基于Hilbert变换实现数字全息高精度相位重建

为了提高数字全息相位重建精度,研究了基于Hilbert变换重建相位的理论和方法,并通过像面数字全息实验对该方法的有效性进行了验证,同时与数字全息常规重建方法得到的结果进行了比较.结果表明:Hilbert变换本身具有消除直流项的作用,对利用频域滤波滤除零级谱后的全息图进行Hilbert变换,能够彻底消除零级衍射项的干扰,从而提高相位重建精度.与常规重建结果相比,基于Hilbert变换的相位重建结果的标准偏差降低了14.0%.本文结果对提高数字全息相位重建精度具有重要的指导意义.

High accuracy phase reconstruction of digital hologram by Hilb ert transform

To improve the phase accuracy of the reconstructed image of the digital hologram, we investigate the theory and method of the phase reconstruction based on the Hilbert transform, then, verify it by the image plane digital holographic experiment, and finally, compare it with the conventional digital holographic reconstruction method. Results show that Hilbert transform itself posseses the effect of eliminating DC term, therefore the effect of the zero-order frequency spectrum of the hologram which is filtered by frequency domain can be completely eliminated by Hilbert transform. Compared with the conventional Fourier reconstruction mehtod, the accuracy of the phase image can be improved by the reconstruction method based on Hilbert transform, and the standard deviation of the phase image is reduced by 14% in the experiment of red blood cell. This result has an important guiding significance to improve the accuracy of the digital holographic phase reconstruction.
Keywords： digital holography image-plane digital holography Hilbert transform phase reconstruction