Recovery of spatial frequencies in coherent diffraction imaging in the presence of a central obscuration

Coherent diffraction imaging (CDI) and its scanning version, ptychography, are lensless imaging approaches used to iteratively retrieve a sample's complex scattering amplitude from its measured diffraction patterns. These imaging methods are most useful in extreme ultraviolet (EUV) and X-ray regions of the electromagnetic spectrum, where efficient imaging optics are difficult to manufacture. CDI relies on high signal-to-noise ratio diffraction data to recover the phase, but increasing the flux can cause saturation effects on the detector. A conventional solution to this problem is to place a beam stop in front of the detector. The pixel masking method is a common solution to the problem of missing frequencies due to a beam stop. This paper describes the information redundancy in the recorded data set and expands on how the reconstruction algorithm can exploit this redundancy to estimate the missing frequencies. Thereafter, we modify the size of the beam stop in experimental and simulation data to assess the impact of the missing frequencies, investigate the extent to which the lost portion of the diffraction spectrum can be recovered, and quantify the effect of the beam stop on the image quality. The experimental findings and simulations conducted for EUV imaging demonstrate that when using a beam stop, the numerical aperture of the condenser is a crucial factor in the recovery of lost frequencies. Our thorough investigation of the reconstructed images provides information on the overall quality of reconstruction and highlights the vulnerable frequencies if the beam stop size is larger than the extent of the illumination NA. The outcome of this study can be applied to other sources of frequency loss, and it will contribute to the improvement of experiments and reconstruction algorithms in CDI.