# Accurate Lens-Distortion Measurement Through Detector Nyquist Sampling

## TL;DR

This paper introduces a new method for accurately measuring lens distortion using detector Nyquist sampling, achieving high precision and repeatability.

## Contribution

A novel lens distortion measurement method using Nyquist sampling and phase-shift algorithms for high-precision industrial imaging lens evaluation.

## Key findings

- The method achieved a magnification deviation factor repeatability accuracy of ±108 nm/cm.
- Third-order distortion-measurement accuracy reached ±108 nm/cm³.
- The method enables high-resolution and high-precision full-field distortion measurements.

## Abstract

What are the main findings?
The method enables fast acquisition, high-resolution, and high-precision full-field distortion measurements.This method achieved a magnification deviation factor repeatability accuracy of approximately ±108 nm/cm and third-order distortion-measurement accuracy of approximately ±108 nm/cm3.

The method enables fast acquisition, high-resolution, and high-precision full-field distortion measurements.

This method achieved a magnification deviation factor repeatability accuracy of approximately ±108 nm/cm and third-order distortion-measurement accuracy of approximately ±108 nm/cm3.

What are the implications of the main findings?
This approach enables a high-precision distortion evaluation for conventional industrial imaging lenses.The derived imaging-magnification factor facilitates a more accurate determination of the focal-plane position of the lens.

This approach enables a high-precision distortion evaluation for conventional industrial imaging lenses.

The derived imaging-magnification factor facilitates a more accurate determination of the focal-plane position of the lens.

Distortion is a key parameter affecting the imaging performance of lenses. In this study, we propose a testing method based on detector Nyquist sampling of image data to achieve high-precision measurements of the distortion distribution of lenses. The distribution patterns of distortions in horizontal and vertical directions can be obtained by analyzing the distribution patterns of Moiré fringes in images under Nyquist sampling conditions and using phase-shift algorithms. The distortion-distribution characteristics of the lens are then calculated using distortion formulas. This method is characterized by high testing accuracy and sampling resolution. The image-plane distortion distribution exhibited a consistent linear trend when the object-plane position varied within a limited spatial range. Furthermore, the proposed method achieved a magnification deviation factor repeatability accuracy of approximately ±108 nm/cm and third-order distortion-measurement accuracy of approximately ±108 nm/cm3. This method enables a high-precision distortion evaluation of conventional industrial imaging lenses.