Optimal spatial resolution in vision-based inspetion of pipes using Catadioptric sensors

Spatial resolution of imaging systems plays a major role in the design of vision-based industrial inspection systems. In this paper we formulate the cylindrical spatial resolution of a Catadioptric sensor that consists of a camera and a hyperbolic mirror for the pipe inspection applications based on the projection models cited in the literature. A laser ring is used as a structured light source for illumination. Also we provide a guideline for selecting the optimal configuration setup, subjected to the changes in the focal length of the perspective pin-hole camera and also the shape of the hyperbolic mirror, that yields highest inspection resolution.