2018/06/21 by Mark Iwen, Iwen, Mark A., Sami Merhi +3
Physics and Astronomy · Materials Science · Engineering · #Advanced X-ray Imaging Techniques #Electron and X-Ray Spectroscopy Techniques #Advancements in Photolithography Techniques
paper · pdf · doi:10.48550/arxiv.1806.08262
In this short note, we consider the worst case noise robustness of any phase\nretrieval algorithm which aims to reconstruct all nonvanishing vectors\n\x \∈ \ℂd (up to a single global phase multiple) from the\nmagnitudes of an arbitrary collection of local correlation measurements.\nExamples of such measurements include both spectrogram measurements of\n\x using locally supported windows and masked Fourier transform\nintensity measurements of \x using bandlimited masks. As a result,\nthe robustness results considered herein apply to a wide range of both\nptychographic and Fourier ptychographic imaging scenarios. In particular, the\nmain results imply that the accurate recovery of high-resolution images of\nextremely large samples using highly localized probes is likely to require an\nextremely large number of measurements in order to be robust to worst case\nmeasurement noise, independent of the recovery algorithm employed. Furthermore,\nrecent pushes to achieve high-speed and high-resolution ptychographic imaging\nof integrated circuits for process verification and failure analysis will\nlikely need to carefully balance probe design (e.g., their effective\ntime-frequency support) against the total number of measurements acquired in\norder for their imaging techniques to be stable to measurement noise, no matter\nwhat reconstruction algorithms are applied.\n