Fast calculation method for parabolic-mirror-reflection holographic 3D display using wavefront segmentation

Convex-parabolic-mirror reflection enables a very wide viewing zone in a holographic three-dimensional (3D) display. In this work, segmentation is introduced to reduce the calculation time of holograms in a convex-parabolic-mirror-reflection holographic 3D display. Wavefront segmentation can practically limit the lateral spread of the wavefront to be considered, which enables the application of geometrical approximation and conventional diffraction theories such as Fresnel diffraction. Thus, diffraction calculation via the convex parabolic mirror can be derived analytically and calculated rapidly using fast Fourier transform (FFT). Our proposed FFT-based method can calculate the diffraction integral 7000 times faster than our previous method, which involved calculating directly the diffraction integral without FFT. In addition, numerical simulation and an optical experiment are presented to verify our proposal.