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where m is the Bragg order (a positive integer), λ B the diffracted wavelength, Λ the fringe spacing of the grating, θ the angle between the incident beam and the normal (N) of the entrance surface and φ the angle between the normal and the grating vector (K G). Radiation that does not match Bragg's law will pass through the VBG undiffracted.
The beam from a laser with near-ideal beam propagation properties may be described as being diffraction-limited. A diffraction-limited laser beam, passed through diffraction-limited optics, will remain diffraction-limited, and will have a spatial or angular extent essentially equal to the resolution of the optics at the wavelength of the laser.
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. However, electron beams are limited in penetration depth compared to X-rays, as electrons have an inherent mass.
The Compton effect can be understood as high-energy photons scattering in-elastically off individual electrons, [26] when the incoming photon gives part of its energy to the electron, then the scattered photon has lower energy and lower frequency and longer wavelength according to the Planck relation: [28]
The equations below assume a beam with a circular cross-section at all values of z; this can be seen by noting that a single transverse dimension, r, appears.Beams with elliptical cross-sections, or with waists at different positions in z for the two transverse dimensions (astigmatic beams) can also be described as Gaussian beams, but with distinct values of w 0 and of the z = 0 location for ...
Material dispersion can be a desirable or undesirable effect in optical applications. The dispersion of light by glass prisms is used to construct spectrometers and spectroradiometers. However, in lenses, dispersion causes chromatic aberration, an undesired effect that may degrade images in microscopes, telescopes, and photographic objectives.
Scherzer's theorem is a theorem in the field of electron microscopy. It states that there is a limit of resolution for electronic lenses because of unavoidable aberrations. German physicist Otto Scherzer found in 1936 [1] that the electromagnetic lenses, which are used in electron microscopes to focus the electron beam, entail unavoidable ...
The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum.It is usually denoted by , and is closely related to the resolving power of the spectrograph, defined as =, where is the smallest difference in wavelengths that can be distinguished at a wavelength of .