An ultrashort throw lens with a catadioptric relay (USTCR) for curved screens has a half-field angle greater than 110°. The angle of the principal ray incident on the aspherical mirror increases according to the height of the ray emitted from the object surface. A larger field angle leads to larger sag amount. Thus, the degree of difficulty in precision machining increases. In this study, we examined how the tangent of the concave mirror surface can be reduced such that it can be manufactured while maintaining the half-field angle and its optical performance. It was found that the interval between imaging points reaching the screen can be made constant by suppressing the change in the principal ray incident on the concave mirror by +/- 1° or less, particularly in the area of a half-field angle of 90° or more, and making the change in the tangent of the concave mirror surface constant. As an index of distortion, we show that the perimeter ratio (Pr) of the frame length, which was equally divided by 5×5 in the screen, improved from 0.26 to 0.73. As one possible application, a projection system that can be realized with only 8 projectors is proposed, as opposed to conventional systems consisting of approximately 20 projectors in omni-directional projection systems.
