Fast polygon-based method for calculating computer-generated holograms in three-dimensional display

Abstract

In the holographic three-dimensional (3D) display, the numerical synthesis of the computer-generated holograms needs tremendous calculation. To solve the problem, a fast polygon-based method based on two-dimensional Fourier analysis of 3D affine transformation is proposed. From one primitive polygon, the proposed method calculates the diffracted optical field of each arbitrary polygon in the 3D model, where the pseudo-inverse matrix, the interpolation, and the compensation of the power spectral density are employed. The proposed method could save the computation time in the hologram synthesis since it does not need the fast Fourier transform for each polygonal surface and the additional diffusion computation. The numerical simulation and the optical experimental results are presented to demonstrate the effectiveness of the method. The results reveal the proposed method could reconstruct the 3D scene with the solid effect and without the depth limitation. The factors that influence the image quality are discussed, and the thresholds are proposed to ensure the reconstruction quality.

3D Capture and 3D Contents Generation for Holographic Imaging

“…Computation of a polygon field is slower than that of a spherical wave emitted by a point light source, but the number of polygons is much smaller than that of point sources and the total computation time is shorter compared to the point cloud approach. The traditional polygon-based method evolved to analytical implementation when the angular spectrum of a triangle of arbitrary size, shape, orientation and location in space is analytically calculated from the known spectrum of a reference triangle [38][39][40]. The analytical method eliminates the need to apply FFT for each polygon.…”

Recent progress in computer-generated holography for three-dimensional scenes

“…The research reported in Refs. [38,39] performed only a single FFT operation on a reference triangle rather than repeated FFT operations for every triangle to reduce the computation time. The local angular spectrum for an arbitrary triangle is obtained by resampling the obtained discrete local angular spectrum of the reference triangle considering the geometric relationship between the given and reference triangles.…”

Analytical brightness compensation algorithm for traditional polygon-based method in computer-generated holography

“…Although many researchers have developed various accelerating methods [2][3][4], to achieve the solid effect, the point-based method needs tremendous computation. The polygon-based method is expected to be the fast computation method since it represents the 3D objects by many polygons, by which the amount of the computation unit is significantly decreased [5][6][7][8][9][10][11][12][13][14][15]. In addition, combining with the rendering algorithms of the computer graphics, the polygon-based method could easily add texture and shade to the 3D scene.…”

“…In recent years, there have been four main approaches under the PWD frame: the traditional polygon-based method [5][6][7][8][9][10], the full analytical method [11,12], the spatial approximate method [13,14], and the 3D affine transformation method [15]. The traditional method depicts the tilted polygon in its local coordinates, computes the corresponding Fourier spectrum, calculates the new frequency from the spatial 3D rotational transformation and rotates the spectrum to the global coordinates by the interpolation approach.…”

“…It uses the pseudoinversion matrix to calculate the parameters of the 3D affine transformation from the vertex vectors of the primitive and the tilted polygon. Using these parameters, it directly connects the spectrum of the primitive and that of the tilted polygon without implicit variable substitution [15]. It saves the FFT but still needs other algorithm to add the texture.…”