基于柯林斯公式的自干涉数字全息系统优化  

Optimization of Self-Interference Digital Holographic System Based on Collins Formula

作　　者：王雅婷 薛孔松 毛梦瑶 许灿华[1] Wang Yating;Xue Kongsong;Mao Mengyao;Xu Canhua(College of Physics and Information Engineering,Fuzhou University,Fuzhou 350116,Fujian,China)

机构地区：[1]福州大学物理与信息工程学院,福建福州350116

出　　处：《光学学报》2025年第1期48-57,共10页Acta Optica Sinica

基　　金：福建省自然科学基金(2023J01396,2022J01546)。

摘　　要：结合光学变换矩阵和柯林斯公式,设计了一个基于几何相位透镜的自干涉数字全息系统,展示了其在处理不同光学配置时的灵活性。推导出的图像重建距离公式仅依赖于4个光学传输矩阵元素B1、B2、D1和D2,简化了计算过程并显著提高了效率。此外,定义了参数k,用于量化受系统几何参数、干涉区域以及衍射距离影响的重建平面上的相对相位变化。通过优化k,在不同实验条件下分别实现了25.398 lp/mm、40.318 lp/mm和50.797 lp/mm的图像分辨率。研究证明,柯林斯公式与光学传输矩阵相结合,可有效优化自干涉数字全息系统,提供了一种提高数字全息图像质量和分辨率的实用方法。Objective Our research aims to optimize the self-interference digital holography(SIDH)system by using the Collins formula.We focus on simplifying the calculation of the reconstruction distance and improving the phase accuracy in holographic image reconstruction.SIDH systems,unlike conventional holography systems that rely on coherent light sources,can use incoherent light sources such as natural light,LED lamps,and flashlights.This flexibility eliminates problems related to speckle noise,which often occur in laser-based holography,and thus improves the quality of holographic imaging.However,traditional diffraction-based models in SIDH systems cause great computational complexity,especially when dealing with complex optical configurations.This complexity not only reduces the imaging performance but also restricts the system's adaptability to various practical applications.In this study,we address these challenges by integrating optical transformation matrices with the Collins formula to optimize the SIDH system.A key aspect of the research is to derive a simplified reconstruction distance formula based on the system's optical parameters.This formula depends only on four optical transfer matrix elements—B1,B2,D1,and D2.Additionally,we introduce the parameter k to measure the phase variations on the reconstruction plane.These variations are affected by the system's geometric parameters,interference region limitations,and diffraction distance.By optimizing this parameter,we improve the system's image resolution and its adaptability to different experimental setups.Methods Our methodology focuses on combining the Collins diffraction formula with optical transformation matrices to model and optimize the light propagation in the SIDH system.The Collins formula provides a mathematical framework for calculating the diffraction patterns generated when light passes through optical elements.This enables accurate prediction of the light's phase and amplitude variations.In the SIDH system,geometric phase lens(GPL)is employed

关 键 词：几何相位透镜 自干涉数字全息 柯林斯公式 重建距离 图像分辨率 光学变换矩阵 

分 类 号：O438[机械工程—光学工程]