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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Diffraction-limited system | 3/3 | https://en.wikipedia.org/wiki/Diffraction-limited_system | reference | science, encyclopedia | 2026-05-05T09:47:17.785058+00:00 | kb-cron |
=== Near-field techniques === The diffraction limit is only valid in the far field as it assumes that no evanescent fields reach the detector. Various near-field techniques that operate less than ≈1 wavelength of light away from the image plane can obtain substantially higher resolution. These techniques exploit the fact that the evanescent field contains information beyond the diffraction limit which can be used to construct very high resolution images, in principle beating the diffraction limit by a factor proportional to how well a specific imaging system can detect the near-field signal. For scattered light imaging, instruments such as near-field scanning optical microscopes and nano-FTIR, which are built atop atomic force microscope systems, can be used to achieve up to 10-50 nm resolution. The data recorded by such instruments often requires substantial processing, essentially solving an optical inverse problem for each image. Metamaterial-based superlenses can image with a resolution better than the diffraction limit by locating the objective lens extremely close (typically hundreds of nanometers) to the object. In fluorescence microscopy the excitation and emission are typically on different wavelengths. In total internal reflection fluorescence microscopy a thin portion of the sample located immediately on the cover glass is excited with an evanescent field, and recorded with a conventional diffraction-limited objective, improving the axial resolution. However, because these techniques cannot image beyond 1 wavelength, they cannot be used to image into objects thicker than 1 wavelength which limits their applicability.
=== Far-field techniques === Far-field imaging techniques are most desirable for imaging objects that are large compared to the illumination wavelength but that contain fine structure. This includes nearly all biological applications in which cells span multiple wavelengths but contain structure down to molecular scales. In recent years several techniques have shown that sub-diffraction limited imaging is possible over macroscopic distances. These techniques usually exploit optical nonlinearity in a material's reflected light to generate resolution beyond the diffraction limit. Among these techniques, the STED microscope has been one of the most successful. In STED, multiple laser beams are used to first excite, and then quench fluorescent dyes. The nonlinear response to illumination caused by the quenching process in which adding more light causes the image to become less bright generates sub-diffraction limited information about the location of dye molecules, allowing resolution far beyond the diffraction limit provided high illumination intensities are used.
== Laser beams == The limits on focusing or collimating a laser beam are very similar to the limits on imaging with a microscope or telescope. The only difference is that laser beams are typically soft-edged beams. This non-uniformity in light distribution leads to a coefficient slightly different from the 1.22 value familiar in imaging. However, the scaling with wavelength and aperture is exactly the same. The beam quality of a laser beam is characterized by how well its propagation matches an ideal Gaussian beam at the same wavelength. The beam quality factor M squared (M2) is found by measuring the size of the beam at its waist, and its divergence far from the waist, and taking the product of the two, known as the beam parameter product. The ratio of this measured beam parameter product to that of the ideal is defined as M2, so that M2=1 describes an ideal beam. The M2 value of a beam is conserved when it is transformed by diffraction-limited optics. The outputs of many low and moderately powered lasers have M2 values of 1.2 or less, and are essentially diffraction-limited. The M2 factor enters various equations, correcting for the non-ideality of the beam. For example, the smallest possible spot size obtainable by focusing a parallel laser beam by a lens is
d
=
4
λ
f
M
2
π
D
{\displaystyle d={\frac {4\lambda fM^{2}}{\pi D}}}
, where
f
{\displaystyle f}
is the focal length of the lens and
D
{\displaystyle D}
is the beam diameter.
== Other waves == The same principle applies to other wave-based sensors, such as radar and the human ear. It can also be generalized to massive particles with the de Broglie wavelength, inversely proportional to the particle momentum, serving as an effective wavelength. For example, an electron at an energy of 10 keV has a wavelength of about 0.01 nm, allowing the electron microscope (SEM or TEM) to achieve high resolution images.
== See also == Rayleigh criterion
== References ==
== External links == Puts, Erwin (September 2003). "Chapter 3: 180 mm and 280 mm lenses" (PDF). Leica R-Lenses. Leica Camera. Archived from the original (PDF) on December 17, 2008. Describes the Leica APO-Telyt-R 280mm f/4, a diffraction-limited photographic lens.