Analysis of the optical center position of an optical system of a camera lens

Abstract

A theory of an optical center of a camera lens is described. The concept of an optical center (a camera center) is used widely in various methods dedicated to the calibration of optical imaging and measuring systems in photogrammetry, computer vision, triangulation sensors, fringe projection techniques, surveying, and machine vision, where the so-called pinhole camera model is used as the camera's basic model. It is shown that the optical center of the optical system with a fixed position does not exist generally, even for an ideal optical system. The optical center can be defined unambiguously for an ideal lens only for one specific object distance in general. Moreover, equations are derived for the calculation of initial design parameters of the three-element optical system composed of thin lens elements having the identical position of object and image principal planes. Such optical systems will have a fixed-position optical center, which does not depend on the object distance. The analysis was presented on several examples of the calculation of parameters of these optical systems.

3D reconstruction method of defocused images based on optical system analysis

“…As a simplified approximate model, pinhole camera model simply and effectively provides the projection between object and image. However, some studies [3] indicated the error of this approximation in defocused image. Modeling according to the ideal optical system is a more accurate approximation of the camera imaging process.…”

“…Mikš and Novák [3] analyzed the ideal optical system of the camera and calculated the difference between the optical center coordinates of the central projection system and the ideal optical system. Bothe et al [4] built the vision ray calibration (VRC), which directly modeled the optical system as a black box, tracing each pixel individually, providing a more accurate calibration method in the optical caustic environment.…”

Projector undistortion for high-accuracy fringe projection profilometry

“…Many projectors are designed to project off-axis and their principal points are often outside imaging planes. As a result, residual distortion is usually observed [20,21], despite the use of depth-dependent pinhole models [22]. For example, Yang et al [9] compensates residual distortion using a calibrated lookup table.…”