Analysis of the Distortion Effects in Holographic Projection Display caused by the Retroreflector Screen

Abstract

Fig. 1. (a-b) Optical system configurations to calculate PSF. (c) Unit cell structure. (d) Effective aperture area. 2. Methodology Figure 1(c) shows the triangular unit cell RR with three orthogonal faces and a centroid. Effective aperture area of a triangular unit cell in RR plane is the area which retroreflects the light back to its source. It can be calculated from red and yellow triangular apertures whose normals are parallel to the diagonal (blue arrow) of a corner cube as in top of Fig.1(d). Red triangle corresponds to the triangular unit cell aperture for input light and yellow triangle corresponds to the inverted triangular aperture after light reflects from all three orthogonal faces inside the red triangle. When the angle between the incident light and the diagonal to the corner cube is parallel, we have ideal hexagonal effective aperture (in gray region) as shown in mid row of Fig.1(d) [1]. For different angles to the diagonal of input light, we have different effective apertures as shown in the bottom row of Fig. 1(d). The region outside of gray area does not retroreflects the light. Considering the conjugate structure of a retroreflector, the positional shift is also introduced depending on the size of unit cell RR. In MATLAB simulations, we used the point symmetric transformation (PST) given by, ′ = (2() – ), (1) where, and ′ indicate the incident and retroreflected position of the optical field with respect to the centroid of each unit cell RR, respectively. Figure 2(a) shows an example of the complex field for a point source calculated just before the RR plane by an angular spectrum (AS) method. Figure 2(b) shows the effective aperture mask for the point source. Note that the effective aperture mask depends on the point source distance and its lateral position. Figure 2(c) shows the complex field after masking. Figure 2(d) shows the complex field after performing PST operation at each unit cell in RR plane. The complex field then propagates back to the original point source distance giving the PSF of the RR screen in the simulation. Fig. 2. Optical wave simulation flow in MATLAB