Fourier ptychography

The image reconstruction algorithms are based on iterative phase retrieval, either related to the Gerchberg–Saxton algorithm or based on convex relaxation methods. Like real space ptychography, the solution of the phase problem relies on the same mathematical shift invariance constraint, except in Fourier ptychography it is the diffraction pattern in the back focal plane that is moving with respect to the back-focal plane aperture. (In traditional ptychography the illumination moves with respect to the specimen.) Many reconstruction algorithms used in real-space ptychography are therefore used in Fourier ptychography, most commonly PIE and variants such as ePIE and 3PIE. Variants of these algorithms allow for simultaneous reconstruction of the pupil function of an optical system, allowing for the correction of the aberrations of the microscope objective, and diffraction tomography which permits the 3D reconstruction of thin sample objects without requiring the angular sample scanning needed for CT scans. ==Advantages==

Fourier ptychography can be easily implemented on a conventional optical microscope by replacing the illumination source by an array of LED and improve the optical resolution by a factor 2 (with only bright-field illumination) or more (when including dark-field images to the reconstruction.) A major advantage of Fourier ptychography is the ability to use a microscope objective with a lower numerical aperture without sacrificing the resolution. The use of a lower numerical aperture allows for larger field of view, larger depth of focus, and larger working distance. Moreover, it enables effective numerical aperture larger than 1 without resorting to oil immersion. ==Relation to ptychography==

Contrary to Fourier ptychography, (conventional) ptychography swaps the role of the focus element, from an objective to become a condenser, and relies on the acquisition of diffractograms with illumination position diversity. However, the two techniques are both based on the determination of the angular spectrum of the object through a phase retrieval procedure, and inherently reconstruct the same information. Therefore, Fourier ptychography and conventional ptychography provides a bridge between coherent diffraction imaging and full-field microscopy. ==See also==