To conform to the widening of head-mounted displays, stereoscopic optical systems require a high resolution of at least 4 K, and a field of view of at least 120°. However, the dimensions of the large-format cameras used to record high-quality content mean an appropriate stereo base cannot be achieved. Moreover, the wide angle of view prevents the use of a half-mirror rig to reduce the stereo base. Therefore, this study presents a solution where the stereo base is reduced using ultrashort throw lenses with a catadioptric relay in which the pupil is formed on the object side. Hence, a basic design for a wide-angle stereoscopic system with a half-field angle of ~126° and a stereo base of 62 mm is proposed.
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.
In the past two decades, to realize high resolutions and low distortions while miniaturizing optical systems, various ultrashort throw lenses (USTs) have been proposed. In this work, ultrashort throw lenses with a catadioptric relay (USTCRs) with rotational symmetry are proposed to provide the solution. First, the initial design method of the USTCR and the optimized design solution are presented. Although this optical system with a throw ratio of 0.26:1 has resolutions and distortions equivalent to those of conventional UST with one aspherical mirror, the depth of focus (DOF) on the panel side becomes 1.31 times deeper with appropriate corrections of the field curvature. The total length of the lens is reduced to 0.89 times, the area of the main mirror is reduced to 0.22 times, and the number of lenses is reduced from 13 to 9 elements. Based on these results, several optical designs for USTCR have been tried and an optical design with robustness has been proposed. By optimizing the power of each lens group, the decenter sensitivity improved to 0.46 times for parallel decenter and 0.55 times for tilt decenter. By optimizing glass materials, the shift of focal plane can be suppressed to 0.56 times when the temperature increases by 30 °C. An USTCR suited for a curved screen has also been proposed. By introducing appropriate constraints that correct distortions, high resolutions and low distortions have been realized while maintaining a wide angle of view. USTCRs suited for various curved screens are currently underway.
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