# Design and Calibration of a Single-Lens Telecentric Four-Camera Array Based on Planar Mirrors and Its Application in Strain Measurement

## TL;DR

This paper introduces a new camera system for accurately measuring strain in aircraft hydraulic pipelines, overcoming imaging limitations with a telecentric design.

## Contribution

A novel virtual telecentric camera array using planar mirrors and a dedicated calibration strategy for non-overlapping fields of view.

## Key findings

- The telecentric system outperforms traditional pinhole models in reprojection errors and scale accuracy.
- Experimental results show high agreement with strain gauge data, validating the system's effectiveness.
- The system effectively reduces parallax errors for micro-scale deformation monitoring.

## Abstract

As the primary power transmission conduits, aircraft hydraulic pipelines are critical for actuating flight control surfaces and landing gear systems. Accurate in situ strain evaluation of these pipelines is essential, as installation-induced pre-loads directly compromise fatigue life and sealing performance, threatening overall system reliability. However, such evaluation is frequently hindered by the perspective distortions and limited depth of field inherent in conventional imaging systems. To overcome these metrological limitations, this study presents a novel virtual telecentric camera array system designed for high-precision, non-contact strain measurement. Unlike traditional pinhole models, the proposed system leverages a catadioptric setup with planar mirrors to create a virtual four-eye telecentric array from a single physical lens, ensuring constant magnification within the depth of field. A comprehensive simulation framework was established to rigorously compare the reprojection errors and scale accuracies between telecentric and pinhole projection models, quantitatively demonstrating the superior stability of the telecentric approach. Furthermore, a dedicated calibration strategy for non-overlapping telecentric fields of view was developed and validated. Experimental results from pipeline installation tests indicate a high concordance with strain gauge data, confirming that the proposed telecentric system effectively mitigates parallax errors and provides a robust solution for static and quasi-static micro-scale deformation monitoring in complex assembly environments.