Missing frequency recovery through ptychography

Abstract

High-resolution imaging at short wavelengths from extreme ultraviolet to hard X-rays has many applications in a plethora of fields from astronomy to biology and semiconductor metrology. Unfortunately, efficient optics for these wavelengths are difficult to manufacture or have limited resolution. For this reason, in the past few years, coherent diffraction imaging (CDI) applications become widely used. In CDI, the object is illuminated by a coherent beam and the diffraction intensity is collected by a 2D pixel detector. In this process, the phase information of the diffracted light is lost. A phase retrieval algorithm is then used to reconstruct the object’s complex amplitude. Ptychography is a scanning version of coherent diffraction imaging and it is based on an iterative reconstruction algorithm that relies on the quality of the recorded diffraction intensity to converge. To obtain diffraction patterns with a high signal-to-noise ratio, a beam stop is used in many ptychography setups to avoid over-saturation and blooming effects on the detector. While using a beam stop in a ptychography setup has become common practice, the limits of affordable data loss due to beam stop have not been systematically investigated. Pixel masking is the conventional method to recover the lost frequencies. In this method, when enforcing the Fourier domain constraint, the invalid pixels are ignored. In the missing data region, the algorithm is allowed to keep the guess from the previous iteration. The illumination conditions of the ptychography experiment play a critical role in the signal recovery procedure. The diffraction pattern on the detector is the convolution of the Fourier transform of the object and the illumination. An illumination with a finite numerical aperture encodes the object information over a larger detector area. This makes the reconstruction algorithm more robust to pixel loss. We provide simulation and experimental results to demonstrate this theory.