Rayleigh Criterion
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Angular resolution describes the ability of any
image-forming device In optics, an image-forming optical system is a system capable of being used for imaging. The diameter of the aperture of the main objective is a common criterion for comparison among optical systems, such as large telescopes. The two traditional ...
such as an
optical Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
or
radio telescope A radio telescope is a specialized antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency ...
, a
microscope A microscope () is a laboratory instrument used to examine objects that are too small to be seen by the naked eye. Microscopy is the science of investigating small objects and structures using a microscope. Microscopic means being invisibl ...
, a
camera A camera is an Optics, optical instrument that can capture an image. Most cameras can capture 2D images, with some more advanced models being able to capture 3D images. At a basic level, most cameras consist of sealed boxes (the camera body), ...
, or an eye, to distinguish small details of an object, thereby making it a major determinant of
image resolution Image resolution is the detail an image holds. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies how ...
. It is used in
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviole ...
applied to light waves, in
antenna theory In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies a ...
applied to radio waves, and in
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
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 In physics and geosciences, the term spatial resolution refers to distance between independent measurements, or the physical dimension that represents a pixel of the image. While in some instruments, like cameras and telescopes, spatial resolutio ...
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 Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
to the ratio of the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of the waves to the
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An opt ...
width. For this reason, high resolution imaging systems such as astronomical
telescope A telescope is a device used to observe distant objects by their emission, absorption, or reflection of electromagnetic radiation. Originally meaning only an optical instrument using lenses, curved mirrors, or a combination of both to observe ...
s, long distance telephoto camera lenses and
radio telescope A radio telescope is a specialized antenna and radio receiver used to detect radio waves from astronomical radio sources in the sky. Radio telescopes are the main observing instrument used in radio astronomy, which studies the radio frequency ...
s have large apertures.


Definition of terms

''Resolving power'' is the ability of an imaging device to separate (i.e., to see as distinct) points of an object that are located at a small
angular distance Angular distance \theta (also known as angular separation, apparent distance, or apparent separation) is the angle between the two sightlines, or between two point objects as viewed from an observer. Angular distance appears in mathematics (in pa ...
or it is the power of an optical instrument to separate far away objects, that are close together, into individual images. The term ''
resolution Resolution(s) may refer to: Common meanings * Resolution (debate), the statement which is debated in policy debate * Resolution (law), a written motion adopted by a deliberative body * New Year's resolution, a commitment that an individual mak ...
'' or ''minimum resolvable distance'' is the minimum distance between distinguishable
objects Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Object (abstract), an object which does not exist at any particular time or place ** Physical object, an identifiable collection of matter * Goal, an ...
in an image, although the term is loosely used by many users of microscopes and telescopes to describe resolving power. As explained below, diffraction-limited resolution is defined by the Rayleigh criterion as the angular separation of two point sources when the maximum of each source lies in the first minimum of the diffraction pattern (
Airy disk In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
) of the other. In scientific analysis, in general, the term "resolution" is used to describe the
precision Precision, precise or precisely may refer to: Science, and technology, and mathematics Mathematics and computing (general) * Accuracy and precision, measurement deviation from true value and its scatter * Significant figures, the number of digit ...
with which any instrument measures and records (in an image or spectrum) any variable in the specimen or sample under study.


The Rayleigh criterion

The imaging system's resolution can be limited either by aberration or by
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
causing blurring of the image. These two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality of the system. On the other hand, diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. The
lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
' circular
aperture In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. An opt ...
is analogous to a two-dimensional version of the single-slit experiment.
Light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
passing through the lens interferes with itself creating a ring-shape diffraction pattern, known as the
Airy pattern In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
, if the
wavefront In physics, the wavefront of a time-varying ''wave field'' is the set (locus) of all points having the same ''phase''. The term is generally meaningful only for fields that, at each point, vary sinusoidally in time with a single temporal freque ...
of the transmitted light is taken to be spherical or plane over the exit aperture. The interplay between diffraction and aberration can be characterised by the point spread function (PSF). The narrower the aperture of a lens the more likely the PSF is dominated by diffraction. In that case, the angular resolution of an optical system can be estimated (from the
diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
of the aperture and the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of the light) by the Rayleigh criterion defined by
Lord Rayleigh John William Strutt, 3rd Baron Rayleigh, (; 12 November 1842 – 30 June 1919) was an English mathematician and physicist who made extensive contributions to science. He spent all of his academic career at the University of Cambridge. Amo ...
: two point sources are regarded as just resolved when the principal diffraction maximum (center) of the
Airy disk In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
of one image coincides with the first minimum of the
Airy disk In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
of the other, as shown in the accompanying photos. (In the bottom photo on the right that shows the Rayleigh criterion limit, the central maximum of one point source might look as though it lies outside the first minimum of the other, but examination with a ruler verifies that the two do intersect.) If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved. Rayleigh defended this criterion on sources of equal strength. Considering diffraction through a circular aperture, this translates into: : \theta\approx 1.22 \frac\quad(\text\,\sin\theta\approx\theta) where ''θ'' is the ''angular resolution'' (
radians The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...
), ''λ'' is the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of light, and ''D'' is the
diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
of the lens' aperture. The factor 1.22 is derived from a calculation of the position of the first dark circular ring surrounding the central
Airy disc In optics, the Airy disk (or Airy disc) and Airy pattern are descriptions of the best- focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light. The Airy disk is of importance in physics, ...
of the
diffraction Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
pattern. This number is more precisely 1.21966989... (), the first zero of the order-one
Bessel function of the first kind Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...
J_(x) divided by π. The formal Rayleigh criterion is close to the
empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
resolution limit found earlier by the English astronomer
W. R. Dawes William Rutter Dawes (19 March 1799 – 15 February 1868) was an English astronomer. Biography Dawes was born at Christ's Hospital then in the City of London (it moved to Horsham, West Sussex in 1902), the son of William Dawes, also an astro ...
, who tested human observers on close binary stars of equal brightness. The result, ''θ'' = 4.56/''D'', with ''D'' in inches and ''θ'' in
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
s, is slightly narrower than calculated with the Rayleigh criterion. A calculation using Airy discs as point spread function shows that at
Dawes' limit Dawes' limit is a formula to express the maximum resolving power of a microscope or telescope. It is so named after its discoverer, W. R. Dawes ,Dawes, W.R., ''Catalogue of Micrometrical Measurements of Double Stars.'' In: Memoirs of the Royal A ...
there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip. Modern
image processing An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensiona ...
techniques including
deconvolution In mathematics, deconvolution is the operation inverse to convolution. Both operations are used in signal processing and image processing. For example, it may be possible to recover the original signal after a filter (convolution) by using a deco ...
of the point spread function allow resolution of binaries with even less angular separation. Using a
small-angle approximation The small-angle approximations can be used to approximate the values of the main trigonometric functions, provided that the angle in question is small and is measured in radians: : \begin \sin \theta &\approx \theta \\ \cos \theta &\approx 1 - \ ...
, the angular resolution may be converted into a ''
spatial resolution In physics and geosciences, the term spatial resolution refers to distance between independent measurements, or the physical dimension that represents a pixel of the image. While in some instruments, like cameras and telescopes, spatial resolutio ...
'', Δ''ℓ'', by multiplication of the angle (in radians) with the distance to the object. For a microscope, that distance is close to the
focal length The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative foca ...
''f'' of the
objective Objective may refer to: * Objective (optics), an element in a camera or microscope * ''The Objective'', a 2008 science fiction horror film * Objective pronoun, a personal pronoun that is used as a grammatical object * Objective Productions, a Brit ...
. For this case, the Rayleigh criterion reads: : \Delta \ell \approx 1.22 \frac. This is the
radius In classical geometry, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
, in the imaging plane, of the smallest spot to which a
collimated A collimated beam of light or other electromagnetic radiation has parallel rays, and therefore will spread minimally as it propagates. A perfectly collimated light beam, with no divergence, would not disperse with distance. However, diffraction p ...
beam of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
can be focused, which also corresponds to the size of smallest object that the lens can resolve. The size is proportional to wavelength, ''λ'', and thus, for example,
blue Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when obs ...
light can be focused to a smaller spot than
red Red is the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625–740 nanometres. It is a primary color in the RGB color model and a secondar ...
light. If the lens is focusing a beam of
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
with a finite extent (e.g., a
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fir ...
beam), the value of ''D'' corresponds to the
diameter In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord of the circle. Both definitions are also valid for ...
of the light beam, not the lens. 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 to a smaller spot than a narrow one. This result is related to the 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 In optics, the f-number of an optical system such as a camera lens is the ratio of the system's focal length to the diameter of the entrance pupil ("clear aperture").Smith, Warren ''Modern Optical Engineering'', 4th Ed., 2007 McGraw-Hill ...
, #: : \Delta \ell \approx 1.22 \frac=1.22 \lambda \cdot (f/\#). Since this is the radius of the Airy disk, the resolution is better estimated by the diameter, 2.44 \lambda \cdot (f/\#)


Specific cases


Single telescope

Point-like sources separated by an
angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two ...
smaller than the angular resolution cannot be resolved. A single optical telescope may have an angular resolution less than one
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
, but
astronomical seeing In astronomy, seeing is the degradation of the image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable distortion. The origin of this effect are rapidly changing v ...
and other atmospheric effects make attaining this very hard. The angular resolution ''R'' of a telescope can usually be approximated by :R = \frac where ''λ'' is the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of the observed radiation, and ''D'' is the diameter of the telescope's
objective Objective may refer to: * Objective (optics), an element in a camera or microscope * ''The Objective'', a 2008 science fiction horror film * Objective pronoun, a personal pronoun that is used as a grammatical object * Objective Productions, a Brit ...
. The resulting ''R'' is in
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...
s. For example, in the case of yellow light with a wavelength of 580  nm, for a resolution of 0.1 arc second, we need D=1.2 m. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources. This formula, for light with a wavelength of about 562 nm, is also called the
Dawes' limit Dawes' limit is a formula to express the maximum resolving power of a microscope or telescope. It is so named after its discoverer, W. R. Dawes ,Dawes, W.R., ''Catalogue of Micrometrical Measurements of Double Stars.'' In: Memoirs of the Royal A ...
.


Telescope array

The highest angular resolutions for telescopes can be achieved by arrays of telescopes called
astronomical interferometer An astronomical interferometer or telescope array is a set of separate telescopes, mirror segments, or radio telescope antenna (radio), antennas that work together as a single telescope to provide higher resolution images of astronomical objects ...
s: These instruments can achieve angular resolutions of 0.001 arcsecond at optical wavelengths, and much higher resolutions at x-ray wavelengths. 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. The angular resolution ''R'' of an interferometer array can usually be approximated by :R=\frac where ''λ'' is the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
of the observed radiation, and ''B'' is the length of the maximum physical separation of the telescopes in the array, called the baseline. The resulting ''R'' is in
radian The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that c ...
s. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources. For example, in order to form an image in yellow light with a wavelength of 580 nm, for a resolution of 1 milli-arcsecond, we need telescopes laid out in an array that is 120 m × 120 m with a dimensional precision better than 145 nm.


Microscope

The resolution ''R'' (here measured as a distance, not to be confused with the angular resolution of a previous subsection) depends on the
angular aperture The angular aperture of a lens is the angular size of the lens aperture as seen from the focal point: :a = 2 \arctan \left( \frac \right) = 2 \arctan \left( \frac \right) where :f is the focal length :D is the diameter of the aperture. ...
\alpha: :R=\frac where \mathrm=n\sin\theta. Here NA is the
numerical aperture 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. By incorporating index of refraction in its definition, NA has the proper ...
, \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 In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
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. It follows that the NAs of both the objective and the condenser should be as high as possible for maximum resolution. In the case that both NAs are the same, the equation may be reduced to: :R=\frac\approx\frac The practical limit for \theta is about 70°. In a dry objective or condenser, this gives a maximum NA of 0.95. In a high-resolution oil immersion lens, the maximum NA is typically 1.45, when using immersion oil with a refractive index of 1.52. Due to these limitations, the resolution limit of a light microscope using
visible light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 te ...
is about 200  nm. Given that the shortest wavelength of visible light is
violet Violet may refer to: Common meanings * Violet (color), a spectral color with wavelengths shorter than blue * One of a list of plants known as violet, particularly: ** ''Viola'' (plant), a genus of flowering plants Places United States * Viol ...
(\lambda \approx 400\,\mathrm), :R=\frac=203\,\mbox which is near 200 nm. Oil immersion objectives can have practical difficulties due to their shallow depth of field and extremely short working distance, which calls for the use of very thin (0.17 mm) cover slips, or, in an inverted microscope, thin glass-bottomed
Petri dish A Petri dish (alternatively known as a Petri plate or cell-culture dish) is a shallow transparent lidded dish that biologists use to hold growth medium in which cells can be cultured,R. C. Dubey (2014): ''A Textbook Of Biotechnology For Class- ...
es. However, resolution below this theoretical limit can be achieved using
super-resolution microscopy Super-resolution microscopy is a series of techniques in optical microscopy that allow such images to have resolutions higher than those imposed by the diffraction limit, which is due to the diffraction of light. Super-resolution imaging techni ...
. These include optical near-fields (
Near-field scanning optical microscope Near-field scanning optical microscopy (NSOM) or scanning near-field optical microscopy (SNOM) is a microscopy technique for nanostructure investigation that breaks the far field resolution limit by exploiting the properties of evanescent waves ...
) or a diffraction technique called
4Pi STED microscopy The 4Pi-STED-microscope is the result of combining the two unrelated concepts of Stimulated emission depletion (STED) microscopy and 4Pi-microscopy. Here, a fluorescent sample is placed in the common focus of two opposing lenses, but excitatio ...
. Objects as small as 30 nm have been resolved with both techniques. In addition to this
Photoactivated localization microscopy Photo-activated localization microscopy (PALM or FPALM) and stochastic optical reconstruction microscopy (STORM) are widefield (as opposed to point scanning techniques such as laser scanning confocal microscopy) fluorescence microscopy imaging meth ...
can resolve structures of that size, but is also able to give information in z-direction (3D).


List of telescopes and arrays by angular resolution


See also

*
Angular diameter The angular diameter, angular size, apparent diameter, or apparent size is an angular distance describing how large a sphere or circle appears from a given point of view. In the vision sciences, it is called the visual angle, and in optics, it is ...
*
Beam width The beam diameter or beam width of an electromagnetic beam is the diameter along any specified line that is perpendicular to the beam axis and intersects it. Since beams typically do not have sharp edges, the diameter can be defined in many differ ...
* Dawes limit *
Diffraction-limited system The resolution of an optical imaging system a microscope, telescope, or camera can be limited by factors such as imperfections in the lenses or misalignment. However, there is a principal limit to the resolution of any optical system, due to t ...
*
Ground sample distance In remote sensing, ground sample distance (GSD) in a digital photo (such as an orthophoto) of the ground from air or space is the distance between pixel centers measured on the ground. For example, in an image with a one-meter GSD, adjacent pixels i ...
*
Image resolution Image resolution is the detail an image holds. The term applies to digital images, film images, and other types of images. "Higher resolution" means more image detail. Image resolution can be measured in various ways. Resolution quantifies how ...
*
Optical resolution Optical resolution describes the ability of an imaging system to resolve detail, in the object that is being imaged. An imaging system may have many individual components, including one or more lenses, and/or recording and display components. ...
*
Sparrow's resolution limit Sparrow's resolution limit is an estimate of the angular resolution limit of an optical instrument. Rayleigh criterion When a star is observed with a telescope, the light is diffracted or spread apart into an Airy disk In optics, the Airy dis ...
*
Visual acuity Visual acuity (VA) commonly refers to the clarity of vision, but technically rates an examinee's ability to recognize small details with precision. Visual acuity is dependent on optical and neural factors, i.e. (1) the sharpness of the retinal ...


Notes


References


External links


"Concepts and Formulas in Microscopy: Resolution"
by Michael W. Davidson, ''Nikon MicroscopyU'' (website). {{Portal bar, Science, Astronomy, Stars, Spaceflight, Outer space, Solar System Angle Optics