# Angular resolution

spatial resolutionresolutionresolvedresolving powerRayleigh criterionresolution limitspot sizeappears ascriteriondiffraction limited
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.wikipedia
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### Optical resolution

resolutionresolvedresolve
The term resolution or minimum resolvable distance is the minimum distance between distinguishable objects in an image, although the term is loosely used by many users of microscopes and telescopes to describe resolving power.
This standard for separation is also known as the Rayleigh criterion.

Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.
The angular resolution of a dish antenna is determined by the ratio of the diameter of the dish to the wavelength of the radio waves being observed.

### Optical telescope

telescopetelescopesoptical
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.
It is analogous to angular resolution, but differs in definition: instead of separation ability between point-light sources it refers to the physical area that can be resolved.

### John William Strutt, 3rd Baron Rayleigh

Lord RayleighRayleighJohn Strutt
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 of one image coincides with the first minimum of the other.
In optics, Rayleigh proposed a well known criterion for angular resolution.

### Bessel function

modified Bessel functionspherical Bessel functionBessel
This number is more precisely 1.21966989..., the first zero of the order-one Bessel function of the first kind J_{1}(x) divided by π.
Angular resolution

### Diffraction

diffraction patterndiffractdiffracted
The imaging system's resolution can be limited either by aberration or by diffraction causing blurring of the image.
In object space, the corresponding angular resolution is

### Airy disk

Airy diffraction patternAiry Patterndiffraction
Light passing through the lens interferes with itself creating a ring-shape diffraction pattern, known as the Airy pattern, if the wavefront of the transmitted light is taken to be spherical or plane over the exit aperture.
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.

### Aperture synthesis

aperture synthesis imagingsynthetic apertureinterferometric imaging
In order to perform aperture synthesis imaging, a large number of telescopes are required laid out in a 2-dimensional arrangement with a dimensional precision better than a fraction (0.25x) of the required image resolution.
Aperture synthesis or synthesis imaging is a type of interferometry that mixes signals from a collection of telescopes to produce images having the same angular resolution as an instrument the size of the entire collection.

### Astronomical interferometer

astronomical interferometryinterferometerinterferometry
The highest angular resolutions can be achieved by arrays of telescopes called astronomical interferometers: These instruments can achieve angular resolutions of 0.001 arcsecond at optical wavelengths, and much higher resolutions at x-ray wavelengths.
The advantage of this technique is that it can theoretically produce images with the angular resolution of a huge telescope with an aperture equal to the separation between the component telescopes.

### Astronomical seeing

seeingatmospheric seeingatmospheric turbulence
A single optical telescope may have an angular resolution less than one arcsecond, but astronomical seeing and other atmospheric effects make attaining this very hard.
The FWHM of the point spread function (loosely called seeing disc diameter or "seeing") is the best possible angular resolution that can be achieved by an optical telescope in a long-exposure image, and corresponds to the FWHM of the fuzzy blob seen when observing a point-like source (such as a star) through the atmosphere.

### Aperture

aperturesaperture stoplens aperture
The lens' circular aperture is analogous to a two-dimensional version of the single-slit experiment.
Angular resolution

### Wavelength

wavelengthsperiodsubwavelength
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 of one image coincides with the first minimum of the other.
Diffraction is the fundamental limitation on the resolving power of optical instruments, such as telescopes (including radiotelescopes) and microscopes.

### Numerical aperture

apertureshigh numerical aperturehyper-NA
Here NA is the numerical aperture, \theta is half the included angle \alpha of the lens, which depends on the diameter of the lens and its focal length, n is the refractive index of the medium between the lens and the specimen, and \lambda is the wavelength of light illuminating or emanating from (in the case of fluorescence microscopy) the sample.
In microscopy, NA is important because it indicates the resolving power of a lens.

### Diffraction-limited system

diffraction limitdiffraction-limiteddiffraction limitation
Diffraction-limited system
The diffraction-limited angular resolution of a telescopic instrument is proportional to the wavelength of the light being observed, and inversely proportional to the diameter of its objective's entrance aperture.

### Dawes' limit

Dawes resolution limit
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.
Dawes' limit is a formula to express the maximum resolving power of a microscope or telescope.

### Near-field scanning optical microscope

near-field scanning optical microscopynear field scanning optical microscopyscanning near-field optical microscopy
These include optical near-fields (Near-field scanning optical microscope) or a diffraction technique called 4Pi STED microscopy.
The minimum resolution (d) for the optical component are thus limited by its aperture size, and expressed by the Rayleigh criterion:

### Objective (optics)

objectiveobjective lensobjectives
For a microscope, that distance is close to the focal length f of the objective.
A telescope's light-gathering power and angular resolution are both directly related to the diameter (or "aperture") of its objective lens or mirror.

### Sparrow's resolution limit

Sparrow's resolution limit
Sparrow's Resolution Limit is an estimate of the angular resolution limit of an optical instrument.

### Visual acuity

20/20 visionvision20/20
Visual acuity
The maximum angular resolution of the human eye at a distance of 1 km is typically 30 to 60 cm. This gives an angular resolution of between 0.02 and 0.03 degrees, which is roughly 1.2–1.8 arc minutes per line pair, which implies a pixel spacing of 0.6–0.9 arc minutes.

### Angular diameter

apparent diameterangular sizeapparent size
Angular diameter
Angular resolution

### Image-forming optical system

image forming opticsimage-forming device
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.

### Microscope

microscopesmicroscopicmicroscopically
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.

### Camera

camerasWebcamexposure control
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.

### Human eye

eyeeyeseyeball
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.

### Image resolution

resolutionhigh resolutionhigh-resolution
Angular resolution or spatial resolution describes the ability of any image-forming device such as an optical or radio telescope, a microscope, a camera, or an eye, to distinguish small details of an object, thereby making it a major determinant of image resolution.