Transparent surface orientation from polarization imaging using vector operation

The existing methods for shape measurement using polarization of transparent objects are based on two assumptions: (1) the paraxial assumption, assuming that the reflected ray is parallel to the optical axis of the imaging system; and (2) the s-component approximation assumption, which assumes that the s-component of the reflected light is predominant and the p-component is neglected. To overcome limitations posed by these two assumptions, this paper proposes a method based on the polarization characteristics of reflection from a transparent surface and vector operation. To overcome the paraxial assumption, the normal vector of the transparent surface is deduced by vector operation, analyzing the relationships between the direction vector of reflection, the normal vector of the reflection plane, the intersection line of the reflection plane and imaging plane, and the normal vector of the transparent surface. To overcome the limitations of the s-component approximation assumption, the angle between the s-component and the polarization direction of the reflected light is analyzed, which yields improved measurement precision. An experiment was performed with transparent targets (flat glass positioned at different angles), and the results show that the measurement error with this method is significantly less than those of existing methods. Thus, we believe this method overcomes the abovementioned limitations while also improving measurement precision.