Sando Yusuke, Goto Yutaro, Barada Daisuke, Yatagai Toyohiko
Appl Opt. 2023 Jul 1;62(19):5276-5281. doi: 10.1364/AO.491807.
In holographic three-dimensional (3D) displays, the surface structures of 3D objects are reconstructed without their internal parts. In diffraction calculations using 3D fast Fourier transform (FFT), this sparse distribution of 3D objects can reduce the calculation time as the Fourier transform can be analytically solved in the depth direction and the 3D FFT can be resolved into multiple two-dimensional (2D) FFTs. Moreover, the Fourier spectrum required for hologram generation is not the entire 3D spectrum but a partial 2D spectrum located on the hemispherical surface. This sparsity of the required Fourier spectrum also reduces the number of 2D FFTs and improves the acceleration. In this study, a fast calculation algorithm based on two sparsities is derived theoretically and explained in detail. Our proposed algorithm demonstrated a 24-times acceleration improvement compared with a conventional algorithm and realized real-time hologram computing at a rate of 170 Hz.
在全息三维（3D）显示中，三维物体的表面结构被重建，而不包括其内部部分。在使用三维快速傅里叶变换（FFT）的衍射计算中，这种三维物体的稀疏分布可以减少计算时间，因为傅里叶变换可以在深度方向上进行解析求解，并且三维FFT可以分解为多个二维（2D）FFT。此外，生成全息图所需的傅里叶频谱不是整个三维频谱，而是位于半球面上的部分二维频谱。所需傅里叶频谱的这种稀疏性也减少了二维FFT的数量并提高了加速比。在本研究中，从理论上推导了一种基于两种稀疏性的快速计算算法并进行了详细解释。我们提出的算法与传统算法相比，加速比提高了24倍，并以170Hz的速率实现了实时全息图计算。
