The propagation of light in turbid media is affected by the optical parameters of the media including absorption coefficient (μ_a), scattering coefficient (μ_s), isotropic coefficient (g), and refractive index (n). These optical parameters are related to the chemical properties, the internal structures, the physical properties of the media, and the boundary difference and speed of light transmission, including the shape, size, and concentration of different scattering components in the turbid media. By measuring the optical parameters of the turbid media, the material properties, physiological states and pathological changes can be determined, which is very important in various applications including biomedical diagnosis and food safety inspection. However, there is a lack of algorithms that can be simultaneously used to identify these four parameters (μ_a,μ_s,g, and n) because the measurement instruments cannot be easily installed. To solve this problem, a method based on a residual neural network is proposed here to determine the four parameters of the turbid media from the diffuse reflection light intensity profiles.

First, the diffuse reflection light intensity profiles under different incident excitation light angles are obtained through the Monte Carlo simulation. The incident light spot diameter and the divergence angle are considered in the simulation process. Second, the diffuse light intensities excited under multiple angles are used to enhance the information richness. Third, a residual neural network is used to establish the machine learning mapping model between the diffuse light intensity profiles and the optical parameters of the turbid media, and the prediction of optical parameters is realized. The extracted light intensity values along the long axis are used as the input of the residual neural network, and the output is the optical parameters. Before training and testing, noise is added to the diffuse reflection data in order to simulate the optical measurements under real conditions. The input data is normalized to ensure the consistency of data range and make the network converge quickly.

In the Monte Carlo simulation, different incident angles are initialized. Seven incident angles ( 24°, 30°, 36°, 42°, 48°, 54°, and 60° ) are applied in this work (Fig. 4). The position projected by each photon on the medium surface is initialized as (x′, y′, z′) and the photon directional cosine is set as (μ_x,μ_y,-μ_z). The diffuse light intensity profiles under different excitation light angles are validated to be linearly independent (Fig. 6). Thus they may provide extra effective independent constraints for the estimation of the four optical parameters. The concept of using more diffuse reflection light intensity profiles to enhance data richness is further proved by the full rank of diffuse reflective light intensity vectors along the long axis. The relative error decreases with the increase of the number of diffuse reflection light intensity profiles used here (Fig. 7). When only the diffuse reflection light intensity at one angle is used to identify the optical parameters of the media, the errors can be several times larger than those when the 7 sets of diffuse reflection light intensity profiles are used. The recognition errors of the four optical parameters have little change when the SNR is changed in the range of 40 dB-80 dB. The results show that the prediction errors for the four optical parameters (μ_a,μ_s,g, and n) are 8.6%, 4.6%, 1.7%, and 0.9%, respectively, when the noise level is 40 dB. Compared with the existing prediction methods, the proposed residual neural network method has high prediction accuracy and short computation time.

A method based on a residual neural network is proposed to estimate the anisotropic coefficient, absorption coefficient, scattering coefficient, and refractive index of a turbid medium. The diffuse light intensities excited under multiple angles are proved to be effective for enhancing the information richness and improving the estimation accuracy of optical parameters. The incident light spot diameter and the divergence angle are considered, and the different levels of noise are added to the diffuse light intensity signals and the generalization ability and anti-noise performance of the network are improved. The results show that the proposed method can estimate the anisotropic coefficient, absorption coefficient, scattering coefficient, and refractive index of the turbid medium accurately with a high noise level and a high efficiency. The diffuse light intensities under seven angels are enough for the determination of the four optical parameters. This work is expected to be useful for various applications including biomedical diagnosis, food safety inspection, and material property detection.