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The result, θ = 4.56/D, with D in inches and θ in arcseconds, is slightly narrower than calculated with the Rayleigh criterion. A calculation using Airy discs as point spread function shows that at Dawes' limit there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip. [3]
Rayleigh defined the somewhat arbitrary "Rayleigh criterion" that two points whose angular separation is equal to the Airy disk radius to first null can be considered to be resolved. It can be seen that the greater the diameter of the lens or its aperture, the greater the resolution.
Rayleigh criterion may refer to: Angular resolution § The Rayleigh criterion , optical angular resolution Taylor–Couette flow § Rayleigh's criterion , instability criterion in Taylor–Couette flow
Dawes' limit is a formula to express the maximum resolving power of a microscope or telescope. [1] It is so named after its discoverer, William Rutter Dawes , [ 2 ] although it is also credited to Lord Rayleigh .
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 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 , traveling in a medium with refractive index and converging to a spot with half-angle will have a minimum resolvable distance of
The Rayleigh criterion for barely resolving two objects that are point sources of light, such as stars seen through a telescope, is that the center of the Airy disk for the first object occurs at the first minimum of the Airy disk of the second. This means that the angular resolution of a diffraction-limited system is given by the same formulae.
In optics, Rayleigh proposed a well-known criterion for angular resolution. His derivation of the Rayleigh–Jeans law for classical black-body radiation later played an important role in the birth of quantum mechanics (see ultraviolet catastrophe). Rayleigh's textbook The Theory of Sound (1877) is still used today by acousticians and