A Single-Pixel Imaging Based Stereo Deflectometry for 3D Reconstruction of Free-Form Transparent Objects With Parasitic Reflections

Deflectometry with structured light for high-precision measurement of optical specular surfaces has attracted considerable attention. However, conventional deflectometry schemes often encounter challenges when they deal with lens-like transparent objects due to parasitic reflections arising from the rear side of objects. To address this issue, we propose a novel stereo deflectometry method that replaces traditional phase-shift patterns with Fourier-based patterns inspired by single-pixel imaging. This method enables the acquisition of Fourier spectra of light response coefficients for each camera pixel. Specifically, through inverse discrete Fourier transform and the Fourier slice theorem, we obtain the light response coefficients of the light source to the camera pixel. Subsequently, a geometry optical analysis method is proposed to separate the light response coefficients components associated with the front surface given the lack of epipolar constraint between the camera and LCD screen. An iterative algorithm integrated with Particle swarm optimization is proposed to accelerate the reconstruction process and obtain the surface normal field of the upper surface of the lens-like transparent object. The wavefront reconstruction algorithm for gradient integration is used on the normal vector field to enables high-precision reconstruction of the object's surface shape. Experiments on actual optical components demonstrate that the proposed method can accurately reconstruct the front surface of transparent lens by eliminating the interference from parasitic reflection, and an error of less than 200 nm is obtained.