Near, far, wherever you are: simulations on the dose efficiency of holographic and ptychographic coherent imaging

TL;DR

This study compares the dose efficiency of near-field holography, near-field ptychography, and far-field ptychography in x-ray microscopy, finding similar image quality across methods when using the same fluence, with slight advantages for far-field ptychography.

Contribution

It provides a numerical comparison of three imaging modes, clarifying their dose efficiency and spatial resolution limits in x-ray microscopy.

Findings

All three methods offer similar image quality at the same fluence.

Far-field ptychography achieves slightly better spatial resolution.

Photon fluence limits the spatial resolution regardless of imaging mode.

Abstract

Different studies in x-ray microscopy have arrived at conflicting conclusions about the dose efficiency of imaging modes involving the recording of intensity distributions in the near (Fresnel regime) or far (Fraunhofer regime) field downstream of a specimen. We present here a numerical study on the dose efficiency of near-field holography (NFH), near-field ptychography (NFP), and far-field ptychography (FFP), where ptychography involves multiple overlapping finite-sized illumination positions. Unlike what has been reported for coherent diffraction imaging (CDI), which involves recording a single far-field diffraction pattern, we find that all three methods offer similar image quality when using the same fluence on the specimen, with far-field ptychography offering slightly better spatial resolution and lower mean error. These results support the concept that (if the experiment and image reconstruction are done properly) the sample can be near, or far; wherever you are, photon fluence on the specimen sets one limit to spatial resolution.

Full text

**Near, far, wherever you are: simulations on the dose

efficiency of holographic and ptychographic coherent imaging

**Supplimentary Materials

Ming Du

Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439 USA

Doǧa Gürsoy

Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439 USA

Department of Electrical Engineering and Computer Science, Northwestern University, Evanston, IL 60208 USA

Chris Jacobsen

Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439 USA

Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208 USA

Chemistry of Life Processes Institute, Northwestern University, Evanston, IL 60208 USA

1 Influence of probe spacing in far-field ptychography reconstruction

When a probe scan grid that is too coarse is used for far-field ptychography (FFP), the number of photons in the “tails” of the probe function becomes low enough that there can be insufficient overlap between probe positions compared to the high-photon-number case. In this case, a grid-like artifact will appear in the reconstructed image [1, 2], especially when using the least-square (LSQ) cost function. The scan grid of $68\times 66$ probe positions we used to generated all reconstructions shown in the main text is fine enough to suppress this artifact at low fluence, but when probe spacing is doubled, the artifacts become obvious. We demonstrate this effect in Fig. S1, which includes far-field ptychography (FFP) reconstructions of the dataset generated with a photon fluence of 20 photons per reconstruction array pixel, using both a fine ($68\times 66$ probe positions) and coarse ($34\times 33$ probe positions) probe spacing grid. Both grids covers the same area indicated by the yellow dashed box, so the coarser grid has twice the probe spacing in the horizontal and vertical directions. To keep the number of photons per reconstruction array pixel equal (and thus the fluence – and the dose to the specimen – equal), we supplied 1/4 the number of photons per probe position in the fine grid relative to the coarse grid. With the same per-pixel photon dose, the coarse grid reconstruction using the LSQ cost function, which is used by popular algorithms like ePIE [3], shows obvious grid artifacts. This grid artifact can produce correlations based on artifacts rather than specimen features when comparing two independent reconstructions in Fourier shell correlation or FSC resolution analysis, and thus can provide a biased measure of higher-than-justified resolution at low exposures.

When using the Poisson cost function, grid artifacts are greatly reduced, and the features in the image become sharper. At the same time, however, another type of artifact (fringes around fine features, as discussed in the main article text) emerges in Poisson reconstructions.