The Objective Conditions Study and Optimization of Digital Imaging System on Color Measurement฀ Case with Jadeite

The application of digital imaging to color measurement is more and more extensive, which also provides new ideas for gemology. In this paper, the single-factor experiment method and orthogonal experiment design are used to study the influence parameters of the digital imaging system (DIS) on gem color measurement. Among them, the illuminance has the most significant impact on the measurement results, followed by the exposure time, and the change of the measurement distance has an insignificant impact on the results; through range analysis and analysis of variance, the most suitable measurement parameters for red jadeite are 1600lx, 12500ms, 25cm.


Introduction
The current methods for evaluating the color of gems include color chips (Munsell, Gem-dialogue), colorimetric stones, ultraviolet-visible spectrophotometers, and spectrophotometers.
Among them, the color chips and the colorimetric stones are used to directly help the eyes to make judgments 1 . These methods are mainly based on the subjective evaluation of the color by the operator, so it takes a lot of time and money to train professional graders. UV-Vis spectrophotometers can provide accurate absorption spectra from which color calculations can be made 2,3 ; however, the complex conversion process has hindered their development in gemstone color measurement; hand-held spectrophotometers, as the mainstream gem color measurement tool at present, has been used to measure the color of jadeite green 4 , jadeite red 5,6 , turquoise 7 , peridot 8,9 , amethyst 10 , chrysoprase 11,12 , and extensive gemstone chromatography studies. Because of its convenient operation and reliable data, this tool has already been favored by researchers. But there are also limitations: 1.
The size of the gemstone is smaller than the smallest aperture that can be measured by the device, which will lead to significant errors caused by the background. 2. The reading color method is uniform color reading and it's hard to distinguish and study color-striped gems.
Furthermore, the use of contact measurement in some precious materials like gems may cause unavoidable damage. With the development of color measurement technology in various research fields, such as reproduction and protection of artwork 13 , remote sensing mapping 14 , and dental medicine 15 , non-contact color measurement is widely used. In food science, many experiments and studies have been conducted on quality control 16 . In the fields of geoscience, the non-contact color measurement method is also widely used to classify and sort ores based on colors and textures 17 Checker color chips to make ICC feature files to correct the errors generated between different digital cameras, so that the digital protection and dissemination of Dunhuang murals can receive strong technical support 23 ; In our other work, experiments by Zhang et al. compared computer vision system   and traditional hand-held spectrophotometer for the measurement and evaluation of various colors of   jadeite, then judged the applicability by experts panel which makes the color matching subjective 24 ; Therefore, in gemology, a digital imaging as one of the non-contact methods can provide researchers with new ideas. In the above-mentioned measurement method, a non-contact measuring device-a spectroradiometer or camera-is used to obtain accurate measurement results under the condition of an external light source. However, in previous studies, the researchers did not discuss the influence of the changes in the measurement conditions on the experimental results, which will lead to this method not being replicated and applied to future studies.
Gem-quality jadeite is mainly from Burma and Guatemala, which is produced in Jadeitite and has beautiful and durable properties 25,26 . Harlow et al. believe that jadeite is a complex fibrous aggregate of minerals 27 , which gives itself a beautiful, varied appearance, also the reason why it is loved by Chinese people. It is usually colorless and translucent without other impurities. The cause of the color of jadeite can be divided into two types: primary color and secondary color 6,28 ; The green of jadeite is the primary color; and the red and yellow is the secondary color, which is caused by exogenous geological activities, and usually produced when impurities, such as water-containing iron oxide, are infiltrated along the cracks and the grain boundaries that are not tightly bound. According to comparative experiments, Wang et al. recognized that the D65 standard light source (representing the average daylight with a color temperature of 6504K) is the most suitable light source for evaluating Jadeite green 29 ; Pan et al., Guo, Li believe that D65 light source is suitable to evaluate the red color of jadeite, tourmaline, and ruby respectively 6,30,31 . The color of jadeite is the most important indicator of value, so it is important to accurately measure and display its color.
In this paper, we use one single factor method to study how the circumstances of the digital imaging system influence the color measurement and ColorChecker calibration to objectively verify the feasibility of DIS. Based on the Orthogonal Design, the analysis of variance (ANOVA) was used to explore the suitable measurement parameters.   The correlations between colorimetric coordinate * * and illuminance is shown in Fig.2. The increment of * is more than * with the increase of illuminance, with a fitting coefficient of 0.013(R 2 =0.998) and 0.007(R 2 =0.997) respectively.
As shown in Fig.3(a), with the gradual increase of illuminance, the lightness * of jadeite increases significantly and the mean lightness change from 1100 to 2900lx is 27.81, which is the same as the observation by the naked eye. By comparing the lightness of jadeite with different hues, it is found that the lightness of yellow jadeite (ℎ°∈ (80,110)) has a greater change, besides, it is found that there is a high positive correlation between colorimetric coordinate 1100 * and the change of lightness from 1100 to 2500lx (R 2 =0.859) (Fig.3b), which indicates that the lightness * of jadeite with a higher colorimetric coordinate * is more sensitive to the illuminance change. So those samples with a yellowish hue show a greater lightness change as the illuminance change (  indicating the jadeite color will be vivid as the illuminance gets higher, which is consistent with the perception that colorfulness rises as illuminance grows in rational range 33 . As shown in Fig.4 The mean hue ℎ° changes(max-min) is 3.12 which indicates jadeite color hue turns to yellow tones as the illuminance gets higher, which corresponds to the Bezold-Brücke hue shift that perceptual changes in hue when the intensity of a stimulus increases or decreases 34,35 . By comparing jadeite with different hue angle variations, the samples were divided into 3 groups. As shown in Fig.5, it shows that the sample whose hue angle ranges from 35° to 50° has a significant rise (red box), because the increase of lightness will expand the wavelength range of yellow light, thereby shifting red to yellow. The main effect of illuminance on reading the color of jadeite is to improve the lightness, chroma, and shift red to yellow, however, excessive illuminance will cause the obtained photos to be overexposed (Fig5. Yellow box) and read unreal data. Figure 6. The lightness histogram of jadeite with different hue angles under different illuminance levels. All the lightness histograms were exported from PhotoShop2020.
The yellow jadeite is dominant by the colorimetric coordinate * , so its lightness and chroma show a higher sensitiveness to the change of illuminance; combined with lightness histogram, when the illuminance reaches 2500lx and above, the lightness histogram of the yellow jadeite is occupied by the high lightness area ( Fig.6 red circle) when the histogram of red and orange jadeite shows a good uniformity, which means there is loss of color data in the yellow sample and causes the reading of unreal color. Therefore, the optimal parameters for the measurement of jadeite with different hues(red-orange-yellow) should be discussed separately.

Influence of Exposure Time (E.T)
The 14 jadeite samples were tested in 10500-13500μs (interval=500μs; 1500lx, 25cm) respectively. As shown in Fig.7(a), the lightness * of jadeite is increasing with the increase of E.T. The mean lightness change from 10500 to 13500μs is 14.11, which corresponds to the objective fact that the luminous flux of the camera is increased. Fig.7(b) shows the Chroma * gets higher as the E.T increases, the mean value of Chroma difference between 10500 and 13500μs is 8.9. By analyzing with samples(#23 and #52), the higher 10500 * and 10500 * (the Chroma and Lightness in initial E.T value) it is, the more * and * will be. The E.T have little influence on the Hue ℎ° of samples, with a mean change ℎ°− ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ =1.37, those jadeites with lower hue angle show a relatively greater sensitiveness than those higher (Fig.7(c)). According to the similar trend of * * ℎ° caused by illuminance and exposure time, the interactive influence between them is considered in the orthogonal experiment subsequently. Since the size and shape of jadeite in the market are very variable, the stability of the color measurement test can be simulated by changing the measurement distance. According to the results, it can be found that the digital image system can provide good stability under the set lighting and background conditions.
Optimal Parameter for Jadeite-red by DIS Six red jadeites from the tested samples were chosen for this chapter. According to the pre-test shown in Fig.8, three levels for each factor were selected for the subsequent orthogonal experiment. The color difference was used here to measure the degree of applicability of the combination of test parameters，the smaller the 00 ̅̅̅̅̅̅̅̅ , the better the combination. Figure 8. The pre-test result for the orthogonal design, which shows the selected 3 levels for each factor with a black box. 00 is the color difference between data from DIS and date from photo calibration calculated by equation (9). The box is the range for the subsequent Orthogonal Design, the reason for the selected levels is based Where m represents the number of levels.
According to the sum of square deviations of each factor , the statistic value can be calculated as: Note: Compare the F value with the F distribution. If F is greater than F0.01 (2,6), the result is very significant (***), greater than F0.05(2,6) is significant (**), greater than F0.10(2,6) represents to have some influence, otherwise deemed to have no significant impact. the k 2 level is the best; the effect of exposure time is significant, and the result shows that the k 3 level is the best; the effect of measurement distance is not obvious, and the level with the lowest color difference k1 can still be selected for the result; the interaction between illuminance and exposure time is not obvious, according to the analysis of the interactive influence, it is found that the A2B3 combination is the best level (Table 3), which corresponds to 1600lx, 12500ms; finally, the optimal parameter level combination for the red jadeite color reading by the DIS is 1600lx, 12,500ms, and 25cm. In the future, more test samples can be added to modify the optimized measurement conditions, and based on this basis, measurement parameters can be obtained for other colors of jadeite.

Conclusion
DIS is a non-contact color measurement system that could help researchers better study unevenly distributed colored gems. The system includes circumstance factors such as light source intensity (illuminance), exposure time, measurement distance, etc., which will affect the color reading of jadeite.
Under the single factor experiment method:1. The influence of illuminance is mainly to improve the lightness and chroma of jadeite, those with a higher hue angle are more sensitive to changes in illuminance, and others with a lower hue angle will shift to yellow. 2. The effect of exposure time is mainly to increase the luminous flux, thereby improving the lightness and chroma of jadeite, and the overall change trend is consistent with the change in illuminance; 3. The DIS shows good stability on the change of measurement distance, which is used to simulate the measurement on jadeites with different sizes and shapes.
Based on the results of single-factor experiments, a three factors three levels orthogonal experiment with two interactive effects was designed. The order of the degree of influence obtained by range analysis and ANOVA is illuminance, exposure time, measurement distance (from high to low).
Combined with the result, the optimal color measurement parameters of jadeite-red for DIS are 1600lx, 12500ms, 25cm; this provides a new case and theoretical support for the future application of DIS on reading the color of gemstones and the establishment of a gem-color database.

Color Space
The CIE (International Commission de l'Éclairage) 1976 * * * uniform color space has been widely used in the color evaluation of various colored gemstones; compared to the CIE1931 color space, the geometric distance between two given colors is inconsistent with human visual perception 36 .
CIE1976 * * * uniform color space has two advantages: (1) good color uniformity and (2) conform to the subjective law that the visual color difference in the yellow-blue direction is bigger than that in the red-green direction. This color system comprises color coordinates * , * and Lightness * . Chroma * and Hue angle ℎ° can be calculated based on * and * : Color Difference Formula To explore the optimal parameter combination of the Digital Image System (DIS) for measuring jadeite, this paper chooses the CIE DE2000 formula to analyze the results of the measured samples. The DE2000 formula is experimentally obtained based on the color difference formulas such as CIE LAB and CIE 94, which is more accurate and more computational: where Δ ′ , Δ ′ , Δ ′ represent the difference in lightness, chroma, and hue angle respectively (between the DIS data and photo calibrated data). The weight functions S L , S C , and S H are used to calibrate the uniformity of the color space, and the function is used to correct the deflection of the color tolerance ellipse in the blue area; the Parameters , , are to correct the experimental conditions, in gemology, where the parameter combination is usually set as (1:1:1) to provide better perceptibility.
The color difference is calculated at the "colortell.com" (developed by ColorTell Tech CO., LTD, Beijing, China) color management website by importing digital imaging system data (samples) and calibrated photo data (standards), after which the color data is calculated by the equation (9).

Digital Imaging System (DIS)
The color of jadeite was measured by the Digital imaging system under the same Munsell N7 background (Fig.9). The images were captured by using a Mako G-507C industrial camera (Allied Vision Technologies, Stadtroda, Germany) equipped with a CMOS-type Sony  All the jadeite samples were well polished and showed a high quality "glassy luster" because of their high refractive index (1.66). To prevent the influence of surface reflection on color measurement, we excluded the reflective areas from the color reading, selected three uniformly colored locations in the measuring area, measured the color, and took the average value as the test result (Fig.10). Some samples containing black or white mineral inclusions were excluded from the measuring area.
Figure10. The reflective area with strong reflection and inclusion in the measuring area should be avoided during the color reading process.

Photograph Calibration
The Nikon Z5 (Nikon, Tokyo, Japan) equipped with a CMOS-type sensor is used to take photos of X-rite Color Checker Passport (X-rite, Shanghai, China Fig.11) (Fig.11) and jadeite samples under the standard D65 light source, and all the samples are placed at the Munsell N7 neutral grey background.
X-rite Color Checker Passport contains a set of three-Color Checker photography targets 37 , a desktop camera calibration application, and an Adobe Photoshop Lightroom camera calibration plug-in to create a DNG profile that reflects specific camera, lens, and lighting conditions to process the calibration of the RAW photo and restore the true color of the jadeite. Each photo was processed in Photoshop 2020, using the established environment DNG feature file for correction (Fig.12), operation steps as follow: 1. Take the picture of ColorChecker and samples under the set circumstance, the output format is RAW.
2. Import the picture including ColorChecker into "ColorChecker Camera Calibration" (developed by X-rite, Shanghai, China) to create a DNG profile.
3. Open picture of samples through Photoshop2020, then set the DNG profile as the configuration file. Figure 11. X-rite Colorchecker passport

Funding
This research received no external funding.