Optimal Design of Omnidirectional Vision System Using Two Mirrors

Abstract

This paper presents an optimal design method with some design examples of the omnidirectional vision system using two curved mirrors, primary and secondary, which was previously proposed and developed by the authors. In the design method, the bore size and position of the primary mirror and the coefficients included in the profile equation of the secondary mirror are chosen as the design parameters.By adjusting the design parameters so as to minimize the performance index representing the sharpness of a panoramic image on the secondary mirror, the arrangement and the shape of the mirrors can be designed so as to realize an omnidirectional vision system with higher image quality. Taking a paraboloid and other shapes as the surface shape of the secondary mirror in the design calculations, optimal designs were made for each catoptric system for each surface shape, and the degrees of aberration on the secondary mirror were evaluated.The results show that the use of an ellipsoid is the best for minimizing the opti-axial range of the image points, the use of a hyperboloid is the best for minimizing the degree of astigmatism and the use of a biquadratic surface is not only efficient for minimizing of both case described above but also provides almost same results as the best results of both case. It is also shown that the degree of aberration obtained by the optimal design strongly depends on the values of the weighting coefficients included in the performance index.