Cylindrical surfaces with complex parameters (CSCP), including off-axis, aspheric, and other properties, constitute fundamental components within complex optical systems. Two-dimensional pseudo lateral shearing interferometry (2DPLSI) is a non-null and generalized method for CSCP. It can eliminate wavefront error of components within systematic and retrace error, thereby achieving high-precision measurement. However, the accuracy of measurement is influenced by factors such as the parameters of the measurement system, rendering the analysis of measurement precision of 2DPLSI to be important. The sources of error in 2DPLSI are discussed in this paper; their effects are simulated using the Monte Carlo (MC) method. Furthermore, a wavefront construction method based on power spectral density (PSD) is proposed, which simulates actual wavefronts more effectively. In addition, experiments are conducted to validate the optimized measurement system parameters derived from the simulation results. Experimental results show that the optimized measurement system parameters effectively improve measurement accuracy, retain low-mid spatial frequency information of wavefront, and eliminate the influence of gridding artifacts.

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.