## 1 Introduction  
Laser-induced coloring of metal surfaces is one of the hot topics in current research in the field of lasers, and how to find the color gamut of material quickly and efficiently is a difficult problem for color reproduction. In color reproduction work, we expect to obtain high-saturation color and a large color gamut in materials to achieve reproduction work. It is meaningful to quickly and efficiently find the color gamut that materials can achieve through color gamut exploration. Laser-induced coloring of metal surfaces is widely used in the field of laser-induced coloring because of its advantages such as high speed, good flexibility, and high accuracy [1, 2, 3, 4, 5]. In the existing studies, laser-induced coloring has been widely applied to stainless steel, titanium alloys, pure titanium, gold, silver, aluminum, and metal oxide film surfaces to form many unique colors. Due to the structured colors' advantages of high corrosion resistance, durability, and erasable rewritability [6], they have been widely used in decoration [7; 8], printing [7], new types of displays [9], and high-precision anti-counterfeiting [10]. It has been shown that laser coloring of metal surfaces can be achieved by laser-induced plasma metal coloring, laser-induced thin-film interference effects from oxide layers, and laser-induced periodic surface structures (LIPSS) [1; 11; 4; 12]. Among them, pulsed lasers can induce the formation of micro-nanostructures on metal surfaces, such that light of different wavelengths interferes, diffuses, or scatters in the micro-nanostructures to produce structural colors [13]. Laser pulses with different parameters can form different micro-nanostructures on the surface of different materials, resulting in different structural colors. By controlling the intensity of the laser, the surface state of the material can be controlled, thus achieving a designable material surface [14; 15; 16]. Laser induction forms a mixed oxide layer of Cr\({}_{2}\)O\({}_{3}\), FeCr\({}_{2}\)O\({}_{4}\), Fe\({}_{2}\)O\({}_{3}\), and NiO on the surface of 304 stainless steel, resulting in the formation of a large number of unique microstructures on the surface of that metal [17; 18; 19]. Light interferes with these microstructures in the oxide film, accompanied by optical effects such as scattering and reflection, producing unique colors. On the surface of titanium and titanium alloys, lasers with different parameters induce the formation of Ti oxide layers with different thicknesses and compositions of Ti, TiO\({}_{2}\), Ti\({}_{2}\)O\({}_{3}\), and Ti\({}_{3}\)O\({}_{5}\), thereby inducing interference effects of light and producing unique structural colors [6; 20; 21; 22]. The thin-film interference effect produced by laser-induced oxidation layers has shown great potential in the field of inkless printing, with the advantages of low cost, wide application areas, and rapidity. The color samples of the oxide layer formed by laser-induced formation on the surface of stainless steel, titanium, and titanium alloys using nanosecond lasers have a wide color gamut, strong UV resistance, and corrosion resistance and have been widely used in scientific research and industry. Studies have shown that laser coloring on metal surfaces is mainly affected by parameters such as scanning speed, frequency, power, and scanning interval [6; 23; 24], and how to quickly and efficiently produce highly saturated colors and explore the color gamut of the material becomes a multi-parameter optimization problem. Regarding the influence of these parameters on the coloring of metal surface, the traditional way of research adopts the idea of the matrix method to combine the parameters, and the matrix combination is used to carry out the research on the influence of parameters on metal coloring and to search for more and better colors on the material [14; 15; 25; 26; 27], which represents the idea of most researchers.