Liang Jinyang, Becker Michael F
Appl Opt. 2014 Sep 20;53(27):G84-94. doi: 10.1364/AO.53.000G84.
Designing near-field computer-generated holograms (CGHs) for a spatial light modulator (SLM) requires backward diffraction calculations. However, direct implementation of the discrete computational model of the Fresnel diffraction integral often produces inaccurate reconstruction. Finite sizes of the SLM and the target image, as well as aliasing, are major sources of error. Here we present a new design prescription for precise near-field CGHs based on comprehensive analysis of the spatial bandwidth. We demonstrate that, by controlling two free variables related to the target image, the designed hologram is free from aliasing and can have minimum error. To achieve this, we analyze the geometry of the target image, hologram, and Fourier transform plane of the target image to derive conditions for minimizing reconstruction error due to truncation of spatial frequencies lying outside of the hologram. The design prescription is verified by examples showing reconstruction error versus controlled parameters. Finally, it is applied to precise three-dimensional image reconstruction.
为空间光调制器（SLM）设计近场计算机生成全息图（CGH）需要进行反向衍射计算。然而，直接实施菲涅耳衍射积分的离散计算模型往往会产生不准确的重建结果。SLM和目标图像的有限尺寸以及混叠是主要的误差来源。在此，我们基于对空间带宽的全面分析，提出了一种用于精确近场CGH的新设计方法。我们证明，通过控制与目标图像相关的两个自由变量，所设计的全息图可避免混叠，并且误差最小。为实现这一点，我们分析目标图像、全息图以及目标图像的傅里叶变换平面的几何结构，以推导由于截断全息图之外的空间频率而使重建误差最小化的条件。通过展示重建误差与控制参数关系的示例验证了该设计方法。最后，将其应用于精确的三维图像重建。
