基于矩阵填充的相位检索

Phase Retrieval Based on Matrix Completion

相位检索利用直接测量得到的强度分布恢复相位信息,从而重建波函数,是光学和图像处理中的重要研究方向。提出衍射成像中新的利用相位掩模的结构光照明设置,在这种新的设置中,物体和掩模紧贴在一起,并且相互之间的位置可以互换,采用多结构光照明,收集多个不同的衍射图样,在没有信号额外信息情况下求解相位。模拟实验结果表明,这种新的设置形式简单,可以成功地实现相位检索。此外,提出应用托普利兹掩模和循环掩模收集衍射图样以检索相位,它们比二进制掩模需要收集更少的衍射图样;与高斯掩模需要收集的衍射图样数目相当,但是物理上比高斯掩模更易于实现。

Phase retrieval technique using the directly measured intensity distribution to recover phase information and reconstruct the wave function is an important research area of optics and image processing. A new setup for structured illuminations in diffraction imaging is proposed. In the new setup, the object is placed against the mask, and mutual position can be interchanged. Multiple structured illuminations are used to collect several diffraction patterns. In the absence of extra information of the signal, the phase information is obtained. Simulation results show that the new setup is simple, and can achieve the success of phase retrieval. In addition, the Toeplitz mask and circulant mask are used to collect diffraction patterns for phase retrieval. The two masks need to collect fewer diffraction patterns than binary mask does and need to collect diffraction patterns as many as Gaussian mask does. Compared with Gaussian mask, the two masks are easy to realize in physics.