Coherent diffraction imaging
[5] A comprehensive review titled Computational microscopy with coherent diffractive imaging and ptychography was published by Miao in Nature in 2025.
The advantage in using no lenses is that the final image is aberration–free and so resolution is only diffraction and dose limited (dependent on wavelength, aperture size and exposure).
The complex diffraction pattern is then collected by the detector and the Fourier transform of all the features that exist on the object’s surface are evaluated.
With the diffraction information being put into the frequency domain, the image is not detectable by the human eye and, thus, very different from what we’re used to observing using normal microscopy techniques.
The hope is that using CDI would produce a higher resolution image due to its aberration-free design and computational algorithms.
[9] In 1998, Miao, Sayre and Chapman used numerical simulations to demonstrate that when the independently measured intensity points is more than the unknown variables, the phase can be in principle retrieved from the diffraction pattern via iterative algorithms.
[10] Finally, Miao and collaborators reported the first experimental demonstration of CDI in 1999 using a secondary image to provide low resolution information.
In a typical reconstruction[2] the first step is to generate random phases and combine them with the amplitude information from the reciprocal space pattern.
In theory this is not necessarily required and algorithms have been developed[18] which impose an evolving support based on the image alone using an auto-correlation function.
The introduction of defects in the crystal leads to an asymmetric diffraction pattern with a complex valued inverse Fourier transform.
Unfortunately, the imaging of complex-valued functions (which for brevity represents the strained field in crystals) is accompanied by complementary problems namely, the uniqueness of the solutions, stagnation of the algorithm etc.
[2] This provides another constraint for the HIO process, thus increasing the efficiency of the algorithm and the amount of information that can be extracted from the diffraction pattern.
Several algorithms exist for this purpose, though they each follow a similar format of iterating between the real and reciprocal space of the object (Pham 2020).
The HIO algorithm relaxes the conditions of ER by gradually reducing the negative densities of the support to zero with each iteration (Fienup 1978).
While HIO allowed for the reconstruction of an image from a noise-free diffraction pattern, it struggled to recover the phase in actual experiments where the Fourier magnitudes were corrupted by noise.
OSS would utilize Gaussian filters to apply a smoothness constraint to the zero-density region which was found to increase robustness to noise and reduce oscillations in reconstruction (Rodriguez 2013).
The magnitude constraint is relaxed into a least-fidelity squares term as a means of lessening the noise in the reciprocal space (Pham 2020).
In one published report[1] a double walled carbon nanotube (DWCNT) was imaged using nano area electron diffraction (NAED) with atomic resolution.
The beam size is limited to nano area with the condenser aperture in order to ensure scattering from only a section of the nanotube of interest.
Using a typical HIO reconstruction method an image is produced with Å resolution in which the DWCNT chirality (lattice structure) can be directly observed.
In 2016 using the coherent diffraction imaging (CXDI) beamline at ESRF (Grenoble, France), the researchers quantified the porosity of large faceted nanocrystalline layers at the origin of photoluminescence emission band in the infrared.
Because of this interference, the static region acts as a time invariant constraint that phases patterns together in fewer iterations (Hung Lo 2018).
Enforcing this static region as a constraint makes in situ CDI more robust to incomplete data and noise interference in the diffraction patterns (Hung Lo 2018).
The extra translational diversity in the data also means the reconstruction procedure can be faster and ambiguities in the solution space are reduced.
