Phase-contrast imaging
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.
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.
If the light is monochromatic (that is, an electromagnetic wave of a single frequency or wavelength), with a frequency close to an atomic transition, the atom will also absorb photons from the light field, reducing the amplitude of the incident wave.
Mathematically, these two interaction mechanisms (dispersive and absorptive) are commonly written as the real and imaginary parts, respectively, of a Complex refractive index.
[citation needed] Dispersive imaging refers strictly to the measurement of the real part of the refractive index.
Since absorption is minimized, the only effect of the gas on the light is to alter the phase of various points along its wavefront.
represents the integral over all small changes in phase to the wavefront due to each point in the area of the object.
Looking at the real part of this expression, we find the sum of a wave with the original unshifted phase
Since imaging systems see only changes in the intensity of the electromagnetic waves, which is proportional to the square of the electric field, we have
The rays which pass through the phase object will diffract as a function of the index of refraction of the medium and diverge as shown by the dotted lines in the figure.
If the sample is magnetically polarized in a direction with non-zero projection onto the light field k-vector, the two circularly polarized beams will interact with the magnetic dipoles of the sample with different strengths, corresponding to a relative phase shift between the two beams.
This phase shift in turns maps to a rotation of the input beam linear polarization.
[citation needed] The quantum physics of the Faraday interaction may be described by the interaction of the second quantized Stokes parameters describing the polarization of a probe light field with the total angular momentum state of the atoms.
Thus, if a BEC or other cold, dense sample of atoms is prepared in a particular spin (hyperfine) state polarized parallel to the imaging light propagation direction, both the density and change in spin state may be monitored by feeding the transmitted probe beam through a beam splitter before imaging onto a camera sensor.
In the dark-field method,[7] the aforementioned phase plate is made completely opaque, such that the 0-order contribution to the beam is totally removed.
By controlling the amount of defocusing one can thus achieve an effect similar to that of the phase plate in standard phase-contrast.
This method leverages the complementary intensity changes of transmitted disks at different scattering angles that provide straightforward, dose-efficient, and noise-robust phase imaging from atomic resolution to intermediate length scales, such as both light and heavy atomic columns and nanoscale magnetic phases in FeGe samples.
[citation needed] Phase contrast is used extensively in optical microscopy, in both biological and geological sciences.
[citation needed] 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.
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[15] 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.
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.
Computer simulations are used to determine what sort of contrast different structures may produce in a phase-contrast image.
These commonly use the multislice method of Cowley and Moodie, [22] and include the phase changes due to the lens aberrations.
Instruments that are specifically designed for phase-contrast imaging are called HRTEMs (high resolution transmission electron microscopes), and differ from analytical TEMs mainly in the design of the electron beam column.
Advances in spherical aberration (Cs) correction have enabled a new generation of HRTEMs to reach significantly better resolutions.
