Speckle suppression of cylindrical holography using deterministic gradient update

Holography is an ideal three-dimensional (3D) display technology as it can obtain a 3D display by reconstructing the recorded amplitude and phase information of the object [1], [2], [3]. Compared with traditional optical holography, computational holography uses a computer to obtain wavefront information and adopts a spatial light modulator (SLM) for optical reconstruction. Therefore, wavefront recording of computational holography is not limited by optical conditions, which can realize a more flexible and dynamic holographic 3D display. However, holographic 3D display technologies are difficult to satisfy commercial applications. There are two main reasons: The first is because the speckle noise in the reconstructed holographic image affects the viewing quality [4], [5], [6]. The second is because the planar holography limits the viewing angle [7], [8]. To solve the issue of viewing angle limitation, researchers have proposed cylindrical holograms and curved holograms. Compared with curved holograms [9], [10], [11], cylindrical holograms have a 360-degree field of view, which is more in line with people’s actual viewing experiences.

Because of the advantage of the large field of view of cylindrical holograms, there are many studies on cylindrical hologram generation algorithm. Sando et al. proposed a convolution algorithm based on the Fast Fourier transform (FFT) to obtain cylindrical holograms by analyzing the space–time invariance of cylinders [12]. This is a concentric cylinder-based convolution algorithm. Jackin et al. further accelerated the calculation of cylindrical diffraction by analyzing the transfer function [13], so that the cylindrical hologram only needs to use two FFTs to calculate the simulated wave propagation. Wang et al. proposed an inside-out propagation model and a fast generation method for cylindrical holograms based on FFT and convolution [14]. Later, through the analysis of the inclination factor, the unification of the inside-outside propagation model and the outside-inside propagation model was realized [15]. Recently, Li et al. proposed a method for occlusion culling of cylindrical holograms using an optical-path limit function. Since these methods are all based on complex amplitude reconstruction, the reconstruction quality degrades drastically because of speckle noise when the reconstruction is performed using phase-only holograms [16]. Therefore, Jin et al. proposed an optimization method by cylindrical self-diffraction iteration (CSDI) to improve the quality of reconstructed images [17]. However, the reconstruction quality is still not high enough to meet the requirements of applications. Therefore, the issue of speckle noise in cylindrical holography needs to be solved further.

In this paper, a deterministic gradient update is proposed for the speckle suppression of cylindrical holography. The proposed method is an optimization method for phase-only cylindrical hologram generation. The optimized hologram is achieved by iteratively updating the phase-only hologram by adding the deterministic gradient phase to the previous phase. The deterministic gradient phase is calculated by the previous phase and the gradient loss, which is the gradient difference between the images of the reconstruction and the object. The most important thing here is to consider the whole process of hologram reconstruction as a function of the phase and to obtain the final optimized phase hologram by calculating the gradient with the chain rule of derivation. Unlike conventional methods such as CSDI, which only add the amplitude information of the object image to the final phase hologram by repeated iterations and cannot effectively use the information of the object image, the key to our proposed method is to iteratively increase the information about the object image contained in the phase hologram by comparing the object image with the reconstructed image. It is able to extract information from the object image in a more efficient way than traditional methods, so that the reconstructed image can achieve speckle suppression and higher quality. Meanwhile, we verify the effectiveness of our proposed method through numerical simulations, and the quality of the reconstructed image is improved by about 10 dB in PSNR compared with the conventional method of CSDI.

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