![]() The first idea was the realization by Sayre in 1952 that Bragg diffraction under-samples diffracted intensity relative to Shannon's theorem. Three ideas developed that enabled the reconstruction of real space images from diffraction patterns. This results in an ill-posed inverse problem as any phase could be assigned to the amplitudes prior to an inverse Fourier transform to real space. ![]() When a diffraction pattern is collected, the data is described in terms of absolute counts of photons or electrons, a measurement which describes amplitudes but loses phase information. In typical microscopy using lenses there is no phase problem, as phase information is retained when waves are refracted. ![]() There are two relevant parameters for diffracted waves: amplitude and phase. The hope is that using CDI would produce a higher resolution image due to its aberration-free design and computational algorithms. Lastly, a computer algorithm transforms the diffraction information into the real space and produces an image observable by the human eye this image is what we would likely see by means of traditional microscopy techniques. 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.Ī reconstructed image is then made through utilization of an iterative feedback phase-retrieval algorithm where a few hundred of these incident rays are detected and overlapped to provide sufficient redundancy in the reconstruction process. 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. The beam is then scattered by the object producing a diffraction pattern representative of the Fourier transform of the object. ![]() Due to this incident light, a spot is illuminated on the object being detected and reflected off of its surface. This beam, although popularly x-rays, has potential to be made up of electrons due to their decreased overall wavelength this lower wavelength allows for higher resolution and, thus, a clearer final image. To begin, a highly coherent light source of x-rays, electrons, or other wavelike particles must be incident on an object. The diffraction pattern picked up by the detector is in reciprocal space while the final image must be in real space to be of any use to the human eye. In CDI, the objective lens used in a traditional microscope is replaced with computational algorithms and software which are able to convert from the reciprocal space into the real space. Image recovered by Inverse Fourier transform Computational algorithms used to retrieve phasesĤ. The overall imaging process can be broken down in four simple steps:ģ. Applying a simple inverse Fourier transform to information with only intensities is insufficient for creating an image from the diffraction pattern due to the missing phase information. 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). Effectively, the objective lens in a typical microscope is replaced with software to convert from the reciprocal space diffraction pattern into a real space image. This recorded pattern is then used to reconstruct an image via an iterative feedback algorithm. The beam scattered by the object produces a diffraction pattern downstream which is then collected by a detector. In CDI, a highly coherent beam of X-rays, electrons or other wavelike particle or photon is incident on an object. This reciprocal space diffraction image was taken by Ian Robinson's Group to be used in the reconstruction of a real space coherent X-ray diffraction image in 2007.Ĭoherent diffractive imaging ( CDI) is a "lensless" technique for 2D or 3D reconstruction of the image of nanoscale structures such as nanotubes, nanocrystals, porous nanocrystalline layers, defects, potentially proteins, and more. A diffraction pattern of a gold nanocrystal formed from using a nano area beam of coherent X-rays.
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