Holography is an ideal three-dimensional (3D) image generation technique. However, conventional holographic displays require ultra-high resolution spatial light modulators (SLMs) to provide a large screen size and a large viewing zone. We have developed the viewing-zone scanning holographic displays employing MEMS SLMs, which enlarge the screen size and the viewing zone by use of the high frame-rate image generation by the MEMS SLMs [Opt. Express, vol. 22, 24713 (2014)]. The multi-channel system has also been developed for the scalable enlargement of the screen size; the two-channel system with a screen size of 7.4 in. and a viewing zone angle of 43º was demonstrated [Opt. Express, vol. 24, 18772 (2016)]. In this study, the hologram calculation technique for the viewing-zone scanning system is explained and the fast calculation technique is proposed.
The viewing-zone scanning system is briefly explained. It consists of a MEMS SLM, a magnifying imaging system, and a horizontal scanner. The MEMS SLM generates hologram patterns at a high frame-rate. The generated hologram patterns are enlarged by the magnifying imaging system to increase the screen size. The magnifying imaging system also converges light to generate a viewing zone. Because the pixel pitch is enlarged, the width of the viewing zone is reduced. The reduced viewing zone is then scanned by the horizontal scanner to enlarge the viewing zone.
The hologram calculation technique is explained. The viewing-zone scanning system sequentially generates number of reduced viewing zones at different horizontal positions during each scan and the same number of hologram patterns are displayed by the MEMS SLM. Because the wavefront produced by each hologram pattern is converged to the corresponding reduced viewing zone, the wavefront should be the object wave subtracted by the spherical wave converging to the reduced viewing zone. We found that the subtracted object wave becomes the object wave emitted from the 3D objects which are geometrically transformed referring to the position of the reduced viewing zone. Therefore, the hologram patterns are calculated for the geometrically transformed 3D objects.
In this study, the point-based model is used to represent 3D objects; 3D objects consist of an aggregate of object points. The half zone-plane technique is used to calculate the hologram patterns [Appl. Opt., vol. 48, H64 (2009)], which allows the elimination of the conjugate image and the zero-order diffraction light using a single-sideband filter placed in the magnifying imaging system. The half zone-plates placed at the object points are added to obtain the hologram pattern. In this study, the half zone-plate is modified into the two-line zone-plate because the viewing-zone scanning system provides only horizontal parallax. A one-line zone-plate, which is a one-dimensional zone-plate, can generate an object point. The addition of the complementary line enables the elimination of the conjugate image and the zero-order diffraction light. This modification reduces the amount of calculation by several times, and greatly shortens the calculation time.