## 2 Experimental
### Experimental Methods  
Laser processing method: For color gamut exploration and image color reproduction, we used the double scanning method [20] to process the samples as shown in Figure 1b. The processing was carried out in the first scan using a 45-degree angle scanning process, where the first processed sample was used as a substrate for subsequent laser-induced coloring, and the actual laser-induced coloring was produced by the second scan. The purpose of this experiment was to explore the color gamut of stainless steel undergoing laser-induced coloring; therefore, in this paper, a point-by-point scanning coloring method was used to process the substrate to ensure that the colors formed on the substrate surface were independent and reliable. As shown in Figure 1b, the laser processing were independent from point to point, and the resulting colors were also independent. Color calculation method: In this paper, we used the CIELAB color space to quantitatively calculate the color parameters. The CIELAB color space is a three-dimensional uniform color space, where \(L\) represents the luminance, ranging from 0 to 100; \(a\) represents the spectrum from red to green; and \(b\) represents the spectrum from blue to yellow. \(a\) and  
Figure 1: (**a**) Schematic diagram of laser-induced metal surface coloring device. (**b**) Illustration of the laser double-scan method. take values in the range of \(-128\) to +127. Considering that the CIELAB color space cannot express the size of the color gamut directly, the CIE 1931 color coordinates are used to express the color gamut. For the calculation of the maximum color gamut, we adopted the CIE 1931 color coordinates to quantitatively measure the size of the color gamut of the current marking samples; mapped the color parameters of each sample to the chromaticity diagram; and converted the measured values of \(L\), \(a\), and \(b\) to the x and y values of CIE 1931 color coordinates. The conversion equation is as follows:  
(1) Convert CIELAB color space to CIEXYZ color space:  
\[X=X_{n}*f\bigg{(}\frac{L}{116}+\frac{a}{500}\bigg{)} \tag{1}\]  
\(X_{n}\) is the \(X\) coordinate of the reference white point in the CIEXYZ color space, and for measurements taken under a D65 standard light source, the value of \(X_{n}\) is 0.95047. \(f\) is a custom function, \(f(t)=t^{1/3}\) when \(t>\left(\frac{6}{9}\right)^{3}\) and \(f(t)=\left(\frac{29}{6}\right)^{2}*t+\frac{4}{29}\) when \(t\leq\left(\frac{6}{9}\right)^{3}\). \[Y=Y_{n}*\left(\frac{L}{116}\right)^{3}\ \ \ \left(L>\left(\frac{6}{29}\right)^{3}\right) \tag{2}\]  
\[Y=Y_{n}*\left(\frac{L}{116}+\frac{16}{116}\right)\ \ \ \left(L\leq\left(\frac{6}{29} \right)^{3}\right) \tag{3}\]  
\(Y_{n}\) is the \(Y\) coordinate of the reference white point in the CIEXYZ color space; for measurements taken under a standard D65 light source, the value of \(Y_{n}\) is 1.00000. \[Z=Z_{n}*f\bigg{(}\frac{L}{116}-\frac{b}{200}\bigg{)} \tag{4}\]  
\(Z_{n}\) is the \(Z\) coordinate of the reference white point in the CIEXYZ color space; for measurements taken under a D65 standard light source, the value of \(Z_{n}\) is 1.08883. (2) Convert CIEXYZ color space to CIE 1931 color coordinates:  
\[x=\frac{X}{X+Y+Z} \tag{5}\]  
\(x\) is the \(x\) coordinate in the CIE 1931 color coordinates. \[y=\frac{Y}{X+Y+Z} \tag{6}\]  
\(y\) is the \(y\) coordinate in the CIE 1931 color coordinates. Calculation method for color gamut: With the help of CIE 1931 color coordinates, the color information can be converted into position information, with different colors corresponding to different \(x\), \(y\) coordinates. Four groups of parameters for the space enclosed within the size of the graphic area are used to predict the degree of representation of the four groups of parameters on the color gamut.