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The observation of sub-wavelength structures with microscopes is difficult because of the Abbe diffraction limit. Ernst Abbe found in 1873, [ 2 ] and expressed as a formula in 1882, [ 3 ] that light with wavelength λ {\displaystyle \lambda } , traveling in a medium with refractive index n {\displaystyle n} and converging to a spot with half ...
In that case, the angular resolution of an optical system can be estimated (from the diameter of the aperture and the wavelength of the light) by the Rayleigh criterion defined by Lord Rayleigh: two point sources are regarded as just resolved when the principal diffraction maximum (center) of the Airy disk of one image coincides with the first ...
Sparrow's resolution limit is nearly equivalent to the theoretical diffraction limit of resolution, the wavelength of light divided by the aperture diameter, and about 20% smaller than the Rayleigh limit. For example, in a 200 mm (eight-inch) telescope, Rayleigh's resolution limit is 0.69 arc seconds, Sparrow's resolution limit is 0.54 arc seconds.
Also common in the microscopy literature is a formula for resolution that treats the above-mentioned concerns about contrast differently. [2] The resolution predicted by this formula is proportional to the Rayleigh-based formula, differing by about 20%. For estimating theoretical resolution, it may be adequate.
Glasses' Abbe numbers, along with their mean refractive indices, are used in the calculation of the required refractive powers of the elements of achromatic lenses in order to cancel chromatic aberration to first order. These two parameters which enter into the equations for design of achromatic doublets are exactly what is plotted on an Abbe ...
The conventional diffraction-limited resolution is given by the Rayleigh criterion as /, where is the numerical aperture and is the wavelength of the illumination source. It is often common to compare the critical feature width to this value, by defining a parameter, k 1 , {\displaystyle k_{1},} such that feature width equals k 1 λ / N A ...
Gaussian beam width () as a function of the axial distance .: beam waist; : confocal parameter; : Rayleigh length; : total angular spread In optics and especially laser science, the Rayleigh length or Rayleigh range, , is the distance along the propagation direction of a beam from the waist to the place where the area of the cross section is doubled. [1]
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