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As an example, a telescope having an f /6 objective and imaging at 0.55 micrometers has a spatial cutoff frequency of 303 cycles/millimeter. High-resolution black-and-white film is capable of resolving details on the film as small as 3 micrometers or smaller, thus its cutoff frequency is about 150 cycles/millimeter.
The Rayleigh criterion shows that the minimum angular spread that can be resolved by an image-forming system is limited by diffraction to the ratio of the wavelength of the waves to the aperture width. For this reason, high-resolution imaging systems such as astronomical telescopes, long distance telephoto camera lenses and radio telescopes ...
The diffraction-limited angular resolution, in radians, of an instrument is proportional to the wavelength of the light being observed, and inversely proportional to the diameter of its objective's entrance aperture. For telescopes with circular apertures, the size of the smallest feature in an image that is diffraction limited is the size of ...
The f-number N is given by: = where f is the focal length, and D is the diameter of the entrance pupil (effective aperture).It is customary to write f-numbers preceded by "f /", which forms a mathematical expression of the entrance pupil's diameter in terms of f and N. [1]
Due to Snell's law, the numerical aperture remains the same: NA = n 1 sin θ 1 = n 2 sin θ 2. In optics, the numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.
The conditions for being in the far field and exhibiting an Airy pattern are: the incoming light illuminating the aperture is a plane wave (no phase variation across the aperture), the intensity is constant over the area of the aperture, and the distance from the aperture where the diffracted light is observed (the screen distance) is large ...
Lens aperture diffraction also limits MTF. Whilst reducing the aperture of a lens usually reduces aberrations and hence improves the flatness of the MTF, there is an optimum aperture for any lens and image sensor size beyond which smaller apertures reduce resolution because of diffraction, which spreads light across the image sensor.
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.
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