Measurement of the Muller matrix for painted surfaces with a kind of scatterometer

Abstract

The polarized light scattered by the surface of a material contains information that can be used to describe the properties of the surfaces. Polarized Bidirectional Reflectance Distribution Function (BRDF) is one of the most important factors used to represent the property of the surface. It uses a 4×4 matrix (Mueller matrix) to describe the properties of the light scattered from the surface. In order to measure the Mueller matrix of the samples, a new three axis automated scatterometer has been developed to measure the Mueller matrix of painted surfaces. It can do measurement at any illumination and viewing geometric of the hemisphere and it is more convenient for far-field measurement is presented. The design of the instrument is different to the traditional scatterometer. The significant characteristic of the instrument is that the detector and polarization analyzer are fixed, while the source and the incident optical elements rotate on a stage together. All the possible incident and viewing positions can be reached through the rotation of three motors. The rotations of the motors are fed back through photoelectric- encoders, the "closed loop" control mode ensured the precision of the position. Through coordinate transformations, the measurement in three dimensions can be simplified in two dimensional form, the details of the coordinate transformations will be described in detail in this paper. The dualrotating retarders method is used to modulate polarizing and analyzing optics. Two retarders rotate synchronously at angular speed and respectively. For every position, 16 measurements were done, and the Discrete Fourier Transform (DFT) method is used to retrieve the Mueller matrix of the sample. Discrete Fourier Transform (DFT) method is used to retrieve the Mueller matrix of the sample. The results of out-plane polarized bidirectional reflectance distribution function for samples coated with different paints are presented.