In the study of new types of displays such as digital holographic displays or augmented reality displays, research on optical properties [1–6] usually takes precedence over color research since color characteristics are mainly affected by the optical properties of a display. However, digital holographic displays that use red (R), green (G) and blue (B) lasers as the primary colors are likely to suffer from the color mismatch problem [7] not related to the optical property of a display. The color mismatch problem, also known as International Commission on Illumination (CIE) colorimetric matching failure, means that the colors shown on digital holographic displays look very different from other conventional displays, while the color measurement values are the same.

CIE is an international organization developing standards for light and lighting. Colors should be measured and reported following CIE colorimetry [8]. Colors with less than a 4-degree field of view (FOV) should be measured using the CIE 1931 standard observer function resulting in tristimulus values, XYZ, and those larger than a 4-degree FOV should use the CIE 1964 standard observer function resulting in tristimulus values, X₁₀Y₁₀Z₁₀.

Theoretically, two colors with the same CIE 1931 XYZ tristimulus values refer to colors with the same color appearance. However, in displays with narrowband spectral characteristics, it has been observed that colors with the same CIE 1931 XYZ values on two different displays look different from each other [7, 9–18]. This CIE colorimetric matching failure phenomenon becomes more significant in displays with narrowband spectral characteristics such as RGB laser projectors [7].

Many studies reporting CIE colorimetric matching failure conducted color matching experiments by adjusting the colors of two spectrally different displays or lightings. For matched colors having the same color appearance, the spectral data of two colors were measured using a spectroradiometer. CIE XYZ tristimulus values were calculated using spectral data and the CIE color matching function (CMF), and the ∆u′v′ or ∆E₀₀ color difference between them was calculated to indicate the degree of color mismatch. If two colors having the same color appearance have the same CIE tristimulus values, the color difference should be zero, but recent studies have shown large color differences, which demonstrated CIE colorimetric matching failure. For example, in a study by Huang et al. [9], color matching using light-emitting diode (LED) panels in a FOV of 5.7° with 70 observers showed a 0.0123 ∆u′v′ color mismatch. Shi and Luo [10] conducted color matching using liquid crystal display (LCD) and OLED displays with 20 observers in 4° of FOV, and the results showed a 4.93 ∆E₀₀ color difference between the reference and matched colors. A study by Wu et al. [11] conducted a color matching experiment using LCD and OLED displays with 50 observers in a 4.77° FOV environment, and the results showed a color difference of 0.0042 ∆u′v′, showing that it was difficult to represent the color matching result with the CIE 1931 color matching function. Shen et al. [12] conducted a color matching experiment using LED panels and LCD in 2°, 4°, 8°, and 13° of FOV with 88 observers, and the results showed 0.0113 ∆u′v′ of color mismatch, indicating that both the CIE 1931 and CIE 1964 color matching functions cannot characterize the color matching results. Ko et al. [7] conducted color matching experiments using various types of displays including LCD, quantum dot light-emitting diode (QLED), OLED displays, and laser projectors, and found that matching using a laser projector, which had the narrowest spectrum in test displays, had the largest color mismatch. Such CIE colorimetric matching failures occur because the CIE standard observer function is not sufficiently accurate for narrowband spectral displays.

Currently, methods to solve this problem include a new color matching function derivation and a correction method using a 3-by-3 matrix. The new color matching function derivation method means using the new CMF instead of CIE 1931 CMF. Huang et al. [9], Shi and Luo [10], Wu et al. [11], and Shen et al. [12] showed that the CIE 2015 cone-fundamental-based CMF [19, 20] works better than CIE 1931 CMF, but studies by Ohno et al. [13] and Shi et al. [14] reported the poor performance of CIE 2015 CMF for older observers. Ko et al. [7] proposed a new CMF based on their color matching experimental sets showing that the new function outperforms the existing CIE functions. The 3-by-3 matrix method applies a 3-by-3 matrix to XYZ tristimulus values obtained from the test display to match the test display color with that of the reference display [10, 15]. The 3-by-3 matrix method is an easy-to-use and practical method, but this color correction is applied only with a given reference-test display set.

Since no prior research has addressed CIE colorimetric matching failure in digital holographic displays, this study conducted a color matching experiment using an RGB laser mixing system and an OLED display, which is the most common display type for smartphones, to indirectly investigate the significance of this issue. Subsequently, color correction methods were explored to achieve perceptual color matching between the two systems.

A color matching experiment was conducted in a darkroom by arranging two displays side-by-side as shown in Fig. 1. The left display is RGB laser lights screened on a diffuser and the right display is the OLED display. Such an experimental setting represents the situation where the color on the digital holographic display is replicated on the smartphone, or vice versa.

Figure 1. Experimental scene for color matching: (a) RGB laser mixing system, (b) OLED display.

Both displays were covered with black paper that has a circular hole in the middle. The observers performed color matching by adjusting the color on the OLED display to match the color appearance with that of RGB laser lighting in a darkroom.

2.1. RGB Laser Mixing System

White light with a magnified size of 1 inch or more was generated using red, green, and blue lasers on an optical table. Figure 2(a) shows a schematic diagram of the optical setup, and Fig. 2(b) shows an actual photograph of the optical system implemented in this study.

Figure 2. Overall diagram of RGB laser mixing system. (a) Schematic diagram of the developed optical setup for conducting the color matching experiment. (b) Image of the practical optical setup.

White light was implemented by using three lasers, red (λ = 632.8 nm, Model No. HNL100LB; Thorlabs Ltd., NJ, USA), green (λ = 532 nm, Model No. CPS532, Thorlabs Ltd.), and blue (λ = 450 nm, Model No. MDL-iii-450L-10Mw; Changchun New Industries Optoelectronics Technology Co., Ltd, Changchun, China), as shown in Fig. 2(a). Each laser light source can control the open and close operations with a motorized mechanical shutter. The optical power of each laser can be continuously controlled through the rotation of a half-wave plate (HWP) installed on the rotation stage and the fixed polarizer. The three lasers used were combined using a dichroic beam splitter and traveled along the same optical path. The three lasers were expanded through a spatial filter system (M-900; Newport Co., CA, USA). The observers saw the expanded laser-based color through a diffuser. In the optical setup, the opening and closing and power control of each laser were implemented to be controlled through a single laptop.

Figure 3 displays the spectral power distribution (SPD) of the RGB lasers, which were measured using a Konica Minolta CS-2000 spectroradiometer (Konica Minolta Co., Tokyo, Japan). The peak wavelength was 633, 532, and 452 nm for each primary and the full width at half maximum (FWHM) was 3 nm for each laser.

Figure 3. Spectral power distribution of RGB lasers.

Three types of optical diffusers with 120, 220, and 600 grit [21] were used as a screen to show the mixed RGB laser lights to the observer. As shown in Fig. 4, different degrees of speckles were visible in the diffusers such that the higher the grit of the diffuser, the less speckles that are seen. The center of each diffuser was the most uniform, and the uniformity decreased further away from the center.

Figure 4. Images of the RGB laser light using three different optical diffusers: (a) 120 grit, (b) 220 grit, and (c) 600 grit.

The color of the RGB laser was controlled by adjusting the rotation of the HWP on the rotation stage in Fig. 2. It was found that the resulting color was unstable, as the measured CIE XYZ values continuously changed over time. Also, large angular dependency was found. Therefore, considering the limitations of the RGB laser mixing system in this study, various cautions were given to the observers during the experiment, which is explained in Section 2.3.

2.2. OLED Display

As an OLED display, an iPhone 12 was used. Figure 5 shows the spectral distribution of red, green, and blue primaries. The peak wavelength was 621, 526, and 461 nm for each primary and the FWHM was around 35, 27, and 17 nm, respectively.

Figure 5. Spectral power distribution of RGB primaries of OLED display.

The OLED display was characterized using a gain-offset-gamma (GOG) model [22] to predict output CIE XYZ values from input RGB values. Thirty-six colors including red, green, blue, and white were displayed on the screen and measured using the spectroradiometer. Then model parameters were optimized to minimize the ∆E*ab color difference between the measured CIELAB values and the predicted CIELAB values using the GOG model. The average color difference was 1.35 ± 1.10 ∆E*ab, indicating that the OLED display color characterization model had good performance.

Equation (1) and Eq. (2) show the model used in this study.

2.3. Color Matching Experiment Procedure

The color matching experiment was conducted in a darkroom. An observer was positioned at the center of the RGB laser mixing system and OLED display. After a training session to become familiar with the color manipulation method, the observer manipulated the color of the OLED display to have the same color appearance as the color of the RGB lasers, without a time limit. During the matching process, the observer was asked to compare the central area of each stimulus to minimize the non-uniformity problem.

The color of the OLED display was controlled using a desktop computer and shown on the OLED display using the screen sharing mode from the desktop. The observers used a keyboard to control the lightness (CIELAB L*), redness-greenness (CIELAB a*), and yellowness-blueness (CIELAB b*) of the color shown on the OLED display. The changed CIELAB values were converted to XYZ tristimulus values, and then to digital RGB values using the GOG model to show the changed color to the observer in real time.

When the observer achieved satisfactory matching, the spectral data of the reference (RGB laser) and matched (OLED) colors were measured using the spectroradiometer, which was placed behind the observer. After that, the observer pressed the enter key to move to the next stimulus.

For color matching, three types of optical diffusers and seven RGB laser intensity mixtures were used, and the color matching was repeated five times for each RGB intensity mixture. Therefore, each observer performed a total of 105 color matchings (7 RGB intensity mixtures × 5 repetitions × 3 diffusers), and the order of the RGB intensity mixture and the order of the diffuser type were presented randomly. The experiment lasted 2 hours to 4 hours on average. Nine observers with normal color vision, who passed the Ishihara color vision test, participated in the experiment. They were seven females and two males with an average age of 23.56 years.

The seven initial RGB intensity mixtures of the laser system consisted of a low-chromatic color with an average luminance of 30.04 cd/m². Even though the same initial rotation of the HWP on the rotation stage was used for all observers, the light intensity from each laser changed over time due to a stability issue of the laser, so that the color used as the reference stimulus gradually shifted to a greenish color and was different for each observer.

The experimental protocols and procedures were approved by the Institutional Review Board of the Ulsan National Institute of Science and Technology (Approval No. UNISTIRB-21-27-A).

3.1. Data Analysis Method

Due to the temporal stability issue of the RGB laser and OLED display, the reference and matched colors were measured right after each color matching. For all color matching data, the XYZ tristimulus values were calculated using the measured spectral data of the reference and matched colors. From the XYZ tristimulus values, CIE u′v′ values were calculated to represent the colors on a CIE u′v′ chromaticity diagram and to calculate the ∆u′v′ color difference between the reference and individual matching colors, as described in Eq. (3), to show the degree of color mismatch.

Note that the CIE 1931 tristimulus values are used for data analysis since the stimuli were designed to subtend a 2° FOV.

3.2. CIE u′v′ Chromaticity Difference in Color Matching

The chromaticities of the reference and the matched colors are compared in Fig. 6 and Table 1.

Figure 6. CIE u′v′ chromaticities of the reference and matched colors for each observer.

TABLE 1. Average chromaticity difference, ∆u′v′ by observer and by optical diffuser.

∆u′v′	120 grit	220 grit	600 grit	Average
Obs1	0.0189	0.0213	0.0216	0.0206 ± 0.0065
Obs2	0.0448	0.0503	0.0478	0.0477 ± 0.0129
Obs3	0.0263	0.0248	0.0183	0.0231 ± 0.0067
Obs4	0.0160	0.0142	0.0132	0.0145 ± 0.0082
Obs5	0.0182	0.0171	0.0174	0.0175 ± 0.0101
Obs6	0.0122	0.0131	0.0110	0.0121 ± 0.0047
Obs7	0.0200	0.0165	0.0168	0.0178 ± 0.0086
Obs8	0.0203	0.0190	0.0201	0.0198 ± 0.0054
Obs9	0.0186	0.0206	0.0228	0.0207 ± 0.0096
Average	0.0217	0.0219	0.0210	-

Figure 6 shows the color matching results of each observer regardless of the diffuser type. The black cross represents the reference colors, and the red circle represents the colors matched by the observer. The blue arrow connects the reference color and the matched color. For all observers, the color chromaticities of all the matched colors are in the CIE -u′ direction from the reference color, indicating that there is a chromaticity shift in a certain direction for all observers. In other words, if two colors have the same CIE u′v′ values, the OLED display looks more reddish than the RGB laser mixing system. As for the CIE v′ perspective, it is different for each observer.

Table 1 summarizes the average chromaticity difference, ∆u′v′ by observer and by optical diffuser. The average chromaticity difference between the reference and matched colors is 0.0215 ± 0.0104 ∆u′v′ (0.0230 ∆u′₁₀v′₁₀), which is as large as a previous study by Ko et al. [7] using a laser projector and LCD display: 0.0345 ∆u′v′ (0.0196 ∆u′₁₀v′₁₀).

For the optical diffuser type, the chromaticity difference was not significantly different in both individual and average data.

3.3. Luminance Difference in Color Matching

In the previous color matching experiment, the luminance difference between the reference and matched colors was not significant; Even the largest difference was about 18% of the reference color [12], and the observer variability for the luminance difference was negligibly small [16]. However, in this experiment, luminance differences between the reference and matched colors were observed. The luminance of the matched colors was much higher than the reference color.

Table 2 summarizes the ratio of the luminance for the matched color to the luminance for the reference color. Overall, the luminance of matched colors was higher for all observers. The average ratio was 5.93 ± 4.25, indicating that the RGB laser color looked much brighter to all the observers than the OLED color with the same luminance. In addition, the luminance ratio by diffuser type was not significantly different in all individual data.

TABLE 2. Luminance ratio between matched and reference colors (luminance of OLED display / luminance of Laser).

Observer	Average Ratio (120, 220, 600 grit)	Max Ratio
Obs1	5.53 ± 1.30 (5.03, 5.59, 5.98)	8.60
Obs2	4.41 ± 0.83 (4.02, 4.56, 4.66)	6.56
Obs3	3.58 ± 1.55 (3.52, 3.33, 3.90)	8.35
Obs4	5.10 ± 1.63 (5.15, 5.04, 5.12)	11.02
Obs5	13.43 ± 4.15 (11.52, 14.49, 14.29)	21.30
Obs6	11.66 ± 3.14 (11.03, 11.37, 12.57)	18.65
Obs7	3.24 ± 1.72 (2.34, 3.40, 3.99)	9.14
Obs8	2.88 ± 1.70 (2.88, 2.51, 3.25)	13.16
Obs9	3.50 ± 1.59 (3.40, 3.49, 3.59)	7.95

This phenomenon is presumed to be due to the speckles of the RGB lasers. The interference of laser light creates a pattern in which the intensity of light increases at certain points and weakens at other points [23]. Observers may use the bright speckles to match the color, so the actual matched color has a high luminance.

4.1. Color Correction Methods for CIE Colorimetric Matching Failure

As shown from the experimental results, there was a systematic color mismatch between the laser mixing system and the OLED display. Therefore, the CIE colorimetric matching failure in a digital holographic display using an RGB laser will cause serious color quality deterioration, emphasizing that a solution for the phenomenon is essential.

In this study, four types of new color matching functions and two types of 3-by-3 matrix were tested. In the case of new CMFs, the CIE 2015 color matching function [19, 20] and the long-, medium-, and short- (LMS) cone-fundamental function by Ko et al. [7] were tested. Also, new CMFs were derived using the method introduced in Asano’s individual colorimetric observer model [16] by minimizing the ∆u′v′ color difference between the matching color and the color predicted by the new LMS function. The average LMS from all observers’ spectral data and individual LMS of each observer were derived. As demonstrated by the chromaticity and luminance difference in the matching results, individual differences were larger in this experiment than in the previous studies, requiring personalized solutions for matching failure. Therefore, test CMFs included the individual LMS color matching function.

Similarly, for the 3-by-3 matrix, the average matrix using all nine individual data and the individual 3-by-3 matrix derived from individual data were tested.

4.2. Performance Test for Color Correction Methods

Using six types of color correction methods, the ∆u′v′ color difference between the matching color and predicted color by correction method was calculated to evaluate the model performance.

Figure 7 shows the average performance test results of the six test color correction methods. The x-axis represents each color correction method, and the y-axis represents the chromaticity difference in the ∆u′v′ color difference. The dotted line represents the average chromaticity difference in color matching results, which is 0.0215 ∆u′v′. Since the degree of color mismatch was calculated using the CIE 1931 color matching function, this line indicates the performance of the CIE 1931 color matching function.

Figure 7. Average performance test results for six color correction methods (four LMS functions and two 3-by-3 matrices).

The results showed that the CIE 2015 CMF and Ko LMS function had larger chromaticity differences than CIE 1931 CMF, showing poor performance. On the other hand, the LMS function and 3-by-3 matrix, which were derived using average and individual color matching data in this experiment, had improved performance.

Especially in all observers and in all optical diffusers, the color correction performance was better in the individual LMS function and individual 3-by-3 matrix than in the average observer method, meaning that individual correction methods are more effective for the RGB laser.

The performance of the individual LMS and 3-by-3 matrix was similar. Since the 3-by-3 matrix can only be applied to the corresponding display dataset and the LMS function can be a universal solution, more studies on individual cone-fundamental LMS functions are needed.

This study conducted a color matching experiment with nine observers using an RGB laser mixing system with three optical diffusers and an OLED display. The results showed a CIE colorimetric mismatch of 0.0215 ∆u′v′ on average. This indicates that there is a serious color mismatch for RGB laser displays such as digital holographic displays. While the presence of speckles did not make a significant difference in chromaticity, it had an impact on the luminance perception in RGB lasers; The ratio of matched to reference color was 5.93 on average. In addition, there were larger individual matching differences in chromaticity and luminance than previous studies.

For color correction methods, the existing CIE 1931 CMF, CIE 2015 CMF, and Ko LMS function did not perform well, and the performance of the individual correction method was the best.

In conclusion, this research clearly indicates the significant CIE colorimetric matching failure anticipated in digital holographic displays and emphasizes the importance of personalized color correction. Since this study is based on limited experimental conditions, more in-depth research is needed to solve the CIE colorimetric matching failure. In particular, since this experiment was based on a uniformly diffused RGB laser, an experiment using an actual digital holographic display is needed. The actual digital holographic display uses a device such as a spatial light modulator (SLM) to show the hologram image at certain depth conditions, thereby creating 3-dimensional (3D) space. Consequently, additional 3D uniformity color correction will be required by collecting location-based color data.

This work was supported by Institute of Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea Government (MSIT) (Grant No. 2021-0-00343, Development of metrology for the properties of reconstructed digital hologram’s space and color).

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data underlying the results presented in this paper are not publicly available at the time of publication but may be obtained from the authors upon reasonable request.