Free
Article  |   June 2013
Best lighting for naturalness and preference
Author Affiliations
Journal of Vision June 2013, Vol.13, 4. doi:10.1167/13.7.4
  • Views
  • PDF
  • Share
  • Tools
    • Alerts
      ×
      This feature is available to authenticated users only.
      Sign In or Create an Account ×
    • Get Citation

      Osamu Masuda, Sérgio M. C. Nascimento; Best lighting for naturalness and preference. Journal of Vision 2013;13(7):4. doi: 10.1167/13.7.4.

      Download citation file:


      © ARVO (1962-2015); The Authors (2016-present)

      ×
  • Supplements
Abstract
Abstract
Abstract:

Abstract  Spectral optimization for naturalness and preference was carried out empirically in a set of psychophysical experiments in which observers adjusted the spectral composition of the illumination to render commercial food counters containing a variety of fruits and vegetables as well as meat and fish. The scenes were simulated with high chromatic precision on a calibrated computer monitor from data obtained by hyperspectral imaging. The illuminants were daylight-like and their metamers, representing a set of nearly arbitrary spectra. For daylights, the most natural colors were produced with illuminants with an average correlated color temperature (CCT) of 6040 K and the most preferred colors with an average CCT of 4410 K. For metamers, the CCT for the two conditions were a little higher than for daylights, and the corresponding spectra were considerably different from daylight with characteristic peaks at both ends of the visible band and at about 490 nm and 560 nm. When compared directly with daylights, these metamers were preferred for most of the scenes. It was hypothesized that observers' choices may be determined by the chromatic volume and the symmetry of the color distributions: The best illuminants for preference produced larger gamuts, and the best illuminants for naturalness produced gamuts with aspect ratios closer to unity, i.e., more symmetrically distributed.

Introduction
Most of the visual stimuli for humans are illuminated objects reflecting to our eyes a fraction of the light impinging on them. Consequently, the color perception of complex scenes is influenced, among other factors, by the spectrum of the illumination (Shevell & Kingdom, 2008). Natural daylight is variable both spectrally and in intensity, e.g., during the day or at different locations (Hernández-Andrés, Romero, & Lee, 2001; Hernández-Andrés, Romero, Nieves, & Lee, 2001; Judd et al., 1964); artificial illumination may vary even more dramatically, e.g., from incandescent to discharge lamps (CIE, 2004; Thornton, 1973). Nevertheless, the visual system has the ability to compensate to some extent for these variations and to recover object colors reliably under natural illumination (Granzier, Brenner, & Smeets, 2009) and under artificial ones (Olkkonen, Hansen, & Gegenfurtner, 2009) almost with constant colors. Color constancy is, however, not perfect (Foster, 2003, 2011), and the effects of different lighting on the color and conspicuity of objects can be quite large and are typically addressed in color rendering (Schanda, 2007). 
The main aspects to be considered in color rendering are fidelity, appeal or preference, and color discrimination. Each is typically equated in terms of indices based on perceptual assumptions and on psychophysical data (for a review of color rendering indices see Guo & Houser, 2004). The general color rendering index (CRI) standardized by the CIE (1995) measures fidelity or degree of naturalness of the colors rendered by an illuminant. In its definition, the main assumption is that the most natural colors are produced by daylight or incandescence. The impression of appeal or preference was first quantified by Judd (Judd, 1967; Thornton, 1974) based on empirical work on color memory (Bartleson, 1960; Newhall, Burnham, & Clark, 1957) and color preference (Sanders, 1959). The potential for color discrimination of an illuminant is quantified by indices related to the color gamut spanned by a set of colored samples or scenes (Linhares & Nascimento, 2012; Rea & Freyssinier-Nova, 2008; Thornton, 1972; Xu, 1993, 2012) that have been used in developing illuminants with high discriminability (Masuda & Nascimento, 2012; Thornton, 1973). More complex indices representing combinations of these perceptual aspects have also been synthesized and evaluated (Davis & Ohno, 2010; Smet, Ryckaert, Pointer, Deconinck, & Hanselaer, 2011a). 
The empirical basis for the assumptions underlying color rendering and the testing of the rendering indices has, however, been constrained to physical existing light sources. Most of the psychophysical testing has been based on rating with LED or standard illuminants (e.g., Schanda & Madár, 2007; Smet, Ryckaert, Pointer, Deconinck, & Hanselaer, 2010, 2011b). The popularization of solid-state lighting has shown the potential for lighting spectra without constraints and challenged the existing knowledge based on a limited set of illuminants. 
Computational spectral design and optimization has been carried out mainly assuming LEDs (Berns, 2011; Žukauskas, Vaicekauskas, Ivanauskas, Vaitkevičius, & Shur, 2008). These studies have produced useful information but not direct experimental data from a perceptual point of view. Empirical optimization has been carried out with lights metameric of D65 and have shown that observers require spectra more structured than daylight to produce the best impression of naturalness and preference (Nascimento & Masuda, 2012). 
The goal of the present study is to determine psychophysically the best spectral power distributions to render natural scenes the most natural and the most pleasant. The experiments were based on images representing simulations of real food counters obtained by spectral imaging carried out in a local supermarket, and the illuminants tested had a wide range of chromaticities and almost arbitrary spectral distribution. Human color vision is thought to have evolved to detect or discriminate ripe food from background or unripe food (Mollon, 1989; Surridge, Osorio, & Mundy, 2003). Finding optimal lighting for food can be of practical benefit and contribute to the understanding of the mechanisms of human color vision. This study was conducted regardless of energy-efficiency aspects or the present availability of light-emitting materials with the specific spectral compositions tested (Protzman & Houser, 2006). 
General methods
Hyperspectral images of commercial food counters
Hyperspectral images of commercial food counters were acquired in a local supermarket. The counters displayed vegetables, fruits, meat, and fish (see Figure 1 for pictures of the counters imaged). These types of objects are appropriate for testing visual aspects of illumination and have been used in classical works although with much more spectrally constrained light sources (Thornton, 1974). The existing illumination of the counters was turned off and replaced by two metal-halide discharge lamps of 1000 W (GW 84 662; Gewiss, Cenate Sotto, Italy), each positioned approximately at 45° relative to the areas imaged. The correlated color temperature (CCT) of the light sources was 7600 K, and their spectral profiles were stable over the scenes. 
Figure 1
 
Scenes tested in the psychophysical experiments. The scenes were digitalized by hyperspectral imaging in a local supermarket. The number on each image is for labeling and was not displayed in the experiments. Images 1–3 represent fruits, images 4–6 vegetables, images 7–9 meat, and images 10–12 fish.
Figure 1
 
Scenes tested in the psychophysical experiments. The scenes were digitalized by hyperspectral imaging in a local supermarket. The number on each image is for labeling and was not displayed in the experiments. Images 1–3 represent fruits, images 4–6 vegetables, images 7–9 meat, and images 10–12 fish.
Spectral data were acquired over the range of 400–720 nm at 10 nm intervals using a fast-tunable liquid-crystal filter (VariSpec VIS-10; Cambridge Research & Instrumentation, Hopkinton, MA) and a low-noise Peltier-cooled digital camera with a spatial resolution of 1344 × 1024 pixels and 12-bit output (ORCA-AG CA4742-80-12AG; Hamamatsu Photonics, Hamamatsu, Japan) in a configuration similar to the one described in detail elsewhere (Foster, Amano, Nascimento, & Foster, 2006; Foster, Nascimento, & Amano, 2004). 
The spectral reflectance of each pixel was estimated from the hyperspectral data by dividing the image data for each wavelength by the spectrum of the light reflected from a gray reference surface with a known spectral reflectance placed in the scene. The gray reference surface was always a flat surface painted with Munsell N7 matt emulsion paint (VeriVide Ltd., Leicester, UK). Images were corrected for noise, stray light, and for the effects of transmission through the optical system, but no compensation was introduced for the spatial variations in intensity of the light sources. Thus, the spectral reflectance functions estimated were spatially modulated by these spatial variations in intensity, and everything is as if the illuminants synthesized for the experiments reproduced the intensity profiles of the light sources at the time of data acquisition. The spatial resolution of the hyperspectral system was at least as good as that of the human eye at the same viewing distance (Foster et al., 2006). The accuracy of the system in recovering spectral reflectance functions is acceptable for visual experiments as the spectral error is about 2% and the colorimetric error is about 2.2 in CIELAB color space (Carvalhal, 2004; Foster et al., 2006; Nascimento, Ferreira, & Foster, 2002). 
Illuminants
Two types of illuminant were used in this study: daylight-like illuminants and the metamers of the daylight-like illuminants. 
Daylight illuminants
Daylight-like illuminants were synthetized from Judd's daylight spectral basis functions (Judd et al., 1964) with variable coefficients such that their color defined a chromaticity grid over and around the Planckian locus. Figure 2 represents this grid expressed in the CIE 1960 uniform chromaticity scale (UCS) diagram. The grid points had the CCT in the range 2222–20000 K. The color temperature (CT) of the idealized Planckian radiator is the absolute temperature of the radiator, and it is related with the spectral power distribution it irradiates. For a real radiator, like a light source, the concept of CCT applies instead. It is the temperature of the Planckian radiator whose chromaticity is closest to that of the light source on the CIE 1960 UCS diagram. We introduced here the chromaticity difference (DC) as the distance between the chromaticities of the light source and of the Planckian radiator of the same CT on the CIE 1960 UCS diagram (CIE, 1995). A positive DC means that the chromaticity is above the Planckian locus, and a negative DC is below the locus. To guarantee more visual uniformity, the CT were equally spaced in reciprocal color temperature (RCT) (Wyszecki & Stiles, 1982) by 25 MK−1. The points on the lines orthogonal to the Planckian locus were in the range −0.01 to +0.01 from the locus at an interval of 0.002 in DC. 
Figure 2
 
Illuminant chromaticities tested expressed in the CIE 1960 UCS diagram. The illuminants were synthetized from Judd's daylight spectral basis functions. The grid points had correlated color temperatures in the range 2222–20,000 K equally spaced in reciprocal color temperature at an interval of 25 MK−1. The points on the lines orthogonal to the Planckian locus were in the range −0.01–+0.01 from the locus at an interval of 0.002 in UCS units.
Figure 2
 
Illuminant chromaticities tested expressed in the CIE 1960 UCS diagram. The illuminants were synthetized from Judd's daylight spectral basis functions. The grid points had correlated color temperatures in the range 2222–20,000 K equally spaced in reciprocal color temperature at an interval of 25 MK−1. The points on the lines orthogonal to the Planckian locus were in the range −0.01–+0.01 from the locus at an interval of 0.002 in UCS units.
Metamers of daylight
At each point on the grid represented in Figure 2, 1000 metamers were generated using Schmitt's simple elements method (Schmitt, 1976). These metameric illuminants had almost arbitrary spectra. The spectral range was 400–720 nm, and the spectral resolution was 10 nm. The simple elements at each chromaticity are all the spectra with three spectral bands producing that chromaticity. Thus, for each grid point, all corresponding simple elements were computed, and the 1000 metamers were obtained by linear combinations of the simple elements. To obtain a reasonable range of spectral profiles, the metamers were generated to be uniformly distributed with regard to the spectral difference against the corresponding daylight spectrum. This difference was quantified by an index defined by the following equation:  where N is the number of spectral bands (33), fk is the intensity of the metamer f at the kth spectral band, and Dk is the intensity of the daylight at the kth spectral band. δ is related to the spectral similarity of the metamer to the daylight with the same chromaticity. It also measures, indirectly, the degree of spectral smoothness. Metamers with low values of δ are spectrally close to natural daylight and smooth. On the contrary, those with large δ are less natural and more irregular and spiky (Nascimento & Masuda, 2012). Figure 3 shows the average spectrum of the simple elements at the grid point (CCT, DC) = (6667 K, 0). The energy of each simple element was normalized such that Display FormulaImage not available = 1. The average spectrum has four peaks at both ends of the visible band and at 490 nm and 570 nm. The wavelengths of the central two peaks varied with each grid point, but this characteristic four-peak pattern in the spectrum appeared at all grid points. This spectral structure reflects natural constraints associated to the chromaticity region considered. 
Figure 3
 
Average spectrum of the simple elements at (CCT, DC) = (6667 K, 0). Error bars show the standard errors at each band.
Figure 3
 
Average spectrum of the simple elements at (CCT, DC) = (6667 K, 0). Error bars show the standard errors at each band.
Stimuli
Stimuli for the experiments were synthetized by multiplying the spectral reflectance functions estimated for each pixel from the hyperspectral data by the spectral distributions of the illuminants. In this way, a spectral radiance and a color were obtained for each pixel. The images were displayed on an LCD monitor (CA750; Samsung, Seoul, South Korea) controlled by a video board (ViSaGe Visual Stimulus Generator; Cambridge Research Systems, Rochester, Kent, UK) in 24-bits-per-pixel true-color mode driven by a PC. The monitor was calibrated in color and luminance with a telespectroradiometer (PR-650 SpectraScan Colorimeter; Photo Research, Chatsworth, CA). The images subtended a 40° × 30° visual angle and were observed at 60 cm distance. Images were subsampled every other pixel from the original resolution of 1344 × 1024 pixels, then trimmed about 20–30 pixels from an edge to delete the reflectance standard from the scene. The average luminance of each displayed image across pixels was 15 cd/m2
Figure 1 shows the 12 scenes tested. Three represent fruits, three vegetables, three various types of meat, and three several sorts of fish. 
Colorimetric accuracy
The colorimetric performance of the monitor was better for food than that of a good CRT because it had a wide gamut in the red-yellow area. The maximum luminance of the LCD was lowered from its original maximum (280 cd/m2) to 130 cd/m2 to achieve a good tone reproduction. Figure 4 shows the error of the display calibration. Small black dots are the grid points shown in Figure 2. Red circles are the actually measured chromaticities of the grid points with PR-650. Red circles were measured only along the DC of −0.01, 0.00, and +0.01. The mean error between the red circles and the corresponding grid points was 0.003, which is less than a half of the just noticeable difference (JND) around this chromaticity area (0.007) estimated as thrice the mean radius of the MacAdam ellipse (MacAdam, 1942). The intended luminance was 15 cd/m2, and the actually reproduced mean luminance was 15.11 ± .02 (standard deviation). The three red points at the upper right of the grid (DC = +0.01, CCT ≤ 2500 K) were out of the display gamut, but these points were actually not selected by the observers. 
Figure 4
 
Calibration of the monitor. Black dots are the intended chromaticities of the grid. Red circles are the actually measured chromaticities. Red circles were measured only along the DC of −0.01, 0.00, and +0.01. The mean error between the red circles and the corresponding grid points was 0.003, which is smaller than the just noticeable difference (JND) around this chromaticity area (0.007) estimated as the thrice of the mean radius of the MacAdam ellipse (MacAdam, 1942).
Figure 4
 
Calibration of the monitor. Black dots are the intended chromaticities of the grid. Red circles are the actually measured chromaticities. Red circles were measured only along the DC of −0.01, 0.00, and +0.01. The mean error between the red circles and the corresponding grid points was 0.003, which is smaller than the just noticeable difference (JND) around this chromaticity area (0.007) estimated as the thrice of the mean radius of the MacAdam ellipse (MacAdam, 1942).
Table 1 shows the mean reproduction errors of 15 color samples defined in the Japanese Industrial Standard (1990) Z8726 simulated on the monitor and measured with PR-650. Fourteen of them are the same as the color samples defined in CIE 13.3 (CIE, 1995). The color difference for each pixel was defined as  where ( Display FormulaImage not available , Display FormulaImage not available , Display FormulaImage not available ) and ( Display FormulaImage not available , Display FormulaImage not available , Display FormulaImage not available ) are the CIELAB coordinates of the intended and measured colors, respectively. Most of the errors within the gamut were close to 2.2, the JND for complex images in CIELAB (Aldaba et al., 2006; Song & Luo, 2000). The grid point at (CCT, DC) = (2222 K, 0.01) was out of the monitor gamut. 
Table 1
 
Mean errors of 15 reproduced color samples in ΔE*ab.
Table 1
 
Mean errors of 15 reproduced color samples in ΔE*ab.
CCT (K)
20,000 6667 4000 2857 2222
DC
 0.01 2.89 2.14 2.73 3.09 N/A
 0.00 2.99 2.80 2.18 3.12 3.22
 −0.01 2.69 2.25 2.23 2.28 3.63
When the color of a pixel was outside the gamut, the color was clipped to the closest RGB value. Figure 5 shows the histograms of the mean color errors due to the gamut limit of the display expressed as the mean color difference across pixels in Δ Display FormulaImage not available between the colorimetrically intended and actually achievable images chosen by the observer in each trial. In Experiment 1, the mean error for 96.4% of the trials was less than the JND (2.2). The trials with errors more than twice the JND (4.4) were 0.4%. In Experiment 2, 90.9% of the trials had mean errors less than the JND, and 4% of the trials had mean errors more than twice the JND. 
Figure 5
 
Histograms of the colorimetric errors due to the gamut limit in Experiment 1 (red striped bars) and Experiment 2 (gray bars). The errors were expressed as the mean color difference in CIELAB across the pixels between the intended and actually achievable images selected by the observer in each trial. In Experiment 1, the mean errors for 96.4% of the trials were less than the JND. In Experiment 2, 90.9% of the trials had errors less than the JND.
Figure 5
 
Histograms of the colorimetric errors due to the gamut limit in Experiment 1 (red striped bars) and Experiment 2 (gray bars). The errors were expressed as the mean color difference in CIELAB across the pixels between the intended and actually achievable images selected by the observer in each trial. In Experiment 1, the mean errors for 96.4% of the trials were less than the JND. In Experiment 2, 90.9% of the trials had errors less than the JND.
Observers
There were six observers. All but one of the authors (OM) were naïve to the purpose of the experiment. Each observer had normal or corrected-to-normal acuity and normal color vision accessed by the Rayleigh anomaloscope and Ishihara plates. Five of them are 20- to 21-year-old females, and the other was a 42-year-old male. The experiments were performed in accordance with the tenets of the Declaration of Helsinki, and informed consent was obtained from all observers. 
Experiment 1: Daylights
In Experiment 1, the goal was to determine the daylight-like illuminants producing the most natural and the most preferable appearance. The illuminants tested were synthetized from the daylight basis functions as described above, and the task of the observers in each trial was to select one of the illuminants from the chromaticity grid represented in Figure 2. Two conditions were tested. In one, the naturalness condition, the observers were instructed to select the illuminant on the scene such that the colors of the objects appear the most natural. In the other, the preference condition, observers were instructed to select the illuminant such that the appearance of the scene was the most pleasant or preferable for them. The instructions to the observers were written and shown to the observers at the beginning of each experimental session. None of the observers found the instructions ambiguous or unclear. 
Procedure
In each trial, the chromaticity of the initial illuminant was selected randomly from the grid. The observer then adjusted the chromaticity of the illuminant with four buttons on a joypad. Each of the four buttons corresponded to one incremental or decremental step on the grid in CCT or in DC. The switching between different illuminants on the grid was fast, less than 0.5 s. When the observer was satisfied with the setting, s/he pressed two dedicated buttons in a specific order to record the result. Each scene was repeated three times per session, condition, and observer. There was no adaptation period before each trial or session. Each observer did two sessions for each condition. Conditions and scenes were tested in random order. 
Results
Figure 6 shows the results obtained in the two conditions averaged across all scenes and observers. The average CCT and DC were computed from the chromaticity of the average spectra. Averaging directly in RCT and DC axes is less meaningful as these are not axes of a chromaticity diagram. The diagram expresses the data vertically in DC. For readability, the horizontal axis is labeled in CCT, but it is spaced uniformly in RCT (25 MK−1/tick). The error bars show the standard errors of the means, but these are now computed directly from the DC and RCT obtained in each trial. 
Figure 6
 
Results obtained in the two conditions of Experiment 1 averaged across all images and observer. Error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT.
Figure 6
 
Results obtained in the two conditions of Experiment 1 averaged across all images and observer. Error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT.
The CCT of the most natural daylight was 6040 K, and the CCT of the most preferred one was 4410 K. The DC of the most natural daylight was −0.0035, and the DC of the most preferred was −0.0036, both of which were considerably different from the Planckian locus (DC = 0) and from the daylight locus (DC = 0.003). Both daylights are shifted to a purplish direction below the locus. 
Figure 7 shows the average CCT obtained across all observers for each scene. The preferred CCTs were consistently lower than the natural ones regardless of the scene contents. 
Figure 7
 
Average CCT across all observers for each scene. Filled symbols connected by solid lines represent the naturalness condition and open symbols connected by dotted lines represent the preference condition. Error bars show the standard errors of the means. For readability the vertical axis is labeled in CCT, but is spaced uniformly in RCT.
Figure 7
 
Average CCT across all observers for each scene. Filled symbols connected by solid lines represent the naturalness condition and open symbols connected by dotted lines represent the preference condition. Error bars show the standard errors of the means. For readability the vertical axis is labeled in CCT, but is spaced uniformly in RCT.
Experiment 2: Metameric lights
In Experiment 1, the illuminants were constrained to daylight-like spectra. In Experiment 2, this constraint was relaxed, and observers were able to select illuminants with almost arbitrary distributions. The illuminants tested had chromaticities at and around the average chromaticity obtained for daylights in Experiment 1 for each scene, observer, and condition and were metamers of the daylight synthesized as described in the General methods section. The conditions of the experiments were the same as in Experiment 1, i.e., naturalness and preference. 
Procedure
Experiment 2.1
The experiment was carried out in two parts. In the first part (Experiment 2.1), a first set of five best metamers was obtained by testing at five chromaticities at and around the chromaticity obtained in Experiment 1 for each scene and observer. Then, in the second part (Experiment 2.2), the best metamer was obtained by testing the five candidates obtained in Experiment 2.1. 
To select the testing points for Experiment 2.1, the chromaticities obtained in Experiment 1 were averaged for each scene, each observer, and each condition, and the chromaticity in the grid nearest to the average was selected as the central (C) point. Then, four grid points surrounding C were computed: The upward (U) point was 1 standard deviation (SD) in DC away from C in the incremental DC direction; the SDs were calculated from the results in Experiment 1 for each scene, observer, and condition. In the same way, the downward (D) point was 1 SD away from C but in the opposite direction. The leftward (L) point was 1 SD in RCT away from C in the decremental RCT direction, and the rightward (R) point was 1 SD away in the opposite direction. If any chromaticity was out of the grid, the nearest point in the grid was selected instead. Figure 8 shows an example of the method of selecting the testing chromaticities. 
Figure 8
 
Example of the selection of the chromaticities for Experiment 2.1. U is 1 SD (0.04 in DC) shifted upward from C, and D is shifted downward by the same amount in the opposite direction. L is shifted 1 SD (100 MK−1 in RCT) leftward from C, and R is shifted 1 SD by the same amount in the opposite direction. The chromaticity of C and SDs were obtained from the corresponding results in Experiment 1.
Figure 8
 
Example of the selection of the chromaticities for Experiment 2.1. U is 1 SD (0.04 in DC) shifted upward from C, and D is shifted downward by the same amount in the opposite direction. L is shifted 1 SD (100 MK−1 in RCT) leftward from C, and R is shifted 1 SD by the same amount in the opposite direction. The chromaticity of C and SDs were obtained from the corresponding results in Experiment 1.
Observers were instructed to select the most appropriate metamer from the metamer set for each of the five chromaticity points, scenes, and conditions. 
The metamer set at each chromaticity was ordered differently for the two conditions. For naturalness, the metamers were ordered linearly according to their CIE general CRI. For the preference condition, they were ordered linearly according to the product of their CRI and their chromatic diversity indices (CDI) (Linhares & Nascimento, 2012). This ordering was adopted to make the changes in appearance more directly related to each condition tested and to facilitate adjustment for the observers, but it is not expected that the ordering itself influenced the outcome of the experiments (Nascimento & Masuda, 2012). 
The observers changed the metamer by scrolling the ordered set in either direction with two buttons or an analog stick on the joypad. The step by the two buttons was 1% of the full scale in CRI or the product of CRI and CDI. The observers were also able to adjust the metamer by the analog stick. The step by the analog stick was proportional to the tilt angle of the stick, and the maximum step was 5% of the full scale. The starting point was randomly selected from among the 1000 metamers at each chromaticity. The adjustment of the order was in a circular fashion, that is, when the next metamer was calculated to be out of the scale, the actual next metamer was bounced back in the opposite direction by the amount of excess. In this way, the observer was not able to know the ends of the scale explicitly. 
When the observer was satisfied with the setting, s/he pressed two dedicated buttons in a specific order to record the result. Each scene was repeated three times in one session for each of the five chromaticities. The order of the trials was randomized for each chromaticity, observer, and condition; the order of the five chromaticities was also randomized. One session consisted of 36 trials (3 repetitions × 12 scenes). Sessions were repeated twice, and the total number of trials for each chromaticity, observer, and condition was 72. 
Experiment 2.2
The spectra of the six metamers obtained in Experiment 1 for each scene, chromaticity, condition, and observer were averaged and constituted the testing set in Experiment 2.2. The observer selected the best metamer from this set of five average spectra (one in each chromaticity tested). The testing methodology was the same as in Experiment 2.1 except that the set of testing metamers was now of only five. Each scene was repeated six times for each condition and each observer. The order of the trials was randomized for each observer and criterion. 
Results
Correlated color temperature and chromaticity difference
Figure 9 shows the results obtained in Experiment 2.2 in the two conditions averaged across all scenes and observers. The average CCT and DC were computed from the average spectra, but the standard errors were calculated directly from the CCT and DC obtained in each trial. The diagram expresses the data vertically in DC and horizontally in CCT. 
Figure 9
 
The filled symbols show CCT and DC obtained in the two conditions of Experiment 2.2 averaged across all scenes and observer. The error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT. The faded open symbols are the replot of Figure 6.
Figure 9
 
The filled symbols show CCT and DC obtained in the two conditions of Experiment 2.2 averaged across all scenes and observer. The error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT. The faded open symbols are the replot of Figure 6.
Both metamers are located below the Planckian locus. The most natural CCT was 6200 K, and the most preferred one was 4550 K. These values were a little higher than those obtained with daylights in Experiment 1. The preferred CCT was considerably different from that of D65, but the natural one was close to that of D65. 
Figure 10 shows the average CCT across observers for each scene. The CCTs selected in Experiment 2.2 were slightly, but almost consistently, higher than those with daylights obtained in Experiment 1 for both conditions. 
Figure 10
 
Average CCT obtained with the metamers (M; solid symbols) for each scene across all the observers in the naturalness (a) and preference (b) conditions. The error bars show the standard errors of the means. The CCT obtained with daylights (D; dashed lines) in Experiment 1 are also shown for comparison.
Figure 10
 
Average CCT obtained with the metamers (M; solid symbols) for each scene across all the observers in the naturalness (a) and preference (b) conditions. The error bars show the standard errors of the means. The CCT obtained with daylights (D; dashed lines) in Experiment 1 are also shown for comparison.
Spectra
Figure 11 shows the averaged best spectra selected by observers in the naturalness condition: Figure 11a is the average across all the observers and scenes, and Figure 11b is the averages across all the observers for each food category. The error bars in Figure 11a represent the standard errors at each spectral band. In the spectra shown in Figure 11, characteristic peaks were found at both ends of the visible band and at about 490 nm and 560 nm. The spectral difference index δ of Figure 11a was 0.49. 
Figure 11
 
Average spectra selected by observers in the naturalness condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average natural daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 11
 
Average spectra selected by observers in the naturalness condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average natural daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 12 shows the averaged best spectra selected by observers in the preference condition: Figure 12a is the average across all the observers and scenes, and Figure 12b is the averages across all the observers for each food category. The error bars in Figure 12a represent the standard errors at each spectral band. Characteristic peaks similar to those obtained in the naturalness condition were found although the peak at 560 nm is less prominent and less sharp. The spectral difference index δ of (Figure 12a) was the same as that of the naturalness condition. 
Figure 12
 
Average spectra chosen by observers in the preference condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average preferred daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 12
 
Average spectra chosen by observers in the preference condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average preferred daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Experiment 3: Control
The results obtained in Experiment 2 were surprising because they mean that the observers preferred artificial spectra to daylight to produce the impression of naturalness. The intention of Experiment 3 was to confirm that the spectra obtained in Experiment 2 were, in fact, preferred to daylight by direct comparison. 
Procedure
In a two-interval forced-choice procedure, the observers compared two images. One was always the simulation of a scene rendered under the best metamer obtained in Experiment 2.2 for each scene, observer, and condition; the other represented the same scene rendered under daylight with a chromaticity around that of the best metamer. The chromaticity of this daylight followed a normal distribution with the mean of that of the metamer and the standard deviation obtained in Experiment 1 for each observer, scene, and condition. The task of the observers was to select the more natural or the more preferred image according to the condition tested. 
Each trial was started with a button pressed by the observer. One of the two images, chosen randomly, was displayed for 500 ms followed by a dark screen for 500 ms. Then, the other image was displayed for 500 ms. The observer selected one of the two for each condition by pressing one of two buttons. Only one scene was selected for this experiment for each food category (scene 2 for fruits, scene 6 for vegetables, scene 10 for meat, and scene 13 for fish). Each scene was repeated 12 times for each observer and condition. 
Results
Table 2 shows the percentages and p values (binomial test) of the choices of metamers against daylights. The best metamers were selected more frequently for each condition than the daylights with the same chromaticities within the range of color-matching error. The difference in the percentage from the chance level was statistically significant in all the food categories with the exception of fish in the preference condition. 
Table 2
 
The percentages and p values of the direct choices of metamers against daylights.
Table 2
 
The percentages and p values of the direct choices of metamers against daylights.
Fruit Veg Meat Fish All
Naturalness
 % 65.3 72.2 59.7 70.8 67.0
p <0.01 ≪0.01 0.04 ≪0.01 ≪0.01
Preference
 % 63.9 76.4 73.6 56.9 67.7
p <0.01 ≪0.01 ≪0.01 0.10 ≪0.01
Discussion
Daylights
In Experiment 1, the daylights selected for naturalness and preference had a CCT, on average, of 6040 K and 4410 K, respectively. The natural CCT was close to 6500 K, the CCT recommended for the assessment of the color of foods by the International Organization for Standardization (ISO, 1999), but was very different from 3000 K, the common practice in most supermarkets (MacDougall, 2002). On the other hand, the preferred CCT was different from both 6500 K and 3000 K. Although the CCT varied across scenes and observers, they were systematically lower for preference than for naturalness. The value of 4410 K = 227 MK−1 obtained in Experiment 1 was relatively close to the results of experiments in which observers adjusted the CCT of daylights such that they produced the best visual impression of artistic paintings and in which the distribution of observers' preferences had a maximum at a CCT of about 5100 K = 196 MK−1 (Pinto, Linhares, & Nascimento, 2008). 
The daylights obtained for naturalness and preference had chromaticities below the daylight (DC = 0.003) and Planckian (DC = 0) loci, i.e., they were shifted to a more purplish direction. This curious effect is not predicted by the CRI. Figure 13 shows a pseudocolor map representing CRI for the daylights tested. If this index was a good predictor of naturalness or preference, the illuminants selected by observers should be close to the areas of larger values, that is, close to the daylight locus. 
Figure 13
 
The pseudocolor map of CRI corresponding to the daylights tested. The symbols show the average psychophysical data obtained in Experiment 1. Standard errors are smaller than the symbol size.
Figure 13
 
The pseudocolor map of CRI corresponding to the daylights tested. The symbols show the average psychophysical data obtained in Experiment 1. Standard errors are smaller than the symbol size.
Why does the preferred CCT have a lower value than natural CCT? A possible reason for this effect is that observers prefer scenes that are more colorful, corresponding to a larger color gamut. This would be consistent with experiments in which the image quality is maximum when average chroma is higher than that obtained with natural illuminants (Fedorovskaya, De Ridder, & Blommaert, 1997). Figure 14a shows the pseudocolor map of the convex hull volume expressed in CIELAB space of the Munsell set rendered by the daylights tested. The volume has a maximum close to the average chromaticity for preference (open circle symbol). It also increases in the direction of negative DC, suggesting that scenes can look more colorful or vivid with these purplish daylights. This result obtained with the Munsell set also holds for the group of scenes tested. The color volume map of each scene was normalized, and the result was averaged across all scenes tested. The CCT producing the maximum chromatic volume of this average map was 4444 K whereas the average experimental data for preference across the same scenes was 4410 K. Figure 15 compares the volumes for the preference and naturalness conditions for the 12 scenes tested. The illuminant for each scene and condition was averaged across all observers. The trend line fitted to the data is steeper than the diagonal line, which means preferred images were more colorful than the corresponding natural images. 
Figure 14
 
Pseudocolor map of the convex hull volume expressed in CIELAB space of the Munsell set rendered by the daylights tested (a) and by the metamers that maximize the volume at each grid point (b). Open square and circle show the natural and preferred daylights in Experiment 1, and filled square and circle show the natural and preferred metamers in Experiment 2.2, respectively. Standard errors are smaller than the symbol size.
Figure 14
 
Pseudocolor map of the convex hull volume expressed in CIELAB space of the Munsell set rendered by the daylights tested (a) and by the metamers that maximize the volume at each grid point (b). Open square and circle show the natural and preferred daylights in Experiment 1, and filled square and circle show the natural and preferred metamers in Experiment 2.2, respectively. Standard errors are smaller than the symbol size.
Figure 15
 
Comparison of volumes by the food images in CIELAB space between the natural and preferred daylights. The trend line fitted to the data (solid line) is steeper than the diagonal (dotted line).
Figure 15
 
Comparison of volumes by the food images in CIELAB space between the natural and preferred daylights. The trend line fitted to the data (solid line) is steeper than the diagonal (dotted line).
The spectra of conventional natural lighting have been assumed with chromaticities on the Planckian or daylight loci, but the data obtained here suggests that this constraint might be unnecessary as larger color volume is obtained for lower or more purplish chromaticities. 
What determines CCT for naturalness? A possible factor is the distribution of chromaticities rather than global volume. To investigate this possibility, the colors of the Munsell set under the daylights found in Experiment 1 were computed and expressed in CIELAB space. Figure 16b and Figure 16d show the corresponding projections in the (a*, b*) plane. Ellipses covering 95% of the points were fitted to each data set, and their ratios of the lengths of the shorter axis to those of the longer ones were calculated. The aspect ratio of the ellipse for the natural daylight (b; 0.859) is closer to the unity than that for the preferred daylight (d; 0.819), meaning a more symmetrical distribution of colors. 
Figure 16
 
Gamuts of Munsell chips projected onto the a*b* plane rendered by (a) the most natural metamer in Experiment 2.2 (b) the most natural daylight in Experiment 1, (c) the most preferable metamer in Experiment 2.2, and (d) the most preferable daylight in Experiment 1. The center of an ellipse is the mean of the data points, and the radii correspond to two standard deviations along the most and least variable direction. An ellipse covers 95% of the data points. The convex hull volumes of the chips in the CIELAB space are (a) 2.91x105, (b) 2.97x105, (c) 3.24x105, and (d) 3.03x105, respectively. The ratios of lengths of the shorter axes to longer ones are (a) 0.863, (b) 0.859, (c) 0.837, and (d) 0.817, respectively.
Figure 16
 
Gamuts of Munsell chips projected onto the a*b* plane rendered by (a) the most natural metamer in Experiment 2.2 (b) the most natural daylight in Experiment 1, (c) the most preferable metamer in Experiment 2.2, and (d) the most preferable daylight in Experiment 1. The center of an ellipse is the mean of the data points, and the radii correspond to two standard deviations along the most and least variable direction. An ellipse covers 95% of the data points. The convex hull volumes of the chips in the CIELAB space are (a) 2.91x105, (b) 2.97x105, (c) 3.24x105, and (d) 3.03x105, respectively. The ratios of lengths of the shorter axes to longer ones are (a) 0.863, (b) 0.859, (c) 0.837, and (d) 0.817, respectively.
Figure 17 shows the map of the aspect ratios of the ellipses fitted to the Munsell set for all daylights tested. The data obtained for naturalness is close to the maximum of the map, supporting the hypothesis that this ratio influences naturalness. 
Figure 17
 
The background pseudocolor plot in (a) shows the aspect ratios of the ellipses fitted to the gamuts of Munsell chips rendered by the daylights on the grid. The pseudocolor plot in (b) shows the average aspect ratios of the ellipses fitted to the gamut of Munsell chips rendered by the metamers with the top 5% aspect ratios.
Figure 17
 
The background pseudocolor plot in (a) shows the aspect ratios of the ellipses fitted to the gamuts of Munsell chips rendered by the daylights on the grid. The pseudocolor plot in (b) shows the average aspect ratios of the ellipses fitted to the gamut of Munsell chips rendered by the metamers with the top 5% aspect ratios.
These results obtained with the Munsell set also hold for the food scenes tested. Figure 18 compares the aspect ratios of the ellipses fitted to the image color gamuts between the preference and naturalness conditions for the 12 scenes tested. The illuminant for each scene and condition was averaged across all observers. Most points are below the diagonal line, which means images in the naturalness condition have more symmetrical color distribution than those in the preference condition. Means of the ratios across the images were 0.498 for naturalness and 0.472 for preference. 
Figure 18
 
Comparison of aspect ratios of the color gamuts by the food images between the natural and preferred daylights. The daylight for each image and condition were averaged across the observers.
Figure 18
 
Comparison of aspect ratios of the color gamuts by the food images between the natural and preferred daylights. The daylight for each image and condition were averaged across the observers.
Metamers
In Experiment 2, the CCTs obtained with metamers were 6200 K for naturalness and 4550 K for preference. They were a little higher than those obtained with daylights. The DC obtained for the natural metamer was close to that for natural daylight. However, the DC for the preferred metamer was shifted in an even more purplish direction in relation to the preferred daylight. Figure 14b shows the pseudocolor map of the average of the convex hull volume expressed in CIELAB space of the Munsell set rendered by the metamer producing the maximum volume at each grid point. The maximum volume is shifted to a higher CCT in relation to the map for daylights in Figure 14a, suggesting that the shift of CCT in the experimental data is explained by this shift. Actually, as shown in Figure 16, the preferred metamer (Figure 16c) had a larger color volume than the preferred daylight (Figure 16d). This result obtained for the Munsell set generalizes for the food scenes tested as shown in Figure 19
Figure 19
 
Comparison of the volumes of the food images in the CIELAB space between the preferred metamer found in Experiment 2 and the preferred daylight found in Experiment 1. The metamer and daylight for each image were averaged across the observers.
Figure 19
 
Comparison of the volumes of the food images in the CIELAB space between the preferred metamer found in Experiment 2 and the preferred daylight found in Experiment 1. The metamer and daylight for each image were averaged across the observers.
A similar shift can be observed for the aspect ratio. Figure 17b shows the pseudocolor map of the average aspect ratios of the ellipses fitted to the Munsell set rendered by the metamers producing the top 5% aspect ratios at each grid point. The maximum aspect ratio is shifted to a higher CCT in relation to the map for daylights (Figure 17a), suggesting that the shift in the experimental data is explained by this shift. Actually as shown in Figure 16, the natural metamer (Figure 16a; 0.863) has a higher aspect ratio than the natural daylight (Figure 16b; 0.859). This result obtained for the Munsell set generalizes for the food scenes tested. The means of the ratios across the images were 0.502 for the metamers and 0.498 for the daylights. 
The relationship found in Figure 18 for daylights also holds for metamers. The average aspect ratio of natural metamers across images (0.502) was higher than that of the preferred metamers (0.446). 
Thus, symmetry in color distribution seems to be critical to naturalness, and colorfulness seems to be critical to preference. Allowing spectral freedom in the selection of the lighting spectra promotes the expression of these trends, and the spectra producing more symmetrical color distributions are seen as more natural even if their spectra themselves are unnatural or artificial. On the other hand, the spectra producing higher colorfulness create more preferable chromatic impressions, also regardless of their origin, natural or artificial. 
The study described here did not include commonly used illuminants, like halogen and fluorescent lights, for example. To investigate how the chromatic effects of these compare with those obtained here experimentally, the color volumes and aspect ratios with the Munsell chips were computed for a representative group of practical, commonly used illuminants. They were three CIE illuminants (A: incandescent lamp; B: direct sunlight; C: average daylight), 27 typical fluorescent lamps (FL1–6: standard; FL7–9: broadband; FL10–12: narrow band; FL3.1–3.3: standard halophosphate; FL3.4–6: deluxe; FL3.7–11: three-band; FL3.12–14: multiband; FL3.15: D65 simulator), five high pressure discharge lamps (HP1: standard sodium; HP2: color enhanced; HP3–5: metal halide), and five white LEDs (LXHL-BW02, LXHL-BW03, LXMLPWC1-0100, LXML-PWN1-0100, and LXML-PWW1-0060 from Luxeon, Philips Lumileds Lighting Company, USA) (CIE, 2004; Linhares & Nascimento, 2012). The largest color volume obtained was 3.05 × 105 with FL11, and the highest aspect ratio was 0.862 with FL3.15; both were smaller than those obtained experimentally in Experiment 2 (3.24 × 105 and 0.863, respectively). Thus, although a direct psychophysical test was not carried out, these data suggest that the experimental metamers we obtained would be preferred to those commonly used illuminants. 
This study has shown that in what concerns illumination observers prefer yellowish illuminants, which seems to contradict the fact that people prefer more bluish color for objects. It has been long known that people like blue and red more than yellow and orange (Eysenck, 1941), a fact that has been confirmed and explained by quantitative studies (Ling & Hurlbert, 2007; Palmer & Schloss, 2010). These studies, however, have focused on abstract uniform patches whereas the present study concerns full complex scenes. Still, this apparent contradiction is puzzling. 
Conclusions
The spectra for best lighting for naturalness and preference were determined psychophysically with stimuli derived from hyperspectral images, simulating the illumination by daylights and the metamers of daylights. For naturalness, the empirical illuminant had a CCT around 6200 K off the Planckian locus in a more purplish direction. For preference, the illuminant had a CCT around 4550 K off the Planckian locus to an even more purplish direction. Both spectra differed from daylight-like illuminants and had the same four characteristic peaks at both ends of the visible bands and at 490 and 560 nm. It was hypothesized that the observers' choices may be determined by the aspect ratio of the color distributions and the colorfulness of the scene: The best illuminants for naturalness produced more symmetrical gamuts with more even aspect ratios than those for preference, and the best illuminants for preference produced more colorful gamuts. 
Acknowledgments
This work was supported by the European Regional Development Fund through Program COMPETE (FCOMP-01-0124-FEDER-009858) and by National Portuguese funds through Fundação para a Ciência e a Tecnologia (grant PTDC/EEA-EEL/098572/2008). We are grateful to the supermarket Pingo Doce do Braga Parque, Grupo Jerónimo Martins, for the permission to acquire spectral data from their food counters. We thank Hélder Tiago Correia for his cooperation in the hyperspectral imaging and João Manuel Maciel Linhares for his contribution to the development of hyperspectral data processing software. 
Commercial relationships: none. 
Corresponding author: Sérgio M. C. Nascimento. 
Email: smcn@fisica.uminho.pt. 
Address: Centro de Física, Universidade do Minho, Braga, Portugal. 
References
Aldaba M. A. Linhares J. M. M. Pinto P. D. Nascimento S. M. C. Amano K. Foster D. H. (2006). Visual sensitivity to color errors in images of natural scenes. Visual Neuroscience, 23 (3–4), 555–559. [PubMed]
Bartleson C. J. (1960). Memory colors of familiar objects. Journal of the Optical Society of America, 50 (1), 73–77. [CrossRef] [PubMed]
Berns R. S. (2011). Designing white-light LED lighting for the display of art: A feasibility study. Color Research & Application, 36 (5), 324–334. [CrossRef]
Carvalhal M. J. A. T. (2004). Digitalização de pintura artística com imagiografia hiperespectral. [Translation: Digitalization of artistic paintings with hyperspectral imaging]. Braga, Portugal: Universidade do Minho, Master's thesis.
Commission Internationale de l'Eclairage [CIE]. (1995). Method of measuring and specifying colour rendering properties of light sources, publication 13.3. Vienna: Commission Internationale de l'Eclairage.
Commission Internationale de l'Eclairage [CIE]. (2004). Colorimetry, publication 15 (3rd ed.). Vienna: Commission Internationale de l'Eclairage.
Davis W. Ohno Y. (2010). Color quality scale. Optical Engineering, 49 (3), 33602. [CrossRef]
Eysenck H. J. (1941). A critical and experimental study of colour preferences. The American Journal of Psychology, 54 (3), 385–394. [CrossRef]
Fedorovskaya E. A. De Ridder H. Blommaert F. J. J. (1997). Chroma variations and perceived quality of color images of natural scenes. Color Research & Application, 22 (2), 96–110. [CrossRef]
Foster D. H. (2003). Does colour constancy exist? Trends in Cognitive Sciences, 7 (10), 439–443. [CrossRef] [PubMed]
Foster D. H. (2011). Color constancy. Vision Research, 51 (7), 674–700. [CrossRef] [PubMed]
Foster D. H. Amano K. Nascimento S. M. C. Foster M. J. (2006). Frequency of metamerism in natural scenes. Journal of the Optical Society of America A, 23 (10), 2359–2372. [CrossRef]
Foster D. H. Nascimento S. M. C. Amano K. (2004). Information limits on neural identification of colored surfaces in natural scenes. Visual Neuroscience, 21 (3), 331–336. [CrossRef] [PubMed]
Granzier J. J. M. Brenner E. Smeets J. B. J. (2009). Reliable identification by color under natural conditions. Journal of Vision, 9 (1): 39, 1–8, http://www.journalofvision.org/content/9/1/39, doi:10.1167/9.1.39. [PubMed] [Article] [CrossRef] [PubMed]
Guo X. Houser K. W. (2004). A review of colour rendering indices and their application to commercial light sources. Lighting Research and Technology, 36 (3), 183–199. [CrossRef]
Hernández-Andrés J. Romero J. Lee R. L. (2001). Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain. Journal of the Optical Society of America A, 18 (2), 412–420. [CrossRef]
Hernández-Andrés J. Romero J. Nieves J. Lee R. L. (2001). Color and spectral analysis of daylight in southern Europe. Journal of the Optical Society of America A, 18 (6), 1325–1335. [CrossRef]
International Organization for Standardization [ISO]. (1999). ISO 11307:1999 Sensory analysis - General guidance and test method for assessment of the colour of foods. Geneva: International Organization for Standardization.
Japanese Industrial Standard [JIS]. (1990). Method of specifying colour rendering properties of light sources, JIS Z8726. Tokyo: Japanese Industrial Standard.
Judd D. B. (1967). A flattery index for artificial illuminants. Illuminating Engineering, 62, 593–598.
Judd D. B. MacAdam D. L. Wyszecki G. Budde H. W. Condit H. R. Henderson S. T. (1964). Spectral distribution of typical daylight as a function of correlated color temperature. Journal of the Optical Society of America, 54 (8), 1031–1040. [CrossRef]
Ling Y. Hurlbert A. (2007). A new model for color preference: Universality and individuality. 15th Color Imaging Conference. (pp. 8–11). Albuquerque, NM: Society for Imaging Science and Technology.
Linhares J. M. M. Nascimento S. M. C. (2012). A chromatic diversity index based on complex scenes. Journal of the Optical Society of America A, 29 (2), A174–A181. [CrossRef]
MacAdam D. L. (1942). Visual sensitivities to color differences in daylight. Journal of the Optical Society of America, 32 (5), 247–274. [CrossRef]
MacDougall D. B. (2002). Colour in food. Cambridge: Woodhead.
Masuda O. Nascimento S. M. C. (2012). Lighting spectrum to maximize colorfulness. Optics Letters, 37 (3), 407–409. [CrossRef] [PubMed]
Mollon J. D. (1989). “Tho' she kneel'd in that place where they grew...” The use and origins of primate colour vision. Journal of Experimental Biology, 146, 21–38. [PubMed]
Nascimento S. M. C. Ferreira F. P. Foster D. H. (2002). Statistics of spatial cone-excitation ratios in natural scenes. Journal of the Optical Society of America A, 19 (8), 1484–1490. [CrossRef]
Nascimento S. M. C. Masuda O. (2012). Psychophysical optimization of lighting spectra for naturalness, preference, and chromatic diversity. Journal of the Optical Society of America A, 29 (2), A144–A152. [CrossRef]
Newhall S. M. Burnham R. W. Clark J. R. (1957). Comparison of successive with simultaneous color matching. Journal of the Optical Society of America, 47 (1), 43–56. [CrossRef]
Olkkonen M. Hansen T. Gegenfurtner K. R. (2009). Categorical color constancy for simulated surfaces. Journal of Vision, 9 (12): 6, 1–18, http://www.journalofvision.org/content/9/12/6, doi:10.1167/9.12.6. [PubMed] [Article] [CrossRef] [PubMed]
Palmer S. E. Schloss K. B. (2010). An ecological valence theory of human color preference. Proceedings of the National Academy of Sciences, USA, 107 (19), 8877–8882. [CrossRef]
Pinto P. D. Linhares J. M. M. Nascimento S. M. C. (2008). Correlated color temperature preferred by observers for illumination of artistic paintings. Journal of the Optical Society of America A, 25 (3), 623–630. [CrossRef]
Protzman J. B. Houser K. W. (2006). LEDs for general illumination: The state of the science. Leukos, 3 (2), 121–142.
Rea M. S. Freyssinier-Nova J. P. (2008). Color rendering: A tale of two metrics. Color Research & Application, 33 (3), 192–202. [CrossRef]
Sanders C. L. (1959). Color preferences for natural objects. Illuminating Engineering, 54, 452–456.
Schanda J. (2007). Colorimetry: Understanding the CIE system. Hoboken, NJ: John Wiley & Sons.
Schanda J. Madár G. (2007). Light source quality assessment. CIE 26th Session (pp. D1-72–D1-75). Beijing, China: Commission Internationale de l'Eclairage.
Schmitt F. J. M. (1976). A method for the treatment of metamerism in colorimetry. Journal of the Optical Society of America, 66 (6), 601–608. [CrossRef] [PubMed]
Shevell S. K. Kingdom F. A. A. (2008). Color in complex scenes. Annual Review of Psychology, 59, 143–166. [CrossRef] [PubMed]
Smet K. Ryckaert W. R. Pointer M. R. Deconinck G. Hanselaer P. (2010). Memory colours and colour quality evaluation of conventional and solid-state lamps. Optical Express, 18 (25), 26229–26244. [CrossRef]
Smet K. Ryckaert W. R. Pointer M. R. Deconinck G. Hanselaer P. (2011 a). Correlation between color quality metric predictions and visual appreciation of light sources. Optics Express, 19 (9), 8151–8166. [CrossRef] [PubMed]
Smet K. Ryckaert W. R. Pointer M. R. Deconinck G. Hanselaer P. (2011 b). Colour appearance rating of familiar real objects. Color Research & Application, 36 (3), 192–200. [CrossRef]
Song T. Luo R. (2000). Testing color-difference formulae on complex images using a CRT monitor. Eighth Color Imaging Conference. (pp. 44–48). Scottsdale, Arizona: Society for Imaging Science and Technology.
Surridge A. K. Osorio D. Mundy N. I. (2003). Evolution and selection of trichromatic vision in primates. Trends in Ecology & Evolution, 18 (4), 198–205. [CrossRef]
Thornton W. A. (1972). Color-discrimination index. Journal of the Optical Society of America, 62 (2), 191–194. [CrossRef] [PubMed]
Thornton W. A. (1973). Fluorescent lamps with high color-discrimination capability. Journal of the Illuminating Engineering Society, 3, 61–64. [CrossRef]
Thornton W. A. (1974). A validation of the colour-preference index. Journal of the Illuminating Engineering Society, 17, 48–52. [CrossRef]
Wyszecki G. Stiles W. S. (1982). Color science: Concepts and methods, quantitative data and formulae (2nd ed.). New York: John Wiley & Sons.
Xu H. (1993). Color-rendering capacity of light. Color Research & Application, 18 (4), 267–269. [CrossRef]
Xu H. (2012). Configuring a spectral power distribution for effective colour rendering. Lighting Research and Technology, 44 (3), 309–315. [CrossRef]
Žukauskas A. Vaicekauskas R. Ivanauskas F. Vaitkevičius H. Shur M. S. (2008). Spectral optimization of phosphor-conversion light-emitting diodes for ultimate color rendering. Applied Physics Letters, 93 (5), 051115. [CrossRef]
Figure 1
 
Scenes tested in the psychophysical experiments. The scenes were digitalized by hyperspectral imaging in a local supermarket. The number on each image is for labeling and was not displayed in the experiments. Images 1–3 represent fruits, images 4–6 vegetables, images 7–9 meat, and images 10–12 fish.
Figure 1
 
Scenes tested in the psychophysical experiments. The scenes were digitalized by hyperspectral imaging in a local supermarket. The number on each image is for labeling and was not displayed in the experiments. Images 1–3 represent fruits, images 4–6 vegetables, images 7–9 meat, and images 10–12 fish.
Figure 2
 
Illuminant chromaticities tested expressed in the CIE 1960 UCS diagram. The illuminants were synthetized from Judd's daylight spectral basis functions. The grid points had correlated color temperatures in the range 2222–20,000 K equally spaced in reciprocal color temperature at an interval of 25 MK−1. The points on the lines orthogonal to the Planckian locus were in the range −0.01–+0.01 from the locus at an interval of 0.002 in UCS units.
Figure 2
 
Illuminant chromaticities tested expressed in the CIE 1960 UCS diagram. The illuminants were synthetized from Judd's daylight spectral basis functions. The grid points had correlated color temperatures in the range 2222–20,000 K equally spaced in reciprocal color temperature at an interval of 25 MK−1. The points on the lines orthogonal to the Planckian locus were in the range −0.01–+0.01 from the locus at an interval of 0.002 in UCS units.
Figure 3
 
Average spectrum of the simple elements at (CCT, DC) = (6667 K, 0). Error bars show the standard errors at each band.
Figure 3
 
Average spectrum of the simple elements at (CCT, DC) = (6667 K, 0). Error bars show the standard errors at each band.
Figure 4
 
Calibration of the monitor. Black dots are the intended chromaticities of the grid. Red circles are the actually measured chromaticities. Red circles were measured only along the DC of −0.01, 0.00, and +0.01. The mean error between the red circles and the corresponding grid points was 0.003, which is smaller than the just noticeable difference (JND) around this chromaticity area (0.007) estimated as the thrice of the mean radius of the MacAdam ellipse (MacAdam, 1942).
Figure 4
 
Calibration of the monitor. Black dots are the intended chromaticities of the grid. Red circles are the actually measured chromaticities. Red circles were measured only along the DC of −0.01, 0.00, and +0.01. The mean error between the red circles and the corresponding grid points was 0.003, which is smaller than the just noticeable difference (JND) around this chromaticity area (0.007) estimated as the thrice of the mean radius of the MacAdam ellipse (MacAdam, 1942).
Figure 5
 
Histograms of the colorimetric errors due to the gamut limit in Experiment 1 (red striped bars) and Experiment 2 (gray bars). The errors were expressed as the mean color difference in CIELAB across the pixels between the intended and actually achievable images selected by the observer in each trial. In Experiment 1, the mean errors for 96.4% of the trials were less than the JND. In Experiment 2, 90.9% of the trials had errors less than the JND.
Figure 5
 
Histograms of the colorimetric errors due to the gamut limit in Experiment 1 (red striped bars) and Experiment 2 (gray bars). The errors were expressed as the mean color difference in CIELAB across the pixels between the intended and actually achievable images selected by the observer in each trial. In Experiment 1, the mean errors for 96.4% of the trials were less than the JND. In Experiment 2, 90.9% of the trials had errors less than the JND.
Figure 6
 
Results obtained in the two conditions of Experiment 1 averaged across all images and observer. Error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT.
Figure 6
 
Results obtained in the two conditions of Experiment 1 averaged across all images and observer. Error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT.
Figure 7
 
Average CCT across all observers for each scene. Filled symbols connected by solid lines represent the naturalness condition and open symbols connected by dotted lines represent the preference condition. Error bars show the standard errors of the means. For readability the vertical axis is labeled in CCT, but is spaced uniformly in RCT.
Figure 7
 
Average CCT across all observers for each scene. Filled symbols connected by solid lines represent the naturalness condition and open symbols connected by dotted lines represent the preference condition. Error bars show the standard errors of the means. For readability the vertical axis is labeled in CCT, but is spaced uniformly in RCT.
Figure 8
 
Example of the selection of the chromaticities for Experiment 2.1. U is 1 SD (0.04 in DC) shifted upward from C, and D is shifted downward by the same amount in the opposite direction. L is shifted 1 SD (100 MK−1 in RCT) leftward from C, and R is shifted 1 SD by the same amount in the opposite direction. The chromaticity of C and SDs were obtained from the corresponding results in Experiment 1.
Figure 8
 
Example of the selection of the chromaticities for Experiment 2.1. U is 1 SD (0.04 in DC) shifted upward from C, and D is shifted downward by the same amount in the opposite direction. L is shifted 1 SD (100 MK−1 in RCT) leftward from C, and R is shifted 1 SD by the same amount in the opposite direction. The chromaticity of C and SDs were obtained from the corresponding results in Experiment 1.
Figure 9
 
The filled symbols show CCT and DC obtained in the two conditions of Experiment 2.2 averaged across all scenes and observer. The error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT. The faded open symbols are the replot of Figure 6.
Figure 9
 
The filled symbols show CCT and DC obtained in the two conditions of Experiment 2.2 averaged across all scenes and observer. The error bars show the standard errors of the means. For readability the horizontal axis is labeled in CCT but is spaced uniformly in RCT. The faded open symbols are the replot of Figure 6.
Figure 10
 
Average CCT obtained with the metamers (M; solid symbols) for each scene across all the observers in the naturalness (a) and preference (b) conditions. The error bars show the standard errors of the means. The CCT obtained with daylights (D; dashed lines) in Experiment 1 are also shown for comparison.
Figure 10
 
Average CCT obtained with the metamers (M; solid symbols) for each scene across all the observers in the naturalness (a) and preference (b) conditions. The error bars show the standard errors of the means. The CCT obtained with daylights (D; dashed lines) in Experiment 1 are also shown for comparison.
Figure 11
 
Average spectra selected by observers in the naturalness condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average natural daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 11
 
Average spectra selected by observers in the naturalness condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average natural daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 12
 
Average spectra chosen by observers in the preference condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average preferred daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 12
 
Average spectra chosen by observers in the preference condition. (a) The average across all the observers and categories. The error bars show the standard errors at each band. The gray dotted line is the average preferred daylight obtained in Experiment 1 for comparison. (b) The averages across all the observers for each category.
Figure 13
 
The pseudocolor map of CRI corresponding to the daylights tested. The symbols show the average psychophysical data obtained in Experiment 1. Standard errors are smaller than the symbol size.
Figure 13
 
The pseudocolor map of CRI corresponding to the daylights tested. The symbols show the average psychophysical data obtained in Experiment 1. Standard errors are smaller than the symbol size.
Figure 14
 
Pseudocolor map of the convex hull volume expressed in CIELAB space of the Munsell set rendered by the daylights tested (a) and by the metamers that maximize the volume at each grid point (b). Open square and circle show the natural and preferred daylights in Experiment 1, and filled square and circle show the natural and preferred metamers in Experiment 2.2, respectively. Standard errors are smaller than the symbol size.
Figure 14
 
Pseudocolor map of the convex hull volume expressed in CIELAB space of the Munsell set rendered by the daylights tested (a) and by the metamers that maximize the volume at each grid point (b). Open square and circle show the natural and preferred daylights in Experiment 1, and filled square and circle show the natural and preferred metamers in Experiment 2.2, respectively. Standard errors are smaller than the symbol size.
Figure 15
 
Comparison of volumes by the food images in CIELAB space between the natural and preferred daylights. The trend line fitted to the data (solid line) is steeper than the diagonal (dotted line).
Figure 15
 
Comparison of volumes by the food images in CIELAB space between the natural and preferred daylights. The trend line fitted to the data (solid line) is steeper than the diagonal (dotted line).
Figure 16
 
Gamuts of Munsell chips projected onto the a*b* plane rendered by (a) the most natural metamer in Experiment 2.2 (b) the most natural daylight in Experiment 1, (c) the most preferable metamer in Experiment 2.2, and (d) the most preferable daylight in Experiment 1. The center of an ellipse is the mean of the data points, and the radii correspond to two standard deviations along the most and least variable direction. An ellipse covers 95% of the data points. The convex hull volumes of the chips in the CIELAB space are (a) 2.91x105, (b) 2.97x105, (c) 3.24x105, and (d) 3.03x105, respectively. The ratios of lengths of the shorter axes to longer ones are (a) 0.863, (b) 0.859, (c) 0.837, and (d) 0.817, respectively.
Figure 16
 
Gamuts of Munsell chips projected onto the a*b* plane rendered by (a) the most natural metamer in Experiment 2.2 (b) the most natural daylight in Experiment 1, (c) the most preferable metamer in Experiment 2.2, and (d) the most preferable daylight in Experiment 1. The center of an ellipse is the mean of the data points, and the radii correspond to two standard deviations along the most and least variable direction. An ellipse covers 95% of the data points. The convex hull volumes of the chips in the CIELAB space are (a) 2.91x105, (b) 2.97x105, (c) 3.24x105, and (d) 3.03x105, respectively. The ratios of lengths of the shorter axes to longer ones are (a) 0.863, (b) 0.859, (c) 0.837, and (d) 0.817, respectively.
Figure 17
 
The background pseudocolor plot in (a) shows the aspect ratios of the ellipses fitted to the gamuts of Munsell chips rendered by the daylights on the grid. The pseudocolor plot in (b) shows the average aspect ratios of the ellipses fitted to the gamut of Munsell chips rendered by the metamers with the top 5% aspect ratios.
Figure 17
 
The background pseudocolor plot in (a) shows the aspect ratios of the ellipses fitted to the gamuts of Munsell chips rendered by the daylights on the grid. The pseudocolor plot in (b) shows the average aspect ratios of the ellipses fitted to the gamut of Munsell chips rendered by the metamers with the top 5% aspect ratios.
Figure 18
 
Comparison of aspect ratios of the color gamuts by the food images between the natural and preferred daylights. The daylight for each image and condition were averaged across the observers.
Figure 18
 
Comparison of aspect ratios of the color gamuts by the food images between the natural and preferred daylights. The daylight for each image and condition were averaged across the observers.
Figure 19
 
Comparison of the volumes of the food images in the CIELAB space between the preferred metamer found in Experiment 2 and the preferred daylight found in Experiment 1. The metamer and daylight for each image were averaged across the observers.
Figure 19
 
Comparison of the volumes of the food images in the CIELAB space between the preferred metamer found in Experiment 2 and the preferred daylight found in Experiment 1. The metamer and daylight for each image were averaged across the observers.
Table 1
 
Mean errors of 15 reproduced color samples in ΔE*ab.
Table 1
 
Mean errors of 15 reproduced color samples in ΔE*ab.
CCT (K)
20,000 6667 4000 2857 2222
DC
 0.01 2.89 2.14 2.73 3.09 N/A
 0.00 2.99 2.80 2.18 3.12 3.22
 −0.01 2.69 2.25 2.23 2.28 3.63
Table 2
 
The percentages and p values of the direct choices of metamers against daylights.
Table 2
 
The percentages and p values of the direct choices of metamers against daylights.
Fruit Veg Meat Fish All
Naturalness
 % 65.3 72.2 59.7 70.8 67.0
p <0.01 ≪0.01 0.04 ≪0.01 ≪0.01
Preference
 % 63.9 76.4 73.6 56.9 67.7
p <0.01 ≪0.01 ≪0.01 0.10 ≪0.01
×
×

This PDF is available to Subscribers Only

Sign in or purchase a subscription to access this content. ×

You must be signed into an individual account to use this feature.

×