clarity” of object colors can be estimated by using a four-color combination composed by red, yellow, green and blue [3], so the colors in each group contained blue, green, yellow and red, while there was no blue fruit, we used purple grapes instead. At the top of each booth, there was a polycarbonate diffuser to optimize color mixing and the tunable LED cluster was 0.23m above the diffuser.
Fig. 3 The objects (1. red paper flower; 2. yellow paper flower; 3. blue paper flower; 4. green paper flower; 5. multicolor paper flower; 6. red can; 7. green can; 8. blue can; 9. green apple; 10. red apple; 11. grape; 12. mango) illuminated under one LED combination of 435 (nm)-519 (nm)-593 (nm) at 5600K, with a uniform illumination of 20 ± 1.2 lx at the inner bottom of the booth. The photograph had a hue shift from the real objects and appeared “cooler”.
Identical object sets shown in Fig. 3, were placed in booth A and booth B. The objects in the two booths were illuminated by different LED light sources. The observers moved along the dash line in Fig. 4, which was 1.50 meters parallel away from the front of the booths, to observe the objects and make comparison according to their visual perception.
Fig. 4 The positions of the adjacent booths and the observer. Observers were free to move along the dash line with a 20° horizontal visual angle when only watching one booth.
3.2 Color temperature tunable LED system
The color temperature tunable LED system contained seven commercially available single-color LEDs with different peak wavelengths: 435nm and 455nm blue LEDs, 508nm and 519nm green LEDs, 593nm amber and 633nm and 657nm red LEDs. Their SPDs are shown in Fig. 5. These LEDs can be divided into three groups according to their peak wavelengths, namely, the short-wavelength group of blue LEDs, the middle-wavelength group of green ones and the long-wavelength group of amber and red ones. A three-chip LED combination consisted of one member from each groups, and we obtained 12 sets of three-chip LED combinations in total. By tuning the relative power of each LED in the three-chip LED combination, we attained 11 CCT from 2500K to 7500K along the Plankian locus for each of those 12 LED combinations. Therefore, 132 SPDs were generated in our experiments altogether.
3.3 Observers
23 male and 27 female students from Peking University Shenzhen graduate school participated in the experiments. Their ages were ranging from 23 to 28, with an average of 25.2 and a standard deviation of 1.47. All the students had the normal color vision and passed the Ishihara blindness test. They had neither participated in similar color experiments nor had the prior knowledge of the light sources that were used for the experiment, so they judged the performance of light sources just from the visual perception only.
3.4 Side-by-side comparison
The adjacent booths were illuminated at 20 lx simultaneously by different three-chip LED combinations. At each CCT, there were 12 types of LED combinations. Thus the total number of comparing pairs for each CCT was 12*(12-1)/2 = 66. The 66 comparison pairs were randomly ordered for each observer. Observers were required to watch the objects in two booths illuminated by 12 different LED combinations for each CCT. They need to compare the color contrast of the ten object pairs in the two booths. The ten pairs are 1/2, 3/6, 4/5, 6/7, 6/9, 7/8, 8/10, 9/10, 9/11 and 11/12 as shown in Fig. 3. For each LED lighting combination, the booth which had 6 or more pairs with higher contrast rating got 1 point, meanwhile the booth with 4 pairs or less get 0 point. If both booths get equal number of pairs, then each booth got 0.5 point.
Prior to the paired comparison experiments, the observers had to take 5 minutes inside the dark room to get dark adaption. In addition, the observer is not allowed to communicate with each other about the experiments. There was no time limit during each comparing procedure. The scoring processes were repeated at 11 CCTs for each of 12 three-chip LED combinations. All the observers observed two different sets of 66 pairs. As a result, there were 100 sets of scores in total, conforming that each CCT had no less than 9 sets of scores. The average scores of the 12 LED combinations are listed in Table 1.
Table 1. The average scores for each of the 12 three-chip LED combinations at 11 CCTs. The “AVE” is the average value of the eleven scores for one combination.
4. Statistical analysis
As shown in Table 1, scores of the LED combinations changed as the CCT increases. The 435 (nm)-519 (nm)-633 (nm) LED combination got the highest average score. Combinations with amber LED performed worse than those with red ones. Combinations with 634nm red performed better than those with 657 nm red. Blue and green LEDs have no significant difference on color discrimination from CCT of 2500 K to 7500 K.
We computed Ra, Qa, Qg, CDI and CSD values of the 12 LED combinations at 11 CCTs, then studied the Pearson correlations between Ra, Qa, Qg, CDI and CSD predictions and listed the correlation coefficients in Table 2.
Table 2. Pearson correlation coefficients between the metric values
The second row in Table 2 shows that Ra is highly (p<0.01) correlated with Qa above 4000K. As shown in the last three rows, Qg, CDI and CSD, the three metrics show an obvious (p<0.01) positive correlation at most of the CCTs. It is also noticed that high negative correlation does exist between Ra, as well as Qa, and other metrics. It is unclear why the CSD has a definition that has no similarity to any other metrics, but statistically correlated with them. We need to compare the metric predictions to the experimental results to learn more about CSD.
The performance of the metrics on color discrimination is assessed by computing the Pearson and Spearman correlation coefficients between the metric predictions with the observers’ ratings at each CCT. All results are shown in Table 3.
Table 3. Pearson and Spearman correlation coefficients of Ra, Qa, Qg, CDI and CSD values with the color discrimination results obtained from the experiments.
The Ra value is the degree of color reproduction of the test light source to the reference illuminants in CRI system. By analyzing the calculation of Ra, we can easily find that Ra penalizes the chromatic deviation from the reference illuminant. However, the reference illuminant is not the optimal light source for color discrimination, and not all the deviations will weaken the color discrimination. Therefore, neither Ra nor Qa is qualified to represent the color discrimination. In Table 3, Ra and Qa have no correlation with the ratings at all CCTs.
The Qg is calculated as the gamut area formed by the (a*, b*) coordinates of the 15 saturated samples illuminated by the light source in the CIELAB color space. The CDI is calculated as the gamut area formed by the (u,v) coordinates of 8 test colors for computing the CRI in a uniform CIE 1960 color space. The gamut areas represent the hue range that can be rendered. With increase in hue range, there is always an increase in gamut area. With closer relation to hue range, both Qg and CDI show better correlation with color discrimination. However, at low CCT, Qg and CDI are not highly correlated with the observers’ ratings. As shown in Fig. 6, at lower CCT, gamut areas formed by (a*, b*) coordinates shift to the third and fourth quadrants; in the (u,v) coordinates (Fig. 7), the area becomes longer and narrower at lower CCT, though the area values are roughly the same, the hue ranges turn out to be relatively smaller. When CCT is above 5000K, Qg have significant Spearman correlations with color discrimination, as shown in Table 3.
Fig. 6 The gamut areas in the CIELAB (a*,b*) color space of the reference illuminant of D65 and twelve three-chip LED combinations at (a) 3000K and (b) 5600K.
Fig. 7 The gamut areas in the 1960 CIE (u, v) chromaticity diagram of the reference illuminant of D65 and twelve three-chip LED combinations at (a) 3000K and (b) 5600K.
The CSD represents the degree of spectral effects on the sensitivity difference between L and M cone cells. It is theoretically reasonable to represent color discrimination, but it hasn’t performed the best in the test among other metrics. At CCTs above 5000K, the CSD has a significant Pearson correlation with the observers’ ratings. The Spearman correlation coefficients are not high for all the CCTs, but it increases as the CCT rises. When CCT is lower than 5000K, the long-wavelength content in the spectra is comparatively higher, and the degree of sensitivity difference between L and M cone cells at long wavelength is rather high, a slight increase or decrease of the long-wavelength part will generate a huge change in CSD, thus the CSD is more sensitive to the long-wavelength spectra and become unstable. In the future study, we can optimize CSD by revising its value at long-wavelength spectra and considering the sensitivity of S cone cell and rod cell at short-wavelength spectra.
5. Summary
In this work, we proposed the CSD metric based on cone cell sensitivity to evaluate the capability of color discrimination of a light source. In order to assess the performance of the new CSD metric and conventional color quality metrics such as Ra, Qa, Qg and CDI, visual physiological experiments were conducted to obtain color discrimination ratings for 12 three-chip LED combinations at 11 CCTs. We further applied Spearman and Pearson correlation coefficients to test the correlation between a metric and the experimental results of color discrimination.
The five metrics had various correlation with observers’ ratings of color discrimination. Both Ra and Qa correlated slightly with color discrimination, despite they were the most popular metrics today for measuring the color rendering quality. Qg and CDI had high (p<0.05) correlation with the scores for the majority of 11 CCTs. The CSD’s correlation coefficients improved as the CCT increased and became significantly (p<0.05) correlated with color discrimination above 5000K.
Qg, CDI and CSD, statistically similar with each other, can represent the color discrimination property of a light source while CSD still needs optimization at lower CCTs. The advantages of the CSD are the independence of color spaces, standard illuminants or color samples, and only counting the L and M cone cell sensitivities. With further modification, the CSD shall be applicable for all the illuminant condition–from photopic to scotopic. In the future study, the sensitivity function of S cone cell and rod cell will be considered in the definition of CSD. This new CSD formula will be an ideal color discrimination metric for not only the solid-state light sources but also for all the conventional light sources.
Acknowledgment
The authors would like to thank Mr. John Rooymans for sharing his early studies in color discrimination under mesopic vision through numerous helpful discussions.
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