  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.
