# Near-field Fourier ptychography: super-resolution phase retrieval via speckle illumination

## TL;DR

This paper introduces near-field Fourier ptychography, a super-resolution imaging technique that uses speckle illumination and phase retrieval to surpass traditional optical resolution limits in microscopic and macroscopic systems.

## Contribution

It presents a novel imaging modality that leverages speckle patterns and ptychographic phase retrieval to achieve high resolution without requiring high-NA lenses.

## Key findings

- Achieved ~7-fold resolution enhancement in macro imaging.
- Reconstructed high-NA images using low-NA optics and speckle illumination.
- Applicable to light, X-ray, and electron imaging systems.

## Abstract

Achieving high spatial resolution is the goal of many imaging systems. Designing a high-resolution lens with diffraction-limited performance over a large field of view remains a difficult task in imaging system design. On the other hand, creating a complex speckle pattern with wavelength-limited spatial features is effortless and can be implemented via a simple random diffuser. With this observation and inspired by the concept of near-field ptychography, we report a new imaging modality, termed near-field Fourier ptychography, for tackling high-resolution imaging challenges in both microscopic and macroscopic imaging settings. The meaning of 'near-field' is referred to placing the object at a short defocus distance with a large Fresnel number. In our implementations, we project a speckle pattern with fine spatial features on the object instead of directly resolving the spatial features via a high-resolution lens. We then translate the object (or speckle) to different positions and acquire the corresponding images using a low-resolution lens. A ptychographic phase retrieval process is used to recover the complex object, the unknown speckle pattern, and the coherent transfer function at the same time. In a microscopic imaging setup, we use a 0.12 numerical aperture (NA) lens to achieve a NA of 0.85 in the reconstruction process. In a macroscale photographic imaging setup, we achieve ~7-fold resolution gain using a photographic lens. The final achievable resolution is not determined by the collection optics. Instead, it is determined by the feature size of the speckle pattern. The reported imaging modality can be employed in light, coherent X-ray, and transmission electron imaging systems to increase resolution and provide quantitative absorption and phase contrast of the object.

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Source: https://tomesphere.com/paper/1901.03057