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Ptychography (/t(a)ɪˈkɒgrəfi/ t(a)i-KO-graf-ee) is a computational microscopy method and a major advance of coherent diffractive imaging (CDI), which was first experimentally demonstrated in 1999 using synchrotron X-rays and iterative phase retrieval. It unifies principles from
microscopy Microscopy is the technical field of using microscopes to view subjects too small to be seen with the naked eye (objects that are not within the resolution range of the normal eye). There are three well-known branches of microscopy: optical mic ...
and
crystallography Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...
to reconstruct high-resolution, quantitative images by analyzing a series of overlapping coherent diffraction patterns acquired as a focused beam is scanned across the sample. Its defining characteristic is translational invariance, which means that the
interference pattern In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater amplitude (constructive int ...
s are generated by one constant function (e.g. a field of illumination or an
aperture stop In optics, the aperture of an optical system (including a system consisting of a single lens) is the hole or opening that primarily limits light propagated through the system. More specifically, the entrance pupil as the front side image of ...
) moving laterally by a known amount with respect to another constant function (the specimen itself or a wave field). The interference patterns occur some distance away from these two components, so that the scattered waves spread out and "fold" (, "ptychē" is 'fold') into one another as shown in the figure. Ptychography can be used with
visible light Light, visible light, or visible radiation is electromagnetic radiation that can be perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400–700 nanometres (nm ...
,
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
s,
extreme ultraviolet Extreme ultraviolet radiation (EUV or XUV) or high-energy ultraviolet radiation is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths shorter than the hydrogen Lyman-alpha line from 121  nm down to ...
(EUV) or
electrons The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
. Unlike conventional lens imaging, ptychography is unaffected by lens-induced aberrations or diffraction effects caused by limited
numerical aperture In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, has the property ...
. This is particularly important for atomic-scale wavelength imaging, where it is difficult and expensive to make good-quality lenses with high numerical aperture. Another important advantage of the technique is that it allows transparent objects to be seen very clearly. This is because it is sensitive to the
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 mathematica ...
of the radiation that has passed through a specimen, and so it does not rely on the object absorbing radiation. In the case of visible-light biological microscopy, this means that cells do not need to be stained or labelled to create contrast.


Phase recovery

Although the
interference pattern In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater amplitude (constructive int ...
s used in ptychography can only be measured in
intensity Intensity may refer to: In colloquial use * Strength (disambiguation) *Amplitude * Level (disambiguation) * Magnitude (disambiguation) In physical sciences Physics *Intensity (physics), power per unit area (W/m2) *Field strength of electric, m ...
, the mathematical constraints provided by the translational invariance of the two functions (illumination and object), together with the known shifts between them, means that the
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 mathematica ...
of the wavefield can be recovered by an inverse computation. Ptychography thus provides a comprehensive solution to the so-called "
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 ...
". Once this is achieved, all the information relating to the scattered
wave In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from List of types of equilibrium, equilibrium) of one or more quantities. ''Periodic waves'' oscillate repeatedly about an equilibrium ...
( modulus and phase) has been recovered, and so virtually perfect images of the object can be obtained. There are various strategies for performing this inverse phase-retrieval calculation, including direct Wigner distribution deconvolution (WDD) and iterative methods. The difference map algorithm developed by Thibault and co-workers is available in a downloadable package calle
PtyPy


Optical configurations

There are many optical configurations for ptychography: mathematically, it requires two invariant functions that move across one another while an interference pattern generated by the product of the two functions is measured. The interference pattern can be a
diffraction pattern Diffraction is the deviation of waves from straight-line propagation without any change in their energy due to an obstacle or through an aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wav ...
, a Fresnel diffraction pattern or, in the case of Fourier ptychography, an
image An image or picture is a visual representation. An image can be Two-dimensional space, two-dimensional, such as a drawing, painting, or photograph, or Three-dimensional space, three-dimensional, such as a carving or sculpture. Images may be di ...
. The "ptycho"
convolution In mathematics (in particular, functional analysis), convolution is a operation (mathematics), mathematical operation on two function (mathematics), functions f and g that produces a third function f*g, as the integral of the product of the two ...
in a Fourier ptychographic image derived from the
impulse response In signal processing and control theory, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse (). More generally, an impulse response is the reac ...
function of the
lens A lens is a transmissive optical device that focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements'') ...
.


The single aperture

This is conceptually the simplest ptychographical arrangement. The
detector A sensor is often defined as a device that receives and responds to a signal or stimulus. The stimulus is the quantity, property, or condition that is sensed and converted into electrical signal. In the broadest definition, a sensor is a devi ...
can either be a long way from the object (i.e. in the
Fraunhofer diffraction In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when plane waves are incident on a diffracting object, and the diffraction pattern is viewed at a sufficiently long distance (a distance satisfying Fraunhofer ...
plane Plane most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface * Plane (mathematics), generalizations of a geometrical plane Plane or planes may also refer to: Biology * Plane ...
), or closer by, in the Fresnel regime. An advantage of the Fresnel regime is that there is no longer a very high-intensity beam at the centre of the diffraction pattern, which can otherwise saturate the detector
pixel In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a Raster graphics, raster image, or the smallest addressable element in a dot matrix display device. In most digital display devices, p ...
s there.


Focused-probe ptychography

A lens is used to form a tight crossover of the illuminating beam at the plane of the specimen. The configuration is used in the scanning transmission electron microscope (STEM), and often in high-resolution
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
ptychography. The specimen is sometimes shifted up or downstream of the probe crossover so as to allow the size of the patch of illumination to be increased, thus requiring fewer diffraction patterns to scan a wide
field of view The field of view (FOV) is the angle, angular extent of the observable world that is visual perception, 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 elec ...
.


Near-field ptychography

This uses a wide field of illumination. To provide
magnification Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a size ratio called optical magnification. When this number is less than one, it refers to a reduction in size, so ...
, a diverging beam is incident on the specimen. An out-of-focus image, which appears as a Fresnel interference pattern, is projected onto the detector. The illumination must have phase
distortion In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
s in it, often provided by a
diffuser Diffuser may refer to: Aerodynamics * Diffuser (automotive), a shaped section of a car's underbody which improves the car's aerodynamic properties * Part of a jet engine air intake, especially when operated at supersonic speeds * The channel bet ...
that scrambles the phase of the incident wave before it reaches the specimen, otherwise the image remains constant as the specimen is moved, so there is no new ptychographical information from one position to the next. In the
electron microscope An electron microscope is a microscope that uses a beam of electrons as a source of illumination. It uses electron optics that are analogous to the glass lenses of an optical light microscope to control the electron beam, for instance focusing it ...
, a lens can be used to map the magnified Fresnel image onto the detector.


Fourier ptychography

A conventional microscope is used with a relatively small
numerical aperture In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. By incorporating index of refraction in its definition, has the property ...
objective lens In optical engineering, an objective is an optical element that gathers light from an object being observed and focuses the light rays from it to produce a real image of the object. Objectives can be a single lens or mirror, or combinations of ...
. The specimen is illuminated from a series of different angles. Parallel beams coming out of the specimen are brought to a
focus Focus (: foci or focuses) may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in East Australia Film *Focus (2001 film), ''Focus'' (2001 film), a 2001 film based on the Arthur Miller novel *Focus (2015 ...
in the back
focal plane In Gaussian optics, the cardinal points consist of three pairs of points located on the optical axis of a rotationally symmetric, focal, optical system. These are the '' focal points'', the principal points, and the nodal points; there are two ...
of the objective lens, which is therefore a Fraunhofer diffraction pattern of the specimen exit wave ( Abbe’s theorem). Tilting the illumination has the effect of shifting the diffraction pattern across the objective
aperture In optics, the aperture of an optical system (including a system consisting of a single lens) is the hole or opening that primarily limits light propagated through the system. More specifically, the entrance pupil as the front side image o ...
(which also lies in the back focal plane). Now the standard ptychographical shift invariance principle applies, except that the diffraction pattern is acting as the object and the back focal plane stop is acting like the illumination function in conventional ptychography. The image is in the Fraunhofer diffraction plane of these two functions (another consequence of Abbe's theorem), just like in conventional ptychography. The only difference is that the method reconstructs the diffraction pattern, which is much wider than the aperture stop limitation. A final
Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the tr ...
must be undertaken to produce the
high-resolution Image resolution is the level of detail of an image. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies ...
image. All the reconstruction algorithms used in conventional ptychography apply to Fourier ptychography, and indeed nearly all the diverse extensions of conventional ptychography have been used in Fourier ptychography.


Imaging ptychography

A lens is used to make a conventional image. An aperture in the image plane acts equivalently to the illumination in conventional ptychography, while the image corresponds to the specimen. The detector lies in the Fraunhofer or Fresnel diffraction plane downstream of the image and aperture.


Bragg ptychography or reflection ptychography

This geometry can be used either to map surface features or to measure strain in crystalline specimens. Shifts in the specimen surface, or the atomic
Bragg plane In physics, a Bragg plane is a Plane (geometry), plane in reciprocal space which bisects a reciprocal lattice vector, \scriptstyle \mathbf, at right angles. The Bragg plane is defined as part of the Von Laue condition for Interference (wave prop ...
s perpendicular to the surface, appear in the phase of the ptychographic image.


Vectorial ptychography

Vectorial ptychography needs to be invoked when the multiplicative model of the interaction between the probe and the specimen cannot be described by scalar quantities. This happens typically when
polarized light , or , is a property of transverse waves which specifies the geometrical orientation of the oscillations. In a transverse wave, the direction of the oscillation is perpendicular to the direction of motion of the wave. One example of a polarize ...
probes an anisotropic specimen, and when this interaction modifies the state of polarization of light. In that case, the interaction needs to be described by the Jones formalism, where field and object are described by a two-component complex vector and a 2×2 complex matrix respectively. The optical configuration for vectorial ptychography is similar to that of classical (scalar) ptychography, although a control of light polarization (before and after the specimen) needs to be implemented in the setup. Jones maps of the specimens can be retrieved, allowing the quantification of a wide range of optical properties (phase,
birefringence Birefringence, also called double refraction, is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light. These optically anisotropic materials are described as birefrin ...
, orientation of neutral axes, diattenuation, etc.). Similarly to scalar ptychography, the probes used for the measurement can be jointly estimated together with the specimen. As a consequence, vectorial ptychography is also an elegant approach for quantitative imaging of coherent vectorial light beams (mixing wavefront and polarization features).


Advantages


Lens insensitive

Ptychography can be undertaken without using any lenses at all, although most implementations use a lens of some type, if only to
condense Condensation is the change of the state of matter from the gas phase into the liquid phase, and is the reverse of vaporization. The word most often refers to the water cycle. It can also be defined as the change in the state of water vapor ...
radiation In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or a material medium. This includes: * ''electromagnetic radiation'' consisting of photons, such as radio waves, microwaves, infr ...
onto the specimen. The detector can measure high angles of scatter, which do not need to pass through a lens. The resolution is therefore only limited by the maximal angle of scatter that reaches the detector, and so avoids the effects of diffraction broadening due to a lens of small numerical aperture or aberrations within the lens. This is key in X-ray,
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
and
EUV Extreme ultraviolet radiation (EUV or XUV) or high-energy ultraviolet radiation is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths shorter than the hydrogen Lyman-alpha line from 121  nm down to t ...
ptychography, where conventional lenses are difficult and expensive to make.


Image phase

Ptychography solves for the phase induced by the
real part In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
of the
refractive index In optics, the refractive index (or refraction index) of an optical medium is the ratio of the apparent speed of light in the air or vacuum to the speed in the medium. The refractive index determines how much the path of light is bent, or refrac ...
of the specimen, as well as
absorption Absorption may refer to: Chemistry and biology *Absorption (biology), digestion **Absorption (small intestine) *Absorption (chemistry), diffusion of particles of gas or liquid into liquid or solid materials *Absorption (skin), a route by which su ...
(the
imaginary part In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form ...
of the refractive index). This is crucial for seeing transparent specimens that do not have significant natural absorption contrast, for example
biological cells The cell is the basic structural and functional unit of all forms of life. Every cell consists of cytoplasm enclosed within a membrane; many cells contain organelles, each with a specific function. The term comes from the Latin word meaning ...
(at
visible light Light, visible light, or visible radiation is electromagnetic radiation that can be perceived by the human eye. Visible light spans the visible spectrum and is usually defined as having wavelengths in the range of 400–700 nanometres (nm ...
wavelength In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same ''phase (waves ...
s), thin high-resolution electron microscopy specimens, and almost all materials at
hard X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
wavelengths. In the latter case, the (
linear In mathematics, the term ''linear'' is used in two distinct senses for two different properties: * linearity of a '' function'' (or '' mapping''); * linearity of a '' polynomial''. An example of a linear function is the function defined by f(x) ...
) phase signal is also ideal for high-resolution X-ray ptychographic
tomography Tomography is imaging by sections or sectioning that uses any kind of penetrating wave. The method is used in radiology, archaeology, biology, atmospheric science, geophysics, oceanography, plasma physics, materials science, cosmochemistry, ast ...
. The strength and contrast of the phase signal also means that far fewer
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless particles that can ...
or
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
counts are needed to make an
image An image or picture is a visual representation. An image can be Two-dimensional space, two-dimensional, such as a drawing, painting, or photograph, or Three-dimensional space, three-dimensional, such as a carving or sculpture. Images may be di ...
: this is very important in electron ptychography, where damage to the specimen is a major issue that must be avoided at all costs.


Tolerance to incoherence

Unlike
holography Holography is a technique that allows a wavefront to be recorded and later reconstructed. It is best known as a method of generating three-dimensional images, and has a wide range of other uses, including data storage, microscopy, and interfe ...
, ptychography uses the object itself as an
interferometer Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber opt ...
. It does not require a
reference beam A reference beam is a laser beam used to read and write holograms. It is one of two laser beams used to create a hologram. In order to read a hologram out, some aspects of the reference beam (namely its angle of incidence, beam profile and wavelen ...
. Although holography can solve the image phase problem, it is very difficult to implement in the electron microscope, where the reference beam is extremely sensitive to magnetic interference or other sources of instability. This is why ptychography is not limited by the conventional "information limit" in conventional electron imaging. Furthermore, ptychographical data is sufficiently diverse to remove the effects of partial coherence that would otherwise affect the reconstructed image.


Self-calibration

The ptychographical
data set A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more table (database), database tables, where every column (database), column of a table represents a particular Variable (computer sci ...
can be posed as a blind deconvolution problem. It has sufficient diversity to solve for both the moving functions (illumination and object), which appear symmetrically in the mathematics of the inversion process. This is now routinely done in any ptychographical
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...
, even if the illumination optics have been previously well characterised. Diversity can also be used to solve retrospectively for errors in the offsets of the two functions, blurring in the scan, detector faults, like missing pixels, etc.


Inversion of multiple scattering

In conventional imaging,
multiple scattering In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiat ...
in a thick sample can seriously complicate, or even entirely invalidate, simple interpretation of an image. This is especially true in electron imaging (where multiple scattering is called " dynamical scattering"). Conversely, ptychography generates estimates of hundreds or thousands of exit waves, each of which contains different scattering information. This can be used to retrospectively remove multiple scattering effects.


Robustness to noise

The number counts required for a ptychography experiment is the same as for a conventional image, even though the counts are distributed over very many diffraction patterns. This is because
dose fractionation Dose fractionation effects are utilised in the treatment of cancer with radiation therapy. When the total dose of radiation is divided into several, smaller doses over a period of several days, there are fewer toxic effects on healthy cells. This m ...
applies to ptychography. Maximum-likelihood methods can be employed to reduce the effects of
Poisson noise Shot noise or Poisson noise is a type of noise which can be modeled by a Poisson process. In electronics shot noise originates from the discrete nature of electric charge. Shot noise also occurs in photon counting in optical devices, where sh ...
.


Applications

Applications of ptychography are diverse because it can be used with any type of radiation that can be prepared as a quasi-monochromatic propagating wave. Ptychographic imaging, along with advances in detectors and computing, has resulted in the development of X-ray microscopes. Coherent beams are required in order to obtain far-field diffraction patterns with speckle patterns. Coherent X-ray beams can be produced by modern
synchrotron radiation Synchrotron radiation (also known as magnetobremsstrahlung) is the electromagnetic radiation emitted when relativistic charged particles are subject to an acceleration perpendicular to their velocity (). It is produced artificially in some types ...
sources,
free-electron laser A free-electron laser (FEL) is a fourth generation light source producing extremely brilliant and short pulses of radiation. An FEL functions much as a laser but employs relativistic electrons as a active laser medium, gain medium instead of using ...
s and high-harmonic sources. In terms of routine analysis, X-ray ptychotomography is today the most commonly used technique. It has been applied to many
materials A material is a substance or mixture of substances that constitutes an object. Materials can be pure or impure, living or non-living matter. Materials can be classified on the basis of their physical and chemical properties, or on their ge ...
problems including, for example, the study of
paint Paint is a material or mixture that, when applied to a solid material and allowed to dry, adds a film-like layer. As art, this is used to create an image or images known as a painting. Paint can be made in many colors and types. Most paints are ...
, imaging battery chemistry, imaging stacked layers of tandem solar cells, and the dynamics of
fracture Fracture is the appearance of a crack or complete separation of an object or material into two or more pieces under the action of stress (mechanics), stress. The fracture of a solid usually occurs due to the development of certain displacemen ...
. In the X-ray regime, ptychography has also been used to obtain a 3D mapping of the disordered structure in the white ''
Cyphochilus ''Cyphochilus'' is a genus of beetles with unusually bright white scales that cover the whole exoskeleton. ''Cyphochilus'' inhabit Southeast Asia. Etymology Probably the same etymology as the former '' Cyphochilus'' orchid: from the Greek ''k ...
'' beetle, and a 2D imaging of the domain structure in a bulk heterojunction for polymer solar cells. Visible-light ptychography has been used for imaging live biological cells and studying their growth, reproduction and motility. In its vectorial version, it can also be used for mapping quantitative optical properties of anisotropic materials such as biominerals or metasurfaces Electron ptychography is uniquely (amongst other electron imaging modes) sensitive to both heavy and light atoms simultaneously. It has been used, for example, in the study of
nanostructure A nanostructure is a structure of intermediate size between microscopic and molecular structures. Nanostructural detail is microstructure at nanoscale. In describing nanostructures, it is necessary to differentiate between the number of dimen ...
drug-delivery mechanisms by looking at drug molecules stained by heavy atoms within light
carbon nanotube A carbon nanotube (CNT) is a tube made of carbon with a diameter in the nanometre range ( nanoscale). They are one of the allotropes of carbon. Two broad classes of carbon nanotubes are recognized: * ''Single-walled carbon nanotubes'' (''S ...
s cages. With
electron beams Cathode rays are streams of electrons observed in discharge tubes. If an evacuated glass tube is equipped with two electrodes and a voltage is applied, glass behind the positive electrode is observed to glow, due to electrons emitted from the ca ...
, shorter-wavelength, higher-energy electrons used for higher-resolution imaging can cause damage to the sample by ionising it and breaking bonds, but electron-beam ptychography has now produced record-breaking images of molybdenum disulphide with a resolution of 0.039 nm using a lower-energy electron beam and detectors that are able to detect single electrons, so atoms can be located with more precision. Ptychography has several applications in the
semiconductor A semiconductor is a material with electrical conductivity between that of a conductor and an insulator. Its conductivity can be modified by adding impurities (" doping") to its crystal structure. When two regions with different doping level ...
industry, including imaging their surfaces using
EUV Extreme ultraviolet radiation (EUV or XUV) or high-energy ultraviolet radiation is electromagnetic radiation in the part of the electromagnetic spectrum spanning wavelengths shorter than the hydrogen Lyman-alpha line from 121  nm down to t ...
, their 3D bulk structure using X-rays, and mapping strain fields by Bragg ptychography, for example, in
nanowire file:[email protected], upright=1.2, Crystalline 2×2-atom tin selenide nanowire grown inside a single-wall carbon nanotube (tube diameter ≈1 nm). A nanowire is a nanostructure in the form of a wire with the diameter of the order of a nanometre ( ...
s.


History


Beginnings in crystallography

The name "ptychography" was coined by Hegerl and Hoppe in 1970 to describe a solution to the
crystallographic Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...
phase problem first suggested by Hoppe in 1969. The idea required the specimen to be highly ordered (a
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
) and to be illuminated by a precisely engineered wave so that only two pairs of diffraction peaks interfere with one another at a time. A shift in the illumination changes the interference condition (by the Fourier shift theorem). The two measurements can be used to solve for the relative phase between the two diffraction peaks by breaking a complex-conjugate
ambiguity Ambiguity is the type of meaning (linguistics), meaning in which a phrase, statement, or resolution is not explicitly defined, making for several interpretations; others describe it as a concept or statement that has no real reference. A com ...
that would otherwise exist. Although the idea encapsulates the underlying concept of
interference Interference is the act of interfering, invading, or poaching. Interference may also refer to: Communications * Interference (communication), anything which alters, modifies, or disrupts a message * Adjacent-channel interference, caused by extra ...
by convolution (ptycho) and translational invariance, crystalline ptychography cannot be used for imaging of
continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...
objects, because very many (up to millions) of beams interfere at the same time, and so the
phase difference In physics and mathematics, the phase (symbol φ or ϕ) of a wave or other periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is expressed in such a s ...
s are inseparable. Hoppe abandoned his concept of ptychography in 1973.


Development of inversion methods

Between 1989 and 2007 Rodenburg and co-workers developed various inversion methods for the general imaging ptychographic phase problem, including Wigner-distribution deconvolution (WDD), SSB, the "PIE"
iterative method In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an " ...
(a precursor of the "ePIE" algorithm), demonstrating proof-of-principles at various wavelengths. Chapman used the WDD inversion method to demonstrate the first implementation of
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
ptychography in 1996. The smallness of
computer A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
s and poor quality of
detectors A sensor is often defined as a device that receives and responds to a signal or stimulus. The stimulus is the quantity, property, or condition that is sensed and converted into electrical signal. In the broadest definition, a sensor is a devi ...
at that time may account for the fact that ptychography was not at first taken up by other workers.


General uptake

Widespread interest in ptychography only started after the first demonstration of
iterative Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...
phase-retrieval
X-ray An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
ptychography in 2007 at the Swiss Light Source (SLS). The conceptual framework of modern ptychography builds on coherent diffractive imaging (CDI), which was first experimentally demonstrated in 1999 by
Miao Miao may refer to: * Miao people, linguistically and culturally related group of people, recognized as such by the government of the People's Republic of China * Miao script or Pollard script, writing system used for Miao languages * Miao (Unicode ...
and colleagues using synchrotron X-rays and iterative phase retrieval. Progress at X-ray wavelengths was then quick. By 2010, the SLS had developed X-ray ptychotomography, now a major application of the technique. Thibault, also working at the SLS, developed the difference-map (DM) iterative inversion algorithm and mixed-state ptychography. Since 2010, several groups have developed the capabilities of ptychography to characterize and improve
reflective Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. The ...
and
refractive In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenome ...
X-ray optics X-ray optics is the branch of optics dealing with X-rays, rather than visible light. It deals with focusing and other ways of manipulating the X-ray beams for research techniques such as X-ray diffraction, X-ray crystallography, X-ray fluorescence, ...
. Bragg ptychography, for measuring strain in
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macros ...
s, was demonstrated by Hruszkewycz in 2012. In 2012 it was also shown that
electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...
ptychography could improve on the resolution of an
electron lens Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a gr ...
by a factor of five, a method which was used in 2018 to provide the highest- resolution transmission image ever obtained earning a
Guinness world record ''Guinness World Records'', known from its inception in 1955 until 1999 as ''The Guinness Book of Records'' and in previous United States editions as ''The Guinness Book of World Records'', is a British reference book published annually, listi ...
, and once again in 2021 to achieve an even better resolution. Real-space light ptychography became available in
commercial system
for
live-cell imaging Live-cell imaging is the study of living cells using time-lapse microscopy. It is used by scientists to obtain a better understanding of biological function through the study of cellular dynamics. Live-cell imaging was pioneered in the first de ...
in 2013. Fourier ptychography using
iterative method In computational mathematics, an iterative method is a Algorithm, mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the ''i''-th approximation (called an " ...
s was also demonstrated by Zheng et al. in 2013, a field which is growing rapidly. The group of
Margaret Murnane Margaret Mary Murnane NAS AAA&S (born 23 January 1959) is an Irish physicist, who served as a distinguished professor of physics at the University of Colorado Boulder, having moved there in 1999, with past positions at the University of Michig ...
and Henry Kapteyn at
JILA JILA, formerly known as the Joint Institute for Laboratory Astrophysics, is a physical science research institute in the United States. JILA is located on the University of Colorado Boulder campus. JILA was founded in 1962 as a joint institute o ...
,
CU Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a public research university in Boulder, Colorado, United States. Founded in 1876, five months before Colorado became a state, it is the flagship university of the University o ...
demonstrated EUV reflection ptychographic imaging in 2014.


See also

* Jianwei (John) Miao – led the first experimental demonstration of coherent diffractive imaging (CDI) and contributed to its evolution into computational microscopy techniques such as atomic electron tomography (AET) and ptychographic AET (pAET). * Coherent diffractive imaging (CDI) *
Phase retrieval Phase retrieval is the process of algorithmically finding solutions to the phase problem. Given a complex spectrum 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 spat ...
* Computational imaging * Fourier ptychography


References


External links


Cornell researchers see atoms at record resolution
cornell.edu at 20 May 2021 {{X-ray science Microscopy Laboratory techniques in condensed matter physics