Abstract
A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution complex sample estimate. Here, we propose a mathematical model of FPM that explicitly connects its operation to conventional ptychography, a common procedure applied to electron and X-ray diffractive imaging. Our mathematical framework demonstrates that under ideal illumination conditions, conventional ptychography and FPM both produce datasets that are mathematically linked by a linear transformation. We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures. In addition, the coherence state of the illumination source used by each imaging platform is critical to successful operation, yet currently not well understood. We apply our mathematical framework to demonstrate that partial coherence uniquely alters both conventional ptychography's and FPM's captured data, but up to a certain threshold can still lead to accurate resolution-enhanced imaging through appropriate computational post-processing. We verify this theoretical finding through simulation and experiment.
Highlights
In ptychographic imaging, commonly referred to as scanning diffraction microscopy, a sample is shifted across a narrow illumination beam and a series of diffraction intensity patterns are recorded
The Fourier ptychographic microscopy (FPM) setup requires no moving components, which suggests it may be capable of greater stability with respect to conventional ptychography (CP)
Working within a high-dimensional space like the Wigner distribution function (WDF)’s is required when including partial coherence, so our model will most immediately impact ptychographic algorithms that must account for the effects of large, highthroughput sources
Summary
Commonly referred to as scanning diffraction microscopy, a sample is shifted across a narrow illumination beam and a series of diffraction intensity patterns are recorded. We hope to encourage a cross-pollination of ideas and efforts to help both techniques progress in high-resolution complex object recovery in the optical regime Because of their convenient form, we choose to represent the data collected by each style of ptychography with a class of function commonly referred to as a phase-space distribution. While [9] presents a theoretical model of partially coherent CP, we derive a new set of expressions for both CP and FPM that clearly establish how the finite shape of an incoherent source uniquely impacts each setup These expressions are verified in simulation and experiment by computationally removing the effects of partial coherence from final reconstructions. While our phase space model is closely connected to a rich array of computational post-processing tools, we explicitly avoid their discussion until the conclusion, where we list several direct extensions that will benefit from this primarily theoretical work
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