It was determined that the most suitable cross sectional shape for lenticular lenses is elliptical. Firstly, the formula of the surface is derived based on the ellipse expression and the requirement of the 3D display system, that is y2+0.5651x2 − 303.4768=0. Secondly, one axial source and 4 off-axial sources placed at the heights of 2.5mm, 5mm, 7.5mm and 8mm are used to analyze the beam splitting quality of the cylindrical and elliptical lens element, respectively. The spot of elliptical lens is smaller which means a better beam splitting quality. Thirdly, Monte Carlo Non-Sequential Ray tracing algorithm is used to simulate the luminance distribution on the viewing plane, the narrower width of vertical stripes means that the aberration is suppressed. Finally, the shape of elliptical can reduce the processing difficulty with the 10μm minimum step width. In a word, the optimization of the surface has a significant effect on the improvement of stereoscopic depth and the reduction of ghost images.
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Ping Su, Shu An, Jianshe Ma, "Optimization of lens shape for autostereoscopic display," Proc. SPIE 10022, Holography, Diffractive Optics, and Applications VII, 100220H (31 October 2016);