Phase-contrast imaging
Phase-contrast imaging is a method of imaging that has a range of different applications. It exploits differences in the refractive index of different materials to differentiate between structures under analysis. In conventional light microscopy, phase contrast can be employed to distinguish between structures of similar transparency, and to examine crystals on the basis of their double refraction. This has uses in biological, medical and geological science. In X-ray tomography, the same physical principles can be used to increase image contrast by highlighting small details of differing refractive index within structures that are otherwise uniform. In  transmission electron microscopy (TEM), phase contrast enables very high resolution (HR) imaging, making it possible to distinguish features a few Angstrom apart (at this point highest resolution is 40 pm). Light microscopy. Phase contrast takes advantage of the fact that different structures have different refractive indices, and either bend, refract or delay the light passage through the sample by different amounts. The changes in the light passage result in waves being 'out of phase' with others. This effect can be transformed by phase contrast microscopes into amplitude differences that are observable in the eyepieces and are depicted effectively as darker  or brighter areas of the resultant image. Phase contrast is used extensively in optical microscopy, in both biological and geological sciences. In biology, it is employed in viewing unstained biological samples, making it possible to distinguish between structures that are of similar transparency or refractive indices. In geology, phase contrast is exploited to highlight differences between mineral crystals cut to a standardised thin section (usually 30 μm) and mounted under a light microscope. Crystalline materials are capable of exhibiting double refraction, in which light rays entering a crystal are split into two beams that may exhibit different refractive indices, depending  on the angle at which they enter the crystal. The phase contrast between the two rays can be detected with the human eye using particular optical filters. As the exact nature of the double refraction varies for different crystal structures, phase contrast aids in the identification of minerals. X-ray imaging. There are four main techniques for X-ray phase-contrast imaging, which use different principles to convert phase variations in the X-rays emerging from the object into intensity variations at an X-ray detector. Propagation-based phase contrast uses free-space propagation to get edge enhancement, Talbot and  polychromatic far-field interferometry uses a set of diffraction gratings to measure the derivative of the phase, refraction-enhanced imaging uses an analyzer crystal also for differential measurement, and x-ray interferometry uses a crystal interferometer to measure the phase directly. The advantages of these methods compared to normal absorption-contrast X-ray imaging is higher contrast for low-absorbing materials (because phase shift is a different mechanism than absorption) and a contrast-to-noise relationship that increases with spatial frequency (because many phase-contrast techniques detect the first or second derivative of the phase shift), which makes it possible  to see smaller details One disadvantage is that these methods require more sophisticated equipment, such as synchrotron or microfocus X-ray sources, x-ray optics, and high resolution X-ray detectors. This sophisticated equipment provides the sensitivity required to differentiate between small variations in the refractive index of X-rays passing through different media. The refractive index is normally smaller than 1 with a difference from 1 between and . All of these methods produce images that can be used to calculate the projections (integrals) of the refractive index in the imaging direction. For propagation-based phase contrast there are phase -retrieval algorithms, for Talbot interferometry and refraction-enhanced imaging the image is integrated in the proper direction, and for X-ray interferometry phase unwrapping is performed. For this reason they are well suited for tomography, i.e. reconstruction of a 3D-map of the refractive index of the object from many images at slightly different angles. For X-ray radiation the difference from 1 of the refractive index is essentially proportional to the density of the material. Synchrotron X-ray tomography can employ phase contrast imaging to enable imaging of the interior surfaces of objects. In this context, phase contrast imaging  is used to enhance the contrast that would normally be possible from conventional radiographic imaging. A difference in the refractive index between a detail and its surroundings causes a phase shift between the light wave that travels through the detail and that which travels outside the detail. An interference pattern results, marking out the detail. This method has been used to image Precambrian metazoan embryos from the Doushantuo Formation in China, allowing the internal structure of delicate microfossils to be imaged without destroying the original specimen. Transmission electron microscopy. In the field of transmission electron microscopy, phase-contrast imaging may  be employed to image columns of individual atoms. This ability arises from the fact that the atoms in a material diffract electrons as the electrons pass through them (the relative phases of the electrons change upon transmission through the sample), causing diffraction contrast in addition to the already present contrast in the transmitted beam. Phase-contrast imaging is the highest resolution imaging technique ever developed, and can allow for resolutions of less than one angstrom (less than 0.1 nanometres). It thus enables the direct viewing of columns of atoms in a crystalline material. The interpretation of phase-contrast images is  not a straightforward task. Deconvolving the contrast seen in an HR image to determine which features are due to which atoms in the material can rarely, if ever, be done by eye. Instead, because the combination of contrasts due to multiple diffracting elements and planes and the transmitted beam is complex, computer simulations are used to determine what sort of contrast different structures may produce in a phase-contrast image. Thus, a reasonable amount of information about the sample needs to be understood before a phase contrast image can be properly interpreted, such as a conjecture as to what crystal  structure the material has. Phase-contrast images are formed by removing the objective aperture entirely or by using a very large objective aperture. This ensures that not only the transmitted beam, but also the diffracted ones are allowed to contribute to the image. Instruments that are specifically designed for phase-contrast imaging are often called HRTEMs (high resolution transmission electron microscopes), and differ from analytical TEMs mainly in the design of the electron beam column. Whereas analytical TEMs employ additional detectors attached to the column for spectroscopic measurements, HRTEMs have little or no additional attachments so as to ensure a  uniform electromagnetic environment all the way down the column for each beam leaving the sample (transmitted and diffracted). Because phase-contrast imaging relies on differences in phase between electrons leaving the sample, any additional phase shifts that occur between the sample and the viewing screen can make the image impossible to interpret. Thus, a very low degree of lens aberration is also a requirement for HRTEMs, and advances in spherical aberration (Cs) correction have enabled a new generation of HRTEMs to reach resolutions once thought impossible.