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Abstract
Whiteness is an important colorimetric characteristic for surface colors. The CIE whiteness formula, the most widely used formula, only characterizes the whiteness of a surface color under CIE standard D65 and requires a sample to be within a small chromaticity region. In this study, 20 observers evaluated the whiteness appearance of 88 samples under four light settings at different CCT levels (i.e., 3000, 4000, 5000, and 6500 K). The 88 samples were carefully selected and the spectral power distributions of the light settings were carefully designed using a spectrally tunable LED device, so that the chromaticities of the samples under each light settings uniformly covered a wide range along the yellow/blue direction in a color space, which had never been realized before. The results, together with the two recent studies, allowed the derivation of ellipsoids for classifying the whiteness appearance for surface colors. For the samples within the derived ellipsoids, though the Uchida whiteness formula with CAT02 (WUchida,CAT02) had a higher correlation to the perceived whiteness than the CIE whiteness formula with CAT02 (WCIE,CAT02), samples that were perceived as white and had a high chroma with a hue angle of blue due to the high violet/ultraviolet radiation in the illumination may had a negative WUchida,CAT02 value. A comprehensive whiteness formula that can accurately characterize the whiteness appearance for surface colors under an arbitrary light source by considering different conditions is still necessary and the work is undergoing.
© 2017 Optical Society of America
1. Introduction
1.1 Whiteness appearance for surface colors
White, an important and familiar color to our visual experience, can be associated with the color of an illumination or a surface. For surface colors, whiteness is an important colorimetric characteristic, as a whiter appearance is always associated with cleanness, freedom from contaminants, and good quality. In comparison to the great efforts being made on investigating the chromaticity of white for illumination in recent years [1–3] due to the wider application of light emitting diodes (LEDs) [3], little attention has been paid on the chromaticity of white for surface colors. It is widely accepted that a surface should have a low chroma level and a certain level of lightness to produce a white appearance. Thus, washing, sun drying, bleaching powder, and blue dyes are commonly used to reduce the chroma level, especially to neutralize the yellow tint of many materials of natural and man-made objects (e.g., cotton fibers and wood-pulps), enhancing the whiteness appearance.
Furthermore, manufacturers add fluorescent whitening agents (FWAs), also known as optical brightening agents (OBAs), to most man-made objects to enhance the whiteness appearance and also modulate the amount to produce a desired whiteness appearance. FWAs absorb the ultraviolet or violet radiation from the illumination and re-emit blue radiation. Such an interaction between FWAs and illumination not only increases the luminance factor of a surface, but also introduces a chromaticity shift towards 470 nm (as shown in Fig. 1), which may make FWA-enhanced whites appear whiter than a perfect reflector. Thus, the spectral content of an illumination, especially the amount of violet or ultraviolet radiation, is critically important to the excitation of FWAs and hence affects the whiteness appearance.
Fig. 1 Illustration about how chromaticity shift introduces the change of color appearance and change of whiteness appearance.
1.2 Whiteness formulas for surface colors
Many formulas have been developed to characterize the whiteness appearance of surface colors since 1934. For the formulas that can only be applied to non-FWA whites, a perfect reflector (e.g., a Magnesium Oxide plate) having a reflectance factor of 100% across the entire visible spectrum is commonly graded to have a highest whiteness value (e.g., 1 or 100); any departure from the chromaticity coordinates of a perfect reflector in a color space is penalized with a lower whiteness value. The larger the departure, the lower the value [4–7]. None of these formulas, however, specify the boundary of a surface color for using the formulas.
The other set of formulas can be applied to both non-FWA whites and FWA whites. All of them are developed based on Ganz formula, as shown in Eq. (1), and rate the whiteness values of FWA-enhanced whites above 100 [8].
where Y is the luminance factor of a sample; (x,y) is the chromaticity coordinate of a sample; D, P, Q, and C are the coefficients to determine the “whiteness bias”.The International Commission on Illumination (CIE) recommended a whiteness formula, shown as Eq. (2) in 1986 [9], which is widely used in surface color industry and adopted by the International Organization for Standardization (ISO) [10, 11].
where Y and (x, y) are the luminance factor and the chromaticity coordinates of a sample under CIE standard D65 illuminant; (xn,yn) are the chromaticity coordinates of CIE standard D65 illuminant. The chromaticity coordinates can be calculated using either the CIE 1931 color matching functions (CMFs) or the CIE 1964 CMFs.
To completely characterize the whiteness appearance of surface colors [12], two tint formulas—Eqs. (3) and (4)—were proposed together with Eq. (2). They characterize the green/red tint as illustrated in Fig. 1. Equation (3) uses the CIE 1931 CMFs; Eq. (4) uses the CIE 1964 CMFs.
It is noted that the CIE whiteness and tint formulas (i.e., Eqs. (2)-(4)) can only be used when 40 < WCIE < 5Y-280 and −4 < TCIE (or T10,CIE) < + 2 [9] (note: some documents limit −3 < TCIE (or T10,CIE) < + 3 [10, 13]).
The CIE whiteness formula, however, can only characterize the whiteness appearance of a surface color under CIE standard D65 illuminant, which is commonly realized using D65 simulators in reality. The formula does not consider the effect of illumination, though the spectral content of an illumination significantly affects the excitation of FWAs, as revealed by psychophysical studies [14–19] and numerical computations [20–22].
In addition to the shortcoming that the CIE whiteness formula does not take the illumination into consideration, it was also found that some samples outside the CIE limit may still be perceived as white [23]. Uchida developed Eqs. (5) and (6) to characterize the whiteness of in-base point samples and out-based samples respectively using 5Y-275 as a base point, but he did not specify the limit or boundary for using the revised formulas.
When 40 < WCIE < 5Y-275:
When WCIE > 5Y-275:
where:
Most of the past studies only focused on how to revise the tint limit defined in the CIE whiteness formula, which is the red/green shift as shown in Fig. 1. Ma et al. proposed to extend the CIE tint limit to −5 < T10,CIE < + 5 [15] and Vik et al. proposed to revise the CIE tint limit to −4 < T10,CIE < + 1 [24], both of which were based on the psychophysical experiments conducted under D65 simulators or 6500 K light settings. Wei et al. [19], however, recently found that samples under the 3000 K light settings were rated less white than those under the 4000 K and 6500 K light settings, which was likely due to the incomplete chromatic adaptation under 3000 K light settings suggested by Smet et al. [25, 26].
As LED lighting, especially spectrally tunable LED lighting, is becoming more and more popular [3], the effect of the spectral power distribution (SPD) of an illumination on the whiteness appearance of surface colors is no longer trivial and the whiteness appearance of surface colors should not only be characterized under D65 simulators. With this in mind, CIE TC1-95 The Validity of the CIE Whiteness and Tint Equation was established in 2016 to extend the applications of the whiteness formula to illuminants other than CIE D65, and to verify the colorimetric limit of white region, which is also listed as one of the top priority research topics in the CIE Research Strategy [27].
This article describes a psychophysical experiment to investigate the whiteness boundary. The investigation was made using both FWA and non-FWA whites and based upon the sample chromaticities under various light settings, so that the effect of illumination was considered. More importantly, this study used a spectrally tunable LED device to significantly increase the violet/ultraviolet radiation that was never realized and studied before, so that the chromaticity coordinates of the white samples covered a large area in a color space, especially along the yellow/blue direction. The data collected in this experiment, together with those collected in two recent studies [15, 19], allowed a comprehensive analysis on whiteness boundary for surface colors and the performance of different whiteness formulas.
2. Methods
The experimental method and protocol were approved by the Institutional Review Board.
2.1 Apparatus, light settings, and color samples
A viewing booth, whose interiors were painted with Munsell N7 spectrally neutral paint and had dimensions of 50 cm (width) × 50 cm (depth) × 60 cm (height), was built for the experiment. A customized 14-channel spectrally tunable LED device was placed above the booth to provide a uniform illumination to the floor of the booth. The intensity of each channel can be adjusted individually and the peak wavelengths covered between 350 and 700 nm.
Four light settings, with nominal CCT levels of 3000, 4000, 5000, and 6500 K, were produced using the LED device. Unlike typical CIE daylight simulators, whose ultraviolet and violet radiations are strictly controlled to mimic the radiation of standard illuminants, we purposely prepared the higher ultraviolet and violet radiations of the four light settings than those used in the earlier studies, so that some of the samples with FWAs had an obvious blue appearance, which allowed us to find the whiteness boundary along yellow/blue direction. Though fluorescence effect was introduced by the strong violet/ultraviolet radiation, it was assumed that the illuminated color samples were still perceived in surface mode. The light settings were calibrated and measured at the center of the floor in the booth, where the white samples were placed for visual evaluations, to have an illuminance of 500 lux using a calibrated JETI specbos 1211TM spectroradiometer, a standard reflectance, and a calibrated Minolta T-10 illuminance meter. The SPDs of the four light settings are shown in Fig. 2, with the colorimetric characteristics being summarized in Table 1. It should be noted that the large Mu values listed in Table 1 indicate that the ultraviolet radiations included in these light settings were much higher than those in typical daylight illuminants due to the reason given above.
Fig. 2 Relative SPDs of the four light settings, as measured using a calibrated JETI specbos 1211TM spectroradiometer with a standard reflectance being placed at the center of the floor in the booth.
Table 1. Summary of colorimetric characteristics of the four light settings
The color samples were very carefully selected under the 6500 K light setting from a large number of samples, including NCS samples, Pantone color samples, fabric samples, plastic samples, and paper samples, with a goal to have the chromaticity coordinates of the samples cover a wide range along the yellow/blue direction in a color space at different luminance factor levels. The chromaticity coordinates were derived from the spectrum of the light reflected from each sample under each light setting measured using the JETI spectroradiometer. Finally, 88 samples were selected, including 45 NCS and Pantone matt samples without FWAs, 28 diffuse fabric samples with FWAs, 10 diffuse paper samples with FWAs, and five diffuse plastic samples with FWAs. Figure 3 shows the chromaticity coordinates (x10, y10) of these 88 samples under the 6500 K light setting at different luminance factor levels. It can be seen that most samples had chromaticity coordinates far away from the white point. The five samples whose chromaticities are shown in Fig. 3 (d) are plastic samples and had high amount of FWAs.
Fig. 3 Distribution of the chromaticity coordinates (x,y) of the 88 samples under the 6500 K light settings at different luminance factor levels (Y), calculated using CIE 1964 CMFs. (a) the chromaticities of the 6500 K light setting, together with the 3-step and 7-step MacAdam ellipses; (b) 40<Y≤60; (c) 60<Y≤80; (d) 80<Y≤100; (e) 100<Y (the FWA samples are labelled with □; the non-FWA samples are labelled with ▲).
2.2 Observers
Forty-four naïve observers (14 females and 30 males) between 21 and 26 years of age (mean = 21.6, std. dev. = 1.25) were recruited for the experiment. Most observers evaluated the whiteness appearance of each sample under two different light settings and some only made evaluations under a single light setting. In total, 20 observers made evaluations under each light setting.
2.3 Experimental procedure
During the experiment, each observer was asked to keep his/her chin and forehead on a rest, so that the observer’s eyes and the sample under illumination formed a geometry of 0°:45°. At the beginning of each session, the observer was asked to look into the booth for three minutes, allowing his or her eyes to chromatically adapt to the light setting. Then, the experimenter placed one sample at the center of the floor in the booth and asked the observer to make two evaluations—a forced choice and a magnitude estimation. The observer was asked to judge whether the color of the sample can be classified as white (i.e., either “yes” or “no”) and what was the whiteness percentage of the sample (i.e., 100% means a pure white and 0% means no trace of white). The 88 samples were presented in a random order. It took around 30 minutes to evaluate the 88 samples under each light setting. In total, 14,080 evaluations (20 observers × 2 evaluations × 88 samples × 4 light settings) were made in the experiment.
3. Results and discussions
3.1 Inter-observer variation and correlation between the two evaluations
The inter-observer variation was characterized using the Standardized Residual Sum of Squares (STRESS) [28] by comparing the whiteness percentage value of each sample rated by each observer and that of each sample rated by an average observer, which is the mean whiteness percentage value of each sample. The mean STRESS values for the 20 observers were 39.7, 35.5, 31.3, and 31.8 for 3000 K, 4000 K, 5000 K, and 6500 K light settings respectively, which were comparable to other studies related to color appearance evaluation [19, 29]. It can be observed that the evaluations under the 3000 K light setting had the largest inter-observer variation.
The two evaluations made by the observers were positively correlated. Samples that were more frequently judged as white were rated to have higher whiteness percentage values, as shown in Fig. 4. It was found that the 50% of the votes corresponded to a whiteness percentage value of 56%. Given the identical whiteness percentage scale employed in this study and in the two recent studies [15, 19] and the high resolution of the whiteness percentage data, the whiteness percentage data collected in this and the two recent experiments were combined in the following analyses, with a total of 1392 average whiteness percentage data. Under each CCT level, 348 samples were evaluated.
Fig. 4 Correlation between the two evaluations—magnitude estimation (i.e., whiteness percentage) and forced choice—made by the observers
3.2 Sample color appearance and CIE whiteness formula limit
The average whiteness percentage ratings of the 348 samples made by the observers under the 6500 K light settings included in the three experiments were used to evaluate the limit of the CIE whiteness formula, which can only be applied to 6500K illuminants. Only 241 of the 348 samples can be correctly classified by the CIE whiteness limit, with 76 samples being classified as non-white and the other 165 being classified as white. All the remaining 107 samples were perceived as white though they were outside the CIE limit. As shown in Fig. 5, the CIE whiteness formula requires samples to have low chroma. The chroma tolerance for the samples with a hue angle around 270° is a little higher than that for the samples with other hue angles, as shown in Fig. 5(c). The chroma versus the hue angle of the samples that were outside the CIE limit but perceived as white shown in Fig. 5(b), however, suggested that the samples with a blue tint, which was caused by the excitation of FWAs from the illumination to have a hue angle around 270°, can have a much higher chroma level, but still perceived as white. Such a result also existed for other CCT levels, as illustrated in Fig. 6.
Fig. 5 CAM02-UCS chroma versus hue angle, color labeled with the average whiteness percentage values evaluated by the observers, for samples under the 6500 K light setting. (a) samples outside the CIE limit and not perceived as white (n = 76); (b) samples outside the CIE limit but perceived as white (n = 107); (c) samples within the CIE limit and perceived as white (n = 165). The FWA-enhanced samples are labelled with square; the non-FWA samples are labelled with diamond.
Fig. 6 CAM02-UCS chroma versus hue angle, color labeled with the average whiteness percentage values evaluated by the observers, for samples under the four levels of CCT. (a) for those that were not perceived as white; (b) for those that were perceived as white. The FWA-enhanced whites are labelled with square; the non-FWA whites are labelled with diamond. (Note: as the lightness of the samples cannot be plotted in this figure, the samples with same chroma and hue may have different lightness, causing different whiteness evaluations).
As shown in Fig. 6, the FWA samples included in this experiment had a much higher chroma level (i.e., can reach 50) due to the high violet radiation included in the light settings, in comparison those included in our earlier two experiments [15, 19] (i.e., the highest was only 22, shown in Fig. 5 in [19]). Also, the samples with a hue angle around 90° (i.e., the hue angle of yellow) in this experiment had a higher chroma level (e.g., can reach 20) than those included in the recent two experiments (i.e., the highest was only 11, as shown in Fig. 5 in [19]). Thus, this experiment allowed us to investigate the boundary in yellow/blue direction.
3.3 Chromaticity boundary for surface colors to be perceived as white
Figure 7(a) and 7(b) show the distribution of the chromaticity coordinates of all the samples under each light setting, calculated using the CIE 1964 CMFs in xy and xY planes respectively. The ellipsoids were also fitted [30] based on the chromaticity coordinates of the samples whose color appearance were evaluated as white. It can be observed that all the four fitted ellipses plotted in xy plane are long and thin and have a similar angle of orientation in the yellow/blue direction. The shape and size of the ellipses, however, are different, with a higher eccentricity value for a lower CCT level in xyY space, which could be due to the non-uniformity and the exclusion of chromatic adaptation in xyY color space.
Fig. 7 The chromaticity coordinates of the samples under each CCT level and the fitted ellipsoids of whiteness boundary of surface colors for each CCT level in xyY color space. Red: perceived as white; Blue: perceived as non-white. (a) xy plane; (b) xY plane. The FWA-enhanced samples are labelled with solid circles; the non-FWA samples are labelled with open circles.
The chromaticity coordinates of each sample under each light setting were then calculated in CAM02-UCS which has been found to be the most uniform color space and also includes CAT02 for considering the chromatic adaptation on color appearance of surface colors [31, 32]. Complete chromatic adaptation was assumed in the calculation, given the high luminance level and the long adaptation time employed in the experiment [32]. Figures 8 and 9 show the distributions of the chromaticity coordinates of the samples and the fitted ellipsoids [30] in a’-J’ and a’-b’ planes in CAM02-UCS respectively. The long-axes of the ellipses shown in Fig. 9 mainly depend on the chromaticity coordinates of the samples that had large shifts towards the blue direction (i.e., the negative direction along the b’ axis). These samples were the paper and plastic samples that had high amounts of FWAs. It can be observed that the ellipses in a’-J’ plane are similar for different CCT levels, in terms of shape and orientation. The ellipses in a’-b’ plane, however, are quite different, especially in terms of the size and shape, as shown in Fig. 9 and summarized in Table 2. The ellipses of the 3000 K and 6500 K differ by a factor of 1.8. The tolerance of high chroma for samples with a blue hue but still perceive as white is higher under 3000 K than under the other three CCT levels, which could be due to the incomplete chromatic adaptation under the 3000 K light setting as identified in Smet et al. [25, 26] and merits further investigation. Given the fact that the ellipses in a’-J’ plane are similar in comparison to those in xY plane, it is better to define the whiteness boundary for surface colors in CAM02-UCS.
Fig. 8 The chromaticity coordinates of the samples and the fitted ellipses of the whiteness boundary of surface colors for different CCT levels in a’-J’ plane of CAM02-UCS. The FWA-enhanced samples are labelled with solid circles; the non-FWA samples are labelled with open circles. Red: perceived as white; Blue: perceived as non-white.
Fig. 9 The chromaticity coordinates of the samples and the fitted ellipses of the whiteness boundary of surface colors for different CCT levels in a’-b’ plane of CAM02-UCS. The FWA-enhanced samples are labelled with solid circles; the non-FWA samples are labelled with open circles. Red: perceived as white; Blue: perceived as non-white.
Table 2. Summary of the ellipses in Fig. 9
3.4 Evaluation of whiteness formula using the whiteness boundary
As most whiteness formulas can only characterize the whiteness of surface colors under CIE standard D65 or D65 simulators, several recent studies tried to adapt the CIE and the Uchida whiteness formulas for an arbitrary light source. David et al. followed the concept of the CIE whiteness formula and derived the coefficients of the whiteness formula for an arbitrary CCT level [33], which was employed by Wei et al. to analyze the performance of various sources in rendering FWA-enhanced whites [20]. Ma et al. [15] and Wei et al. [19] employed CAT02 to transform the color appearance of a sample under a light setting with an arbitrary CCT level to that under D65 and used the CIE whiteness formula and the Uchida whiteness formula to characterize the whiteness appearance. Wei et al. [19] found that the CIE whiteness formula together with CAT02 can provide the most accurate prediction of the perceived whiteness appearance of the samples, regardless of whether FWAs are contained or not, among the six whiteness formulas. The comparisons, however, were made by limiting the samples within the limit of the CIE whiteness formula (i.e., −4 < T10,CIE < + 2) and all the samples were within 40 < WCIE < 5Y-280.
Here, we compare the performance between the CIE whiteness formula and the Uchida whiteness formula with CAT02 by limiting the samples within the ellipsoids identified above. The perceived whiteness versus the calculated whiteness values using WUchida,CAT02 and WCIE,CAT02 are shown in Fig. 10. Though WCIE,CAT02 has a lower correlation to the perceived whiteness than WUchida,CAT02, as summarized in Table 3, neither of them had a decent performance. For the paper and plastic samples having high chorma values with a hue angle around 270° due to the high amount of FWAs, they were still classified as white sample but were rated to have relatively lower whiteness value by the observers. However, their WCIE,CAT02 values were still high, as shown in the left column of Fig. 10, as WCIE,CAT02 does not penalize blue shift. On the contrary, the Uchida whiteness formula adopts the base-point to identify the samples with excessive FWA-enhancement and penalizes these samples, but such a penalization causes negative WUchida,CAT02 values, as shown in the right column of Fig. 10.
Fig. 10 Scatter plots of the perceived whiteness rated by the observers and the whiteness values calculated using the CIE whiteness formula and the Uchida whiteness formula with CAT02. Only the samples that were rated as white are plotted, with the FWA-enhanced samples being labelled in blue and non-FWA samples being labelled in red. The correlation coefficients are summarized in Table 3. Left: the CIE whiteness formula with CAT02; Right: the Uchida whiteness formula with CAT02.
Table 3. Performance of WCIE,CAT02 and WUchida,CAT02 in terms of the correlation coefficients between the calculated and the perceived whiteness values.
The scatter plot of WUchida,CAT02 versus WCIE,CAT02, as shown in Fig. 11, provides a direct comparison. There exist large discrepancies between WCIE,CAT02 and WUchida,CAT02 for some FWA-enhanced samples, which were rated with low whiteness percentage values and had high chroma values with hue angles around 270° due to the strong ultraviolet/violet radiation contained in the illumination. These samples had high WCIE,CAT02 but low WUchida,CAT02, as the Uchida whiteness formula classified these samples as out-based samples and the strong FWA-enhancement was penalized (Eq. (6)). Many of these samples, however, had negative WUchida,CAT02 values, which suggests the failure of the Uchida formula in correctly characterize their whiteness appearance.
Fig. 11 Scatter plot of WUchida,CAT02 versus WCIE,CAT02 for the samples that were rated as white, color labeled with the average whiteness percentage values evaluated by the observers. The FWA-enhanced samples are labelled with square; the non-FWA samples are labelled with diamond.
The results presented here clearly suggest that a new whiteness formula for surface colors is necessary. The formula should be able to characterize the whiteness appearance of a surface color under an arbitrary light source, no matter it contains FWAs or not, whose chromaticity coordinates are within the boundary defined in this article. Such a formula should also consider the decrease of whiteness appearance when an illumination contains an excessive amount of ultraviolet and violet radiation, which is not considered in the CIE and Uchida whiteness formulas. Furthermore, this formula can also be used to guide the adjustment of SPDs, especially at the ultraviolet and violet region, for high quality LED sources at an arbitrary CCT level, so that they can render white objects in a desired and familiar way.
4. Conclusion
A psychophysical experiment was conducted to investigate the boundary of whiteness appearance for surface colors. Twenty observers with normal color vision evaluated the whiteness appearance of 88 samples (i.e., 45 NCS and Pantone matt samples without FWAs, 28 diffuse fabric samples with FWAs, 10 diffuse paper samples with FWAs, and five diffuse plastic samples with FWAs) under four light settings at different CCT levels (i.e., 3000, 4000, 5000, and 6500 K) generated using a 14-channel spectrally tunable LED device. The samples were carefully selected from a large sample set and the spectral power distributions of the light settings were carefully adjusted to have an extremely high violet and ultraviolet radiation, so that the chromaticities of the samples covered a large area in the color space, which was never achieved and studied before. The data collected from this experiment, together with those from Ma et al. [15] and Wei et al. [19], allowed a comprehensive investigation of the whiteness boundary and whiteness characterization for surface colors.
The data clearly revealed the shortcomings of the CIE whiteness formula in requiring samples to be within a small region in a color space. It was found that around 30% of the samples under the 6500 K light setting were outside the CIE whiteness limit, which had a high chroma in blue hue due to the excitation of the FWAs caused by the violet/ultraviolet radiation included in the illumination may outside the CIE whiteness limit, but they were still perceived as white. Ellipsoids were derived as the whiteness boundary for judging whether a sample can be classified as white for each CCT level, with a higher tolerance of chroma under 3000 K.
For the samples within the derived whiteness boundary, though the whiteness values calculated using the Uchida whiteness formula with CAT02 were found to have a higher correlation to the perceived whiteness than those calculated using the CIE whiteness formula with CAT02, the negative whiteness values were problematic. These negative whiteness values were mainly for the samples with a high chroma value and a hue angle around 270°, which was caused by the excitation of the FWAs by the high ultraviolet/violet radiation included in the illumination.
Thus, the CIE whiteness formula with CAT02 can generally characterize the whiteness appearance for surface colors under an arbitrary source, if they are within the CIE limit. For the samples that are outside the CIE limit, the Uchida whiteness formula with CAT02 can identify if the samples had a strong FWA effect due to the high ultraviolet/violet radiation in an illumination, but it cannot accurately characterize their whiteness appearance. The development of a comprehensive formula that can accurately characterize the whiteness appearance of surface colors under an arbitrary light source by considering different conditions is necessary and is undergoing. This formula should also consider the decrease of whiteness when the excessive amount of ultraviolet and violet radiation contained in a source. LED manufacturers can use this formula to adjust the spectrum, especially at the ultraviolet and violet region, for high quality LED sources at an arbitrary CCT level, so that they can render white objects in a desired and familiar way.
Funding
Research Grant Council of the Hong Kong Special Administrative Region, China (PolyU 252029/16E).
References and links
1. K. A. Smet, G. Deconinck, and P. Hanselaer, “Chromaticity of unique white in illumination mode,” Opt. Express 23(10), 12488–12495 (2015). [PubMed]
2. M. S. Rea and J. P. Freyssinier, “White lighting,” Color Res. Appl. 38, 82–92 (2013).
3. M. Wei and K. W. Houser, “Status of solid-state lighting based on entries to the 2010 US DOE Next Generation Luminaire competition,” Leukos 8, 237–259 (2012).
4. D. B. Judd, “A method for determining whiteness of paper,” Paper Trade Journal 100, 40–42 (1935).
5. D. B. Judd, “A method for determining whiteness of paper II,” Paper Trade Journal 103, 38–44 (1936).
6. E. Ganz, “Whiteness: photometric specification and colorimetric evaluation,” Appl. Opt. 15(9), 2039–2058 (1976). [PubMed]
7. Y. J. Cho, L.C. Ou, G. Cui, and M. R. Luo, “New color appearance scales for describing saturation, vividness, blackness, and whiteness,” Color Res Appl., published online (2017).
8. E. Ganz, “Whiteness measurement,” J. Color Appearance 1, 33–41 (1971).
9. CIE, “Colorimetry,3rd edition,” in CIE15:2004, CIE, Vienna, Austria, (2004).
10. ISO, “Paper and board - determination of CIE whiteness, D65/10° (outdoor daylight),” in ISO 11475:2004 (ISO, Jersey City, NJ, USA, 2004).
11. ISO, “Paper and board - determination of CIE whiteness, C/2° (indoor illumination conditions),” in ISO 11476:2010 (ISO, Jersey City, NJ, USA, 2004).
12. E. Ganz, “Whiteness formulas: a selection,” Appl. Opt. 18(7), 1073–1078 (1979). [PubMed]
13. H. Uchida, “A new whiteness formula,” Color Res. Appl. 23, 202–209 (1998).
14. K. W. Houser, M. Wei, A. David, and M. R. Krames, “Whiteness perception under LED illumination,” Leukos 10, 165–180 (2014).
15. S. Ma, M. Wei, J. Liang, B. Wang, Y. Chen, M. Pointer, and M. R. Luo, “Evaluation of whiteness metrics,” Lighting Res Technol., published online (2016).
16. M. Wei, S. Ma, and M. Luo, “The necessity of a whiteness scale for FWA-enhanced whites,” in Proceedings of 24th Color and Imaging Conference (2016), pp. 237–241.
17. J. Lin, R. Shamey, and D. Hinks, “Factors affecting the whiteness of optically brightened material,” J. Opt. Soc. Am. A 29(11), 2289–2299 (2012). [PubMed]
18. M. Wei, K. W. Houser, A. David, and M. R. Krames, “Perceptual responses to LED illumination with color rendering indices of 85 and 97,” Light. Res. Technol. 47, 810–827 (2015).
19. M. Wei, S. Ma, Y. Wang, and M. R. Luo, “Evaluation of whiteness formulas for FWA and non-FWA whites,” J. Opt. Soc. Am. A 34(4), 640–647 (2017). [PubMed]
20. M. Wei, K. W. Houser, A. David, and M. R. Krames, “Blue-pumped White LEDs Fail to Render Whiteness,” in Proceedings of CIE 2014 Lighting Quality & Energy Efficiency, (2014), 150–159.
21. M. Wei and S. Chen, “Impact of spectral power distribution of daylight simulators on whiteness specification for surface colors,” Color Res. Appl.in press.
22. J. C. Zwinkels and M. Noel, “CIE whiteness assessment of papers: impact of LED illumination,” in Proceedings of the 27th Session of the CIE (2011), pp. 323–330.
23. H. Uchida and T. Fukuda, “Estimation of whiteness of fluorescent whitened objects,” J. Color Sci. Assoc. Jpn. 11, 113–120 (1987).
24. M. Vik, M. Vikova, and M. Pechova, “Evaluation of whiteness in case of highly tinted white materials,” in Proceedings of Asia and Africa Science Platform Program Seminar Series 10 (2017).
25. K. A. G. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, Part I: neutral illuminants,” Opt. Express 25(7), 7732–7748 (2017). [PubMed]
26. K. A. G. Smet, Q. Zhai, M. R. Luo, and P. Hanselaer, “Study of chromatic adaptation using memory color matches, Part II: colored illuminants,” Opt. Express 25(7), 8350–8365 (2017). [PubMed]
27. CIE, “CIE Research Strategy” (Accessed Jun 26, 2017) http://www.cie.co.at/index.php/Research+Strategy.
28. P. A. García, R. Huertas, M. Melgosa, and G. Cui, “Measurement of the relationship between perceived and computed color differences,” J. Opt. Soc. Am. A 24(7), 1823–1829 (2007). [PubMed]
29. W. Xu, M. Wei, A. K. G. Smet, and Y. Lin, “The prediction of perceived color differences by color fidelity metrics,” Light. Res. Technol.in press.
30. M. Cheung and B. Rigg, “Color-difference ellipsoids for five CIE color centers,” Color Res. Appl. 11, 185–195 (1986).
31. M. R. Luo, G. Cui, and C. Li, “Uniform color spaces based on CIECAM02 color appearance model,” Color Res. Appl. 31, 320–330 (2006).
32. M. D. Fairchild, Color Appearance Models, 3rd ed. (John Wiley & Sons, 2013).
33. A. David, M. R. Krames, and K. W. Houser, “Whiteness metric for light sources of arbitrary color temperatures: proposal and application to light-emitting-diodes,” Opt. Express 21(14), 16702–16715 (2013). [PubMed]
