# Parameter Optimization Method for Metal Surface pBRDF Model Based on Improved Strawberry Algorithm
## 1 Introduction  
Polarization is a fundamental property of light [1]. Using the polarization characteristics of reflected light from the target surface, the multi-dimensional optical information of the target can be estimated, and the accuracy of target recognition and characterization features can be significantly improved [2]. It has become a hot topic in remote sensing [3], industrial production [4], biomedical [5] and other fields. Among the most common materials in industrial production, metal is often used for various equipment and instruments. So, it is of great theoretical and practical significance to study the polarization reflection characteristics of metal surfaces. The bidirectional reflectance distribution function (BRDF) describes specular and diffuse reflection from a target surface, which is usually described by establishing mathematical models, such as T-S [6], Phong [7], Maxwell Bear [8], C-T [9] models, etc. However, BRDF only reflects the intensity distribution of reflected light. In order to better present the valuable target information about the material features and the responding physical and chemical properties, polarization characteristics have been integrated into BRDF, and the polarization bidirectional reflection distribution function (pBRDF) has been proposed. For example, [PERSON] et al. proposed that combining BRDF with a Muller matrix based on the T-S model provided a complete definition and corresponding application solution, while the difference between model calculations and experimental results seems slightly large [10]. From then, many improved pBRDF models have been proposed by supplementing or modifying the shadowing function, microfacet distribution and reflection component separation. [PERSON] et al. established an improved pBRDF model by introducing a diffuse component into the reflecting part to retrieve metal characteristic parameters with better accuracy, while the impact of multiple reflections was not considered [11]. To solve this issue, [PERSON] et al. comprehensively investigated the shadowing effect and diffuse reflection on a target surface and used the Minnaert model to characterize the diffuse component, proposing a six-parameter pBRDF model, by which the fitting accuracy is further improved [12]. From a deeper analysis of the above-mentioned pBRDF, it can be seen that the traditional methods mainly start from a model whose parameters are usually retrieved with a least squares method. For example, [PERSON] et al. proposed a four-parameter pBRDF model whose parameters were retrieved just using least squares, by which the real and imaginary parts of the effective refractive index, grazing incidence absorption and angular scattering were obtained [13]. [PERSON] et al. used the least square method to retrieve the real and imaginary parts of the target surface refractive index, as well as the surface slope parameters [14]. However, these methods did not pay enough attention to the possible influence of extreme points and missing data values on the retrieved model parameters. So, [PERSON] et al. improved the model and proposed a pBRDF hybrid model based on the microfacet theory and obtained key model parameters from the experimental data by a genetic algorithm; the extraction ability for target polarization features was enhanced [15]. Meanwhile, [PERSON] proposed a five-parameter model through a hybrid particle swarm genetic parameter optimization algorithm, by which the fitting accuracy and convergence speed were significantly improved compared to the genetic or particle swarm algorithm under the same conditions [16]. The above-mentioned algorithms not only obtained good local search ability but also improved global search capacity in the parameter retrieval process, though the retrieval results still depend on the initial selected values to a large extent, which is prone to falling into local optimal solutions for multi-dimensional problems.