Angular resolution: Difference between revisions

Revision as of 02:21, 10 March 2024

Revision as of 01:03, 25 June 2024

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{{More citations needed|date=January 2012}}

[[File:Event Horizon Telescope and Apollo 16.png|thumb|A series of images representing the magnification of [[M87*]] with an [[angular size]] of some [[microarcsecond]]s, comparable to viewing a tennis ball on the Moon (magnification from top left corner counter−clockwise to the top right corner).]]

'''Angular resolution''' describes the ability of any [[image-forming device]] such as an [[Optical telescope|optical]] or [[radio telescope]], a [[microscope]], a [[camera]], or an [[Human eye|eye]], to distinguish small details of an object, thereby making it a major determinant of [[image resolution]]. It is used in [[optics]] applied to light waves, in [[antenna (radio)|antenna theory]] applied to radio waves, and in [[acoustics]] applied to sound waves. The colloquial use of the term "resolution" sometimes causes confusion; when an optical system is said to have a high resolution or high angular resolution, it means that the perceived distance, or actual angular distance, between resolved neighboring objects is small. The value that quantifies this property, ''θ,'' which is given by the Rayleigh criterion, is low for a system with a high resolution. The closely related term [[spatial resolution]] refers to the precision of a measurement with respect to space, which is directly connected to angular resolution in imaging instruments. 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 [[telescope]]s, long distance [[telephoto lens|telephoto camera lenses]] and [[radio telescope]]s have large apertures.

==Definition of terms==

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:<math> \Delta \ell \approx 1.22 \frac{ f \lambda}{D}</math>.

This is the [[radius]], in the imaging plane, of the smallest spot to which a [[collimated]] beam of [[light]] can be focused, which also corresponds to the size of the smallest object that the lens can resolve.<ref>

{{cite web

|date=2002

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|archive-url=https://web.archive.org/web/20110708214325/http://www.cvimellesgriot.com/products/Documents/TechnicalGuide/fundamental-Optics.pdf

|archive-date=2011-07-08

}}</ref> The size is proportional to wavelength, ''λ'', and thus, for example, [[blue]] light can be focused to a smaller spot than [[red]] light. If the lens is focusing a beam of [[light]] with a finite extent (e.g., a [[laser]] beam), the value of ''D'' corresponds to the [[diameter]] of the light beam, not the lens.{{refn|group=Note|name=GaussianNote|In the case of laser beams, a [[Gaussian beam|Gaussian Optics]] analysis is more appropriate than the Rayleigh criterion, and may reveal a smaller diffraction-limited spot size than that indicated by the formula above.}} Since the spatial resolution is inversely proportional to ''D'', this leads to the slightly surprising result that a wide beam of light may be focused toon a smaller spot than a narrow one. This result is related to the [[Fourier uncertainty principle|Fourier properties]] of a lens.

A similar result holds for a small sensor imaging a subject at infinity: The angular resolution can be converted to a spatial resolution on the sensor by using ''f'' as the distance to the image sensor; this relates the spatial resolution of the image to the [[f-number]], {{f/}}#: