DiProI Research

Coherent Diffraction Imaging (CDI)

In Coherent Diffraction Imaging (CDI), when coherent X-rays impinge on the sample, the magnitude of the scattered radiation field is detected as a diffraction pattern; provided that the pattern is sufficiently "oversampled" to recover the radiation phases, it can be mathematically "inverted" to recover an image of the object's charge-density distribution.
In this lensless microscopy technique, a phase retrieval algorithm applied to the acquired diffraction pattern replaces the image-forming optics, used in classical X-ray microscopes, making CDI free of the resolution limitations imposed by optics aberrations and efficiency. Using FELs, CDI is approaching the theoretical spatial resolution, determined only by the FEL wavelength, in the nanometer range, the degree of beam coherence and the angle to which the speckle pattern is detected. Thanks to the almost full coherence and extreme brightness of the FEL pulses, CDI has become a key technique for sampling building blocks of matter.
Femtosecond single shot CDI experiments not only allow to image the sample before radiation-induced changes occur, but also make femtosecond time resolved experiments possible.
Example depicting optical camera imaging and lensless imaging
In lensless imaging, the role of the focusing optics between sample and detector is replaced by a phase retrieval algorithm applyed to the acquired diffraction pattern.

Phase retrieval algorithm

The microscopy image of the sample is the inverse Fourier transform of the complex electromagnetic field observed at the detector plane. Since the detectors can record only the intensity of the speckles, the phase is lost and has to be recovered through computational trials to reconstruct the specimen. Many kinds of recursive phase retrieval algorithms can be implemented, depending on previous knowledge of the sample, symmetry, boundary conditions.
Starting from the acquired diffraction pattern, with arbitrary phases given to each point, as a guess for the electromagnetic field at the detector, a first guess of the sample’s image is obtained through an inverse fast Fourier transform. Real space constraints are applied before implementing a fast Fourier transform, giving a second guess for the electromagnetic field, which phases are kept, while intensities are replaced with the actual data image.
After several iterations, the algorithm converges to the two actual complex images, both in the Fourier space and in the real space domain, giving the desired microscopy image of the sample.
Last Updated on Wednesday, 16 October 2019 12:22