Sub-Nyquist sampling rate temporal correlation method for measuring the surface of the transparent planar element

When deflectometry is applied to measure transparent planar elements, parasitic reflection from the back surface can introduce errors in the reconstruction result. Traditional frequency-domain methods typically require over thousands of fringe patterns to satisfy the Nyquist sampling law, which allows for the separation of parasitic reflection. Failure to meet the requirement of the sampling rate can lead to accuracy decrease of the screen coordinate extracted by the frequency-domain method, deteriorating the accuracy of surface reconstruction. To address this issue, this paper proposes a sub-Nyquist sampling rate temporal correlation method. By using less than five hundred fringe patterns, this method effectively reconstructs the front surface of the transparent element with sub-Nyquist sampling rate. The proposed method achieves an RMS surface error of 113 nm. Compared with Wang's method requiring 1000 seconds (16.67 minutes), while the proposed method only requires 205 seconds (3.42 minutes), saving 13.25 minutes.