Reconstruction of Misalignment Aberrations for Cylindrical Surfaces with Complex Parameters in Pseudo Lateral Shearing Interferometry

Cylindrical surfaces with complex parameters (CSCPs) have off-axis and aspheric properties. High-precision measurement of cylindrical surfaces is a key research focus in optical metrology. Two-dimensional pseudo lateral shearing interferometry (2DPLSI) enables non-null generalized interferometry for cylindrical surfaces. However, due to the non-rotational symmetry of cylindrical surfaces with complex parameters, measuring them using two-dimensional pseudo lateral shearing interferometry inevitably introduces misalignment aberrations, degrading the accuracy of cylindrical surface reconstruction. To address this issue, we propose a novel non-null testing method: the cylindrical surface is translated in the orthogonal directions to carry out the shearing process, and wavefront errors are eliminated through second-order differencing. Furthermore, a reconstruction algorithm in one direction is proposed. Using only the partial derivative in the x direction, the wavefront error of misalignment aberrations can be reconstructed, enabling high-precision recovery of the cylindrical surface. Experimental results using a Fizeau interferometer demonstrate that the proposed method effectively reconstructs misalignment aberrations. The reconstructed cylindrical surface achieves a peak-to-valley (PV) value of 0.45λ (λ = 632.8 nm) and a root-mean-square (RMS) value of 0.12λ, comparable to the 0.37λ PV and 0.09λ RMS obtained via null testing. The repeatability of the proposed method is superior to λ/1000 RMS.