Coherent and phase-sensitive imaging

Alternating projections method

The alternating projections method is an iterative technique that solves constraint problems by projecting an estimate onto constraint sets in turn, underpinning phase retrieval algorithms like Gerchberg-Saxton.

Coherent diffraction imaging

Coherent diffraction imaging (CDI) is a lensless imaging method that reconstructs images of noncrystalline objects from X-ray or electron diffraction patterns, replacing the objective lens with computational phase retrieval.

Coherent diffractive imaging

Coherent diffractive imaging (CDI) reconstructs an image of a sample from the diffraction pattern of a coherent X-ray or electron beam, replacing the lens with computational phase retrieval.

Diffraction before destruction

Diffraction before destruction is a principle in X-ray crystallography in which an ultrashort, intensely bright X-ray pulse records the diffraction pattern of a sample before radiation damage destroys it.

Diffraction microscopy

Diffraction microscopy, also known as coherent diffractive imaging (CDI), is a lensless imaging method that reconstructs a specimen's image computationally from its measured diffraction pattern.

Fourier shell correlation

Fourier shell correlation (FSC) is a resolution measure in three-dimensional electron microscopy, computed between two independently reconstructed 3D volumes, and the standard global metric in cryo-EM.

Fourier transform holography

Fourier transform holography (FTH) is a lensless imaging technique that reconstructs an object from a hologram with a reference wave by a single Fourier transform.

Holographic reconstruction

Holographic reconstruction is a computational imaging method that numerically recovers an object's amplitude and phase from recorded holograms, applied across optical, electron, and X-ray imaging, where the recovered phase carries quantitative information invisible to ordinary cameras.

In-line holography

In-line holography is a holographic imaging technique in which the reference beam and object-scattered light share one optical axis, devised by Dennis Gabor in 1947.

Off-axis holography

Off-axis holography is a holographic recording geometry in which the reference wave strikes the medium at an angle, separating the twin image from the reconstruction.

Phase-shifting holography

Phase-shifting holography is a digital holography technique, proposed by Ichirou Yamaguchi and Tong Zhang in 1997, that recovers the complex object wave from interferograms with known phase shifts.

Ptychographic microscopy

Ptychographic microscopy is a lensless computational imaging method that reconstructs an image from overlapping diffraction patterns, delivering deep sub-ångström resolution in electron microscopy and nanoscale X-ray tomography.

Ptychographic X-ray computed tomography

Ptychographic X-ray computed tomography (PXCT) is a lensless X-ray imaging technique combining ptychography with computed tomography to reconstruct 3D electron density at nanometer resolution, first demonstrated in 2010.

Ptychographic X-ray laminography

Ptychographic X-ray laminography (PyXL) is a non-destructive X-ray imaging technique producing nanoscale 3D images of flat samples, demonstrated in 2019 on integrated circuits at 18.9 nm resolution.

Ptychographic X-ray tomography

Ptychographic X-ray tomography is a lensless 3D X-ray imaging method that scans a focused beam and reconstructs quantitative electron density, achieving resolutions better than 15 nm.

Ptychography

Ptychography is a lensless coherent-diffraction imaging method that scans a probe across a specimen, records overlapping diffraction patterns, and computationally reconstructs amplitude and phase at high resolution.

Single-particle imaging

Single-particle imaging is an X-ray method in which femtosecond pulses from an X-ray free-electron laser record diffraction patterns from individual particles, which are merged into 3D structures without crystallization or radiation damage.

Support constraint

A support constraint in phase retrieval restricts an unknown object to a known finite region, zero outside, driving iterative algorithms like error reduction and hybrid input-output.

Transport-of-intensity equation

The transport-of-intensity equation (TIE) is an equation of optics, derived by Michael Teague in 1982, that recovers a beam's phase from intensity measurements alone, without interferometry.