提出了一种基于Gabor小波变换的菲涅耳全息图的数值再现方法, 实现无需空间滤波处理, 即可对物光波进行数值再现。给出Gabor小波变换以及小波变换脊的定义, 并从理论上证明通过对全息图进行Gabor小波变换, 提取小波变换脊对应的小波变换系数, 包括幅值与相位信息, 即可直接获得与+1级频谱相对应的被测物光在全息面上的强度与相位分布, 并同时直接消除零级衍射像以及孪生像的影响。通过计算机模拟再现光波经全息图衍射后的传播规律实现数值再现, 得到清晰的再现像。通过计算机模拟一相位型物体以及实验证明该方法的有效性。

A digital reconstruction method of Fresnel hologram with a ridge of Gabor wavelet transform is described. Applied the Gabor wavelet transform to the digital holography, the object wave can be numerical reconstructed without the spatial filtering. The Gabor wavelet transform and the ridge of the wavelet transform are introduced. It proves that by abstracting the wavelet coefficients at the ridge of the wavelet transform of the hologram, the intensity and the phase of the object wave corresponding to the +1-order spectrum at the hologram plane are obtained, at the same time the effect of the zero-order diffraction image and the twin image is eliminated. Multiplying the wavelet coefficients at the ridge by an ideal wave corresponding to a replica of the reference wave and propagating for the corresponding propagation distance, the reconstructed wave at the image plane is reconstructed, and a clear image is obtained. The results of a simulated phase object and an experiment show that the method is effective.