Coherent diffraction imaging

Coherent 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. In CDI, a highly coherent beam of X-rays, electrons or other wavelike particle or photon is incident on an object.

The beam scattered by the object produces a diffraction pattern downstream which is then collected by a detector. This recorded pattern is then used to reconstruct an image via an iterative feedback algorithm. 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. 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). 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. This is called the phase problem.

Imaging process

The overall imaging process can be broken down in four simple steps:
1. Coherent beam scatters from sample
2. Modulus of Fourier transform measured
3. Computational algorithms used to retrieve phases
4. Image recovered by Inverse Fourier transform

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. 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.

To begin, a highly coherent light source of x-rays, electrons, or other wavelike particles must be incident on an object. 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. Due to this incident light, a spot is illuminated on the object being detected and reflected off of its surface. The beam is then scattered by the object producing a diffraction pattern representative of the Fourier transform of the object. The complex diffraction pattern is then collected by the detector and the Fourier transform of all the features that exist on the object’s su