Colorful holographic display of 3D object based on scaled diffraction by using non-uniform fast Fourier transform

Abstract

We proposed a new method to calculate the color computer generated hologram of three-dimensional object in holographic display. The three-dimensional object is composed of several tilted planes which are tilted from the hologram. The diffraction from each tilted plane to the hologram plane is calculated based on the coordinate rotation in Fourier spectrum domains. We used the nonuniform fast Fourier transformation (NUFFT) to calculate the nonuniform sampled Fourier spectrum on the tilted plane after coordinate rotation. By using the NUFFT, the diffraction calculation from tilted plane to the hologram plane with variable sampling rates can be achieved, which overcomes the sampling restriction of FFT in the conventional angular spectrum based method. The holograms of red, green and blue component of the polygon-based object are calculated separately by using our NUFFT based method. Then the color hologram is synthesized by placing the red, green and blue component hologram in sequence. The chromatic aberration caused by the wavelength difference can be solved effectively by restricting the sampling rate of the object in the calculation of each wavelength component. The computer simulation shows the feasibility of our method in calculating the color hologram of polygon-based object. The 3D object can be displayed in color with adjustable size and no chromatic aberration in holographic display system, which can be considered as an important application in the colorful holographic three-dimensional display.