Ptychography
Encyclopedia
Ptychography is a name given to a technique invented by Walter Hoppe
that aims to solve the diffraction-pattern phase problem by interfering adjacent Bragg reflections coherently and thus determining their relative phase. In the original formulation, Hoppe envisaged that such interference could be effected by placing a very narrow aperture in the plane of the specimen so that each reciprocal-lattice point would be spread out and thus overlap with one another. The name ptychography, from the Greek for fold, derives from this optical configuration; each reciprocal lattice
point is convolved with some function, and thus made to interfere with its neighbors. In fact, measuring only the intensities of interfering adjacent diffracted beams still leads to an ambiguity of two possible complex conjugates for each underlying complex diffraction amplitude. The original formulation of ptychography is equivalent to the well known theorem that for a finite specimen (that is one delineated by a narrow aperture, sometimes known as a finite support), the one dimensional phase problem is soluble to within an ambiguity of 2N, where N is the number of Fourier components that make up the specimen. However, such ambiguities may be resolved by changing the phase, profile or position of the illuminating beam in some way. The fact that not only the intensities of the diffracted beams but also the intensities lying midway between the beams, where the convolved Bragg beams interfere, is an alternative statement of the Nyquist–Shannon sampling theorem
for components of diffracted intensity. These components generally have twice the frequency (in reciprocal space) of their underlying complex amplitudes.
Ptychographic imaging along with advances in detectors and computing have resulted in X-ray microscope
s with increased spatial resolution without the need for lenses.
Walter Hoppe
Walter Hoppe was a German physicist and electron microscopist.Walter Hoppe was born in Wallsee/Donau, Austria and obtained his doctorate in chemistry at the German University in Prague under Professor J...
that aims to solve the diffraction-pattern phase problem by interfering adjacent Bragg reflections coherently and thus determining their relative phase. In the original formulation, Hoppe envisaged that such interference could be effected by placing a very narrow aperture in the plane of the specimen so that each reciprocal-lattice point would be spread out and thus overlap with one another. The name ptychography, from the Greek for fold, derives from this optical configuration; each reciprocal lattice
Reciprocal lattice
In physics, the reciprocal lattice of a lattice is the lattice in which the Fourier transform of the spatial function of the original lattice is represented. This space is also known as momentum space or less commonly k-space, due to the relationship between the Pontryagin duals momentum and...
point is convolved with some function, and thus made to interfere with its neighbors. In fact, measuring only the intensities of interfering adjacent diffracted beams still leads to an ambiguity of two possible complex conjugates for each underlying complex diffraction amplitude. The original formulation of ptychography is equivalent to the well known theorem that for a finite specimen (that is one delineated by a narrow aperture, sometimes known as a finite support), the one dimensional phase problem is soluble to within an ambiguity of 2N, where N is the number of Fourier components that make up the specimen. However, such ambiguities may be resolved by changing the phase, profile or position of the illuminating beam in some way. The fact that not only the intensities of the diffracted beams but also the intensities lying midway between the beams, where the convolved Bragg beams interfere, is an alternative statement of the Nyquist–Shannon sampling theorem
Nyquist–Shannon sampling theorem
The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...
for components of diffracted intensity. These components generally have twice the frequency (in reciprocal space) of their underlying complex amplitudes.
Ptychographic imaging along with advances in detectors and computing have resulted in X-ray microscope
X-ray microscope
An X-ray microscope uses electromagnetic radiation in the soft X-ray band to produce images of very small objects.Unlike visible light, X-rays do not reflect or refract easily, and they are invisible to the human eye. Therefore the basic process of an X-ray microscope is to expose film or use a...
s with increased spatial resolution without the need for lenses.