Systematic framework for the optimization and validation of a compact optical system using commercial off-the-shelf...

This study presents and validates a systematic design framework for developing high-performance, low-magnification, compact optical systems composed of commercial off-the-shelf (COTS) components, specifically tailored for industrial applications under stringent spatial constraints. The efficacy of this methodology is demonstrated through the development of a machine vision system for the precision alignment of semiconductor probe cards. The design process is initiated by selecting the Cooke triplet as the foundational architecture, a fundamental anastigmatic structure capable of simultaneously correcting all primary aberrations. Subsequently, through a simulation-driven iterative optimization process, supplementary COTS lenses are strategically incorporated to achieve demanding performance specifications while adhering to a compact total track length of less than 50 mm. A rigorous tolerance analysis was performed to ensure the manufacturability of the design and to forecast the production yield. Following the finalization of the optical design, the corresponding optomechanical components were developed, and a prototype was assembled. The performance of the prototype was experimentally validated using a series of metrological standards, including a microscope stage micrometer, a USAF 1951 resolution test chart, and a grid distortion target. The empirical results exhibit a high degree of correlation with the predictions from a comprehensive system model that incorporates sensor effects, thereby validating the efficacy and predictive fidelity of the proposed framework. This methodology offers a robust and efficient pathway for creating high-performance, cost-effective optical solutions within spatially constrained industrial environments.