离轴数字全息波前重建算法讨论

Discussion of Wavefront Reconstruction Algorithm of Off-Axis Digital Holography

在离轴数字全息的应用研究中,将数字全息图视为单位振幅平面波照射下的光波场,利用1次快速傅里叶变换(FFT)计算菲涅耳衍射积分是最流行的物光波前重建方法(简称1-FFT法)。然而,用球面波为重建波,利用像平面滤波技术及角谱衍射理论,存在需要4次FFT的另一种波前重建方法(简称FIMG4FFT法)。基于快速傅里叶变换理论对这两种方法进行研究。结果表明,尽管FIMG4FFT重建方法需要进行4次FFT计算,却能用较少的计算资源高效率地重建同等质量的物光场。为便于实际应用,详细给出FIMG4FFT方法在彩色数字全息图像重建及物体微形变检测中的应用实例。

In the study of off-axis digital holography, digital hologram may be considered as a light wave field which is illuminated by the unit amplitude plane wave. The Fresnel diffraction integral can be calculated by only one fast Fourier transform （FFT）. It is the most popular method of wavefront reconstruction （called 1-FFT）. However, applying the spherical wave as the reconstruction wave, there is another method of wavefront reconstruction using the angular spectral diffraction theory and image plane filtering. This method requires four fast Fourier transforms （called FIMG4FFT）. Two methods are researched based on the fast Fourier transform theory. The result demonstrates that the FIMG4FFT method needs four FFTs, but it can use less computation resource to reconstruct the equivalent quality object wave field. Finally, the application examples of the FIMG4FFT method are shown in detail in the reconstruction of color digital holograms and micro deformation detection.