Fourier ptychography is a computational imaging technique based on

optical microscopy Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...

that consists in the synthesis of a wider numerical aperture from a set of full-field images acquired at various coherent illumination angles, resulting in increased resolution compared to a conventional microscope. Each image is acquired under the illumination of a coherent light source at various angles of incidence (typically from an array of LEDs); the acquired image set is then combined using an iterative phase retrieval algorithm into a final high-resolution image that can contain up to a billion pixels (a gigapixel) with

diffraction-limited The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to t ...

resolution, resulting in a high space-bandwidth product. Fourier ptychography reconstructs the complex image of the object (with quantitative

phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...

information), but contrary to

holography Holography is a technique that enables a wavefront to be recorded and later re-constructed. Holography is best known as a method of generating real three-dimensional images, but it also has a wide range of other applications. In principle, i ...

, it is a non-interferometric imaging technique and thus often easier to implement. The name "ptychography" comes from the ancient Greek word πτυχή ("to fold", also found in the word

triptych A triptych ( ; from the Greek adjective ''τρίπτυχον'' "''triptukhon''" ("three-fold"), from ''tri'', i.e., "three" and ''ptysso'', i.e., "to fold" or ''ptyx'', i.e., "fold") is a work of art (usually a panel painting) that is divided ...

), because the technique is based on multiple "views" of the object.

Image reconstruction algorithms

The image reconstruction algorithms are based on iterative

phase retrieval Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex signal F(k), of amplitude , F (k), , and phase \psi(k): ::F(k) = , F(k), e^ =\int_^ f(x)\ e^\,dx where ''x'' is an ''M''-dimensional spatia ...

, either related to the

Gerchberg–Saxton algorithm The Gerchberg–Saxton (GS) algorithm is an iterative phase retrieval algorithm for retrieving the phase of a complex-valued wavefront from two intensity measurements acquired in two different planes. Typically, the two planes are the image plane ...

or based on

convex Convex or convexity may refer to: Science and technology * Convex lens, in optics Mathematics * Convex set, containing the whole line segment that joins points ** Convex polygon, a polygon which encloses a convex set of points ** Convex polytop ...

relaxation methods. Like real space ptychography, the solution of the

phase problem In physics, the phase problem is the problem of loss of information concerning the phase that can occur when making a physical measurement. The name comes from the field of X-ray crystallography, where the phase problem has to be solved for the de ...

relies on the same mathematical shift invariance constraint, except in Fourier ptychography it is the

diffraction pattern Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a ...

in the back focal plane that is moving with respect to the back-focal plane

aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An ...

. (In traditional

ptychography Ptychography (/t(ʌ)ɪˈkogræfi/ t(a)i-KO-graf-ee) is a computational method of microscopic imaging. It generates images by processing many coherent interference patterns that have been scattered from an object of interest. Its defining char ...

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 The pupil function or aperture function describes how a light wave is affected upon transmission through an optical imaging system such as a camera, microscope, or the human eye. More specifically, it is a complex function of the position in the pu ...

of an optical system, allowing for the correction of the aberrations of the microscope objective, and

diffraction tomography Diffraction tomography is an inverse scattering technique used to find the shape of a scattering object by illuminating it with probing waves and recording the reflections. It is based on the diffraction slice theorem and assumes that the scatte ...

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 The field of view (FoV) is the extent of the observable world that is seen at any given moment. In the case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation. Human ...

, larger

depth of focus Depth of focus is a lens optics concept that measures the tolerance of placement of the image plane (the film plane in a camera) in relation to the lens. In a camera, depth of focus indicates the tolerance of the film's displacement within the ca ...

, and larger working distance. Moreover, it enables effective numerical aperture larger than 1 without resorting to

oil immersion In light microscopy, oil immersion is a technique used to increase the resolving power of a microscope. This is achieved by immersing both the objective lens and the specimen in a transparent oil of high refractive index, thereby increasing the ...

Relation to ptychography

Contrary to Fourier ptychography, (conventional) ptychography swaps the role of the focus element, from an

objective Objective may refer to: * Objective (optics), an element in a camera or microscope * ''The Objective'', a 2008 science fiction horror film * Objective pronoun, a personal pronoun that is used as a grammatical object * Objective Productions, a Brit ...

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 The angular spectrum method is a technique for modeling the propagation of a wave field. This technique involves expanding a complex wave field into a summation of infinite number of plane waves of the same frequency and different directions. Its ...

of the object through a

procedure, and inherently reconstruct the same information. Therefore, Fourier ptychography and conventional ptychography provides a bridge between

coherent diffraction imaging Coherent diffractive imaging (CDI) is a "lensless" technique for 2D or 3D reconstruction of the image of nanoscale structures such as nanotubes, nanocrystals, porous nanocrystalline layers, defects, potentially proteins, and more. In CDI, a highl ...

and full-field microscopy.

References

{{reflist Microscopy Imaging

Image reconstruction algorithms

Advantages

Relation to ptychography

See also

References