Study On The Algorithm Of Computer Generated Hologram Based On Diffraction Theory

Computer generated hologram (CGH) has become an important basis for the development of dynamic holographic 3D display. Compared with the traditional hologram recorded by optical interference, CGH has many advantages such as simple production, easy to storage and transmit, capable to calculate and display virtual objects.it can display not only static objects, but also dynamic three-dimensional animation by combining with the high-speed spatial light modulator. However, in the reconstruction from the CGH calculated by traditional methods, the existing of zero-order diffraction noise, speckle noise and chromatic aberration will degrade the quality of the reconstructed image. Moreover, the calculation of CGH for 3D object not only needs to store huge information, but also requires a lot of computing time, and the CGH can only reconstruct 3D object with fixed size. All of the problems limit the further development and application of holographic display. In this paper, the algorithm of the CGH is investigated in order to solve the mentioned problems. The contents and results of this paper are as follows:1. The algorithm of fractional Fourier transform based phase-only CGH is proposed. The fractional Fourier transform is used to calculate the diffraction in the lens system and the phase-only fractional Fourier CGH is calculated based on the modified GS iterative algorithm. Compared with the conventional Fourier phase-only CGH, the fractional Fourier phase-only CGH can reconstruct image at any distance after the lens, by adjusting the order of the transform. Due to this advantage the zero-order diffraction can be removed by placing a filter in the focal of the lens, and therefore avoid the presence of zero-order wave to reduce image quality. This is demonstrated by the optical experiments. Compared with the phase-only CGH generated by non-iterative algorithm, the phase-only CGH generated by our method can reduce the error with up to 45 gray-levels in the reconstruction. This system can be applied to holographic retina display, the fractional Fourier CGH can display three-dimensional images of different depths on the retina, the eye lens is acted as the lens in the fractional Fourier transform. The three-dimensional effect can be observed by the human eye zoom adjustment function. These work have been published in Optics Communications and Journal of Display Technology.2. We propose to use the non-uniform Fourier transform algorithm to calculate the CGH of three-dimensional object. The conventional method cuts a three-dimensional light field into many parallel planes, and the light distribution on the hologram plane is calculated from each plane separately. So the storage space is wasted by using a lot of useless data in the calculation.we propose a method by assigning different sampling rates for each sampling point depending on the depth information and the CGH is calculated by using the non-uniform Fourier transform algorithm in only one step. The advantage is that no segmentation of three-dimensional object is needed and the calculation is between two dimensional domains and saving a lot of data in calculation. We find that compared to the conventional method, the proposed algorithm requires only half the amount of data used to calculate the hologram.Then we further calculate the CGH of polygon-based three-dimensional object based on the characteristics of the non-uniform Fourier transform. the sampling rate can be adjusted in the calculation. The experiment results show that the CGH can reconstruct three-dimensional object with different sizes, which break the limitation of object size in conventional CGH calculation method. Based on this, a clear view of the depth of field of three-dimensional object can be seen. These work have been published in Chinese Optics Letters and Optics Express.3. The algorithm of phase-only CGH based on error diffusion filter is proposed. In the reconstruction from conventional phase-only CGH calculated by GS algorithm, the uncontrolled random phase distribution of the reconstructed light field brings constructive interference among adjacent pixels, from which the summary of intensity cause the speckle noise. We propose to calculate the phase-only CGH by using the error diffusion algorithm. The advantages of this algorithm are:1) The calculation speed of the phase-only CGH is increased.2) The phase-only CGH calculated in this way can reconstruct image with both of optimized amplitude and phase distribution. So the interference among pixels will be greatly weakened. The speckle noise can be suppressed in this way and is demonstrated in the optical experiment. This work is oral presented by the author in the conference of 2015 Digital Holography and 3D imaging and is published in the conference proceedings.4. The algorithm of CGH of color object is proposed based on convolution theory. Generally the color image is first divided into red, green and blue component, and the CGH of each component is calculated separately. However, in the calculation of each component CGH, fast Fourier transform (FFT) algorithm is used and the size of the reconstruction images of red, green and blue components will be different due to the Nyquist sampling theory in the FFT calculation, which will bring the chromatic aberration in the reconstruction. We propose a method to calculate the CGH by using the convolution algorithm, in which the spatial sampling rates on both of the hologram plane and image plane can be set arbitrary, which makes it possible for setting the size of the reconstructed image in the calculation, therefore the color image can be reconstructed without chromatic aberration. In the optical experiment, the red, green and blue laser illuminate each CGH separately and the reconstructed images of three components are in the same position with same size to fix into a color image. This work is oral presented by the author in the conference of SID 2014 and is published in the conference proceedings.