In this paper, we use optical coherence theory to define the limit for the spatial coherence length with respect to the degree of overlap between adjacent probe positions in ptychography. The influence of the degree of curvature of the probe in relation to partial coherence in the Fresnel geometry for a fixed overlap is also considered. This work has implications for the application of ptychographic coherent imaging using partially coherent sources. We validate these results through a simulation study of coherence versus overlap parameter and curvature.
The requirements on the spatial and temporal coherence for conventional Coherent Diffractive Imaging
(CDI) have been well-established in the literature based on Shannon sampling of the diffracted intensities. The
spatial coherence length of the illumination must be larger than twice the lateral dimensions of the sample whilst the
temporal coherence length must be larger than the maximum optical path length difference between the two edges of
the sample for the highest order diffraction peaks. However, recent approaches to CDI which have included
knowledge of the spatial and temporal coherence information in the image reconstruction have allowed us to relax
these conventional coherence constraints, extending the applicability of the technique to less coherent sources. In
light of these developments it is useful to revisit the idea of a coherence limit in partially coherent CDI and establish
a ‘universal’ limit on the partial coherence that can be tolerated without any loss of information. In this paper we
present a simple and straightforward description of the limit of spatial and temporal coherence in partially coherent
CDI.
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