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Considering green light around 500 nm and a NA of 1, the Abbe limit is roughly = = (0.25 μm), which is small compared to most biological cells (1 μm to 100 μm), but large compared to viruses (100 nm), proteins (10 nm) and less complex molecules (1 nm). To increase the resolution, shorter wavelengths can be used such as UV and X-ray microscopes.
The formal Rayleigh criterion is close to the empirical resolution limit found earlier by the English astronomer W. R. Dawes, who tested human observers on close binary stars of equal brightness. The result, θ = 4.56/ D , with D in inches and θ in arcseconds , is slightly narrower than calculated with the Rayleigh criterion.
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.
The ability of a lens to resolve detail is usually determined by the quality of the lens, but is ultimately limited by diffraction.Light coming from a point source in the object diffracts through the lens aperture such that it forms a diffraction pattern in the image, which has a central spot and surrounding bright rings, separated by dark nulls; this pattern is known as an Airy pattern, and ...
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 ...
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 ...
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By 1978, the first theoretical ideas had been developed to break the Abbe limit, which called for using a 4Pi microscope as a confocal laser-scanning fluorescence microscope where the light is focused from all sides to a common focus that is used to scan the object by 'point-by-point' excitation combined with 'point-by-point' detection. [14]