基于减采样技术的快速高分辨数字全息重建算法

Fast reconstruction algorithm for high-resolution digital holography based on downsampling technique

为了缓和传统数字全息重建算法在分辨率和计算量之间的相互制约关系,基于欠采样数字解调理论,通过对恢复后的物波场先进行空域或频域减采样,滤除物波中的冗余信息,然后通过补零算法提高有用信息的重建分辨率,从而实现高分辨数字全息的快速重建。分别给出了减采样菲涅尔重建(FR)算法和减采样角谱重建(AS)算法的最大允许采样间隔,推导了两种减采样重建算法所需像素与分辨率提高倍率和减采样倍率之间的定量关系。结果表明,减采样数字全息重建算法非常适合高分辨数字全息的快速重建。通过实验对该算法进行了分析和验证。

For releasing the computation burden of high resolution reconstruction with conventional algorithm,based on the undersampling digital demodulation theory, a fast and high-resolution reconstruction algorithm for digital holography based on downsapling technique is proposed. It is done by three steps： retrieving the object wave on CCD through filtering or phase-shifting technique, downsampling the re- trieved object wave in spatial domain or frequency domain and zero padding the downsampled object wave. Consequently the fast reconstruction of high-resolution digital hologram can be realized. The al- lowable maximum downsampled intervals are presented for the downsapling Fresnel reconstruction （FIR） algorithm and the downsampling angular spectrum （AS） reconstruction algorithm. The performance of the downsampling reconstruction algorithm can be expressed by three parameters：the needed pixel num- ber, the resolution increasing ratio and the downsampling ratio. The analytical relations of the three parameters are deduced. The analytical results show that the proposed downsampling reconstruction algorithms are adapted for fast reconstruction of high-resolution digital holography. At last the experiments are presented to demonstrate the judgements.