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

## TL;DR

A new interferometric method is introduced to accurately measure cylindrical surfaces by reconstructing misalignment errors using a single-direction partial derivative.

## Contribution

The method eliminates the need for complex matrix operations and model matching in reconstructing misalignment aberrations.

## Key findings

- Misalignment aberrations can be reconstructed using only the partial derivative in one direction.
- The proposed method achieves high-precision recovery of cylindrical surfaces with PV and RMS values comparable to null testing.
- The method's repeatability is better than λ/1000 RMS.

## Abstract

What are the main findings?
A novel non-null interferometric measurement method for cylindrical surfaces with complex parameters is presented.Misalignment aberrations can be reconstructed using only the partial derivative in one direction.

A novel non-null interferometric measurement method for cylindrical surfaces with complex parameters is presented.

Misalignment aberrations can be reconstructed using only the partial derivative in one direction.

What are the implications of the main findings?
Various wavefront errors and the impact of other optics are eliminated in measurements.The reconstruction of misalignment aberrations does not require complex matrix operations or model matching.

Various wavefront errors and the impact of other optics are eliminated in measurements.

The reconstruction of misalignment aberrations does not require complex matrix operations or model matching.

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.