In astronomy, luminosity is the total amount of energy emitted per unit of time by a star, galaxy, or other astronomical object. As a term for energy emitted per unit time, luminosity is synonymous with power. In SI units luminosity is measured in joules per second or watts. Values for luminosity are given in the terms of the luminosity of the Sun, L⊙. Luminosity can be given in terms of the astronomical magnitude system: the absolute bolometric magnitude of an object is a logarithmic measure of its total energy emission rate, while absolute magnitude is a logarithmic measure of the luminosity within some specific wavelength range or filter band. In contrast, the term brightness in astronomy is used to refer to an object's apparent brightness: that is, how bright an object appears to an observer. Apparent brightness depends on both the luminosity of the object and the distance between the object and observer, on any absorption of light along the path from object to observer. Apparent magnitude is a logarithmic measure of apparent brightness.
The distance determined by luminosity measures can be somewhat ambiguous, is thus sometimes called the luminosity distance. In astronomy, luminosity is the amount of electromagnetic energy; when not qualified, the term "luminosity" means bolometric luminosity, measured either in the SI units, watts, or in terms of solar luminosities. A bolometer is the instrument used to measure radiant energy over a wide band by absorption and measurement of heating. A star radiates neutrinos, which carry off some energy, contributing to the star's total luminosity; the IAU has defined a nominal solar luminosity of 3.828×1026 W to promote publication of consistent and comparable values in units of the solar luminosity. While bolometers do exist, they cannot be used to measure the apparent brightness of a star because they are insufficiently sensitive across the electromagnetic spectrum and because most wavelengths do not reach the surface of the Earth. In practice bolometric magnitudes are measured by taking measurements at certain wavelengths and constructing a model of the total spectrum, most to match those measurements.
In some cases, the process of estimation is extreme, with luminosities being calculated when less than 1% of the energy output is observed, for example with a hot Wolf-Rayet star observed only in the infra-red. Bolometric luminosities can be calculated using a bolometric correction to a luminosity in a particular passband; the term luminosity is used in relation to particular passbands such as a visual luminosity of K-band luminosity. These are not luminosities in the strict sense of an absolute measure of radiated power, but absolute magnitudes defined for a given filter in a photometric system. Several different photometric systems exist; some such as the UBV or Johnson system are defined against photometric standard stars, while others such as the AB system are defined in terms of a spectral flux density. A star's luminosity can be determined from two stellar characteristics: size and effective temperature; the former is represented in terms of solar radii, R⊙, while the latter is represented in kelvins, but in most cases neither can be measured directly.
To determine a star's radius, two other metrics are needed: the star's angular diameter and its distance from Earth. Both can be measured with great accuracy in certain cases, with cool supergiants having large angular diameters, some cool evolved stars having masers in their atmospheres that can be used to measure the parallax using VLBI. However, for most stars the angular diameter or parallax, or both, are far below our ability to measure with any certainty. Since the effective temperature is a number that represents the temperature of a black body that would reproduce the luminosity, it cannot be measured directly, but it can be estimated from the spectrum. An alternative way to measure stellar luminosity is to measure the star's apparent brightness and distance. A third component needed to derive the luminosity is the degree of interstellar extinction, present, a condition that arises because of gas and dust present in the interstellar medium, the Earth's atmosphere, circumstellar matter.
One of astronomy's central challenges in determining a star's luminosity is to derive accurate measurements for each of these components, without which an accurate luminosity figure remains elusive. Extinction can only be measured directly if the actual and observed luminosities are both known, but it can be estimated from the observed colour of a star, using models of the expected level of reddening from the interstellar medium. In the current system of stellar classification, stars are grouped according to temperature, with the massive young and energetic Class O stars boasting temperatures in excess of 30,000 K while the less massive older Class M stars exhibit temperatures less than 3,500 K; because luminosity is proportional to temperature to the fourth power, the large variation in stellar temperatures produces an vaster variation in stellar luminosity. Because the luminosity depends on a high power of the stellar mass, high mass luminous stars have much shorter lifetimes; the most luminous stars are always young stars, no more than a few million years for the most extreme.
In the Hertzsprung–Russell diagram, the x-axis represents temperature or spectral type while the y-axis represents luminosity or magnitude. The vast majority of stars are found along the main sequence with blue Class O stars found at the top left of the chart while red Class M stars fall to the bottom right. Certain stars like Deneb and Betelgeuse are
N. R. Pogson
Norman Robert Pogson, CIE was an English astronomer who worked in India at the Madras observatory. He made observations on comets, he introduced a mathematical scale of stellar magnitudes with the ratio of two successive magnitudes being the fifth root of one hundred and referred to as Pogson's ratio. Norman was born in Nottingham, the son of George Owen Pogson, a hosiery manufacturer, lace dealer and commission agent, "with enough income to support an extended family", his wife, Mary Ann, it was intended that he should follow his father into business, he was accordingly sent for "commercial education", but he was fascinated by science, his mother supported and encouraged this interest. His early education was informal, he left school at 16. At the age of eighteen, he calculated with the help of John Russell Hind of the Royal Astronomical Society, the orbits of two comets, he was introduced to astronomy through George Bishop's Observatory at South Villa Regent's Park from 1846. He took an interest in comets and studied Iris, a minor planet, discovered.
He was engaged as an assistant at the Radcliffe Observatory in 1852. After working as an assistant at the South Villa Observatory in 1851, he moved to the Radcliffe Observatory in Oxford in 1852, he received the Lalande medal upon his discovery of the minor planet Isis. His Oxford period was spent studying other routine research. In 1854 he helped. Pogson was appointed as director at the Hartwell Observatory belonging to John Lee in 1859, he published around fourteen papers from 1859 to 1860 in the Monthly Notices of the Royal Astronomical Society on variable stars and on minor planets. Sir Charles Wood appointed him as government astronomer for Madras in October 1860. Reaching India in 1861 and working at the Madras Observatory he worked tirelessly, discovering the asteroid 67 Asia. In the next seven years he found seven variable stars, he continued worked on Taylor's Madras Catalogue of 11,015 stars, published in 1835 based on work begun in 1831 by T. G. Taylor. Pogson continued work on this to add 51,101 observations and after his death in 1891 the catalogue was revised by Arthur Downing and published in 1901.
Despite Pogson's isolation he had at the time of his death discovered 134 stars, 106 variable stars, 21 possible variable stars and 7 possible supernovae. Pogson made special expeditions, observing a total solar eclipse on 18 August 1868 at Masulipatnam and making spectrometric studies, he observed and commented on the spectral line associated with Helium yet to be discovered. His most notable contribution was to note that in the stellar magnitude system introduced by the Greek astronomer Hipparchus, stars of the first magnitude were a hundred times as bright as stars of the sixth magnitude. Pogson's suggestion in 1856 was to make this a standard; this fifth root of 100 is known as Pogson's Ratio. The magnitude relation is given as follows: m1 - m2 = -2.5 log10 where m is the stellar magnitude and L is the luminosity, for stars 1 and 2. In 1868 and 1871, Pogson joined the Indian solar eclipse expeditions, he received a telegram from Ernst Friedrich Wilhelm Klinkerfues on November 30, 1872 which read Biela touched Earth on 27th.
Search near Theta Centauri, a message so esoteric that it caught the fancy of the newspapers of the time. The skies were cloudy in Madras and when it cleared up on December 2, 1872, he observed an object which he believed to be a return of Biela's Comet but was found to be a different object, called "Pogson's comet". One of Pogson's assistants was Chintamani Raghunatha Chary, he worked for many years with Pogson and his retirement in 1878 was a blow to Pogson. Pogson got into increasing difficulties with his collaborators in England as well as the bureacuracy in India. George Airy, who had admired Pogson once became unsupportive and downright dismissive of Pogson's applications for help from the government as well as to help him return to England. Pogson on his part had been stubborn in not supporting a southern-sky survey. Pogson served for 30 years at Madras, his health declined and he died in June 1891. He is buried at Chennai. Pogson was married in London in 1849 to Elizabeth Jane Ambrose, she died on 5 November 1869.
On 25 October 1883 he married Edith Louisa Stopford Sibley in Madras, daughter of Charles W. Sibley of the 64th regiment and a widow, aged 33, by whom he had a further three children: Frederick Vere, Edith Vera and Edith Gladys, born in 1889; the asteroid Vera, first discovered by Pogson on 6 February 1885, was named at the suggestion of his second wife, Edith Pogson.. Edith outlived him and retired to Wimbledon where she died on 31 December 1946. Pogson's daughter Elizabeth Isis Pogson served as his assistant at the Madras observatory from 1873 to 1881, she went on to become meteorological reporter for Madras. First proposed for a Fellowship of the Royal Astronomical Society in 1886, she was admitted to that honour in 1920. Pogson was created a Companion of the Most Eminent Order of the Indian Empire in January 1879; the following celestial features are named after him: Ast
A point source is a single identifiable localised source of something. A point source has negligible extent. Sources are called point sources because in mathematical modeling, these sources can be approximated as a mathematical point to simplify analysis; the actual source need not be physically small, if its size is negligible relative to other length scales in the problem. For example, in astronomy, stars are treated as point sources though they are in actuality much larger than the Earth. In three dimensions, the density of something leaving a point source decreases in proportion to the inverse square of the distance from the source, if the distribution is isotropic, there is no absorption or other loss. In mathematics, a point source is a singularity from which flow is emanating. Although singularities such as this do not exist in the observable universe, mathematical point sources are used as approximations to reality in physics and other fields. A source of light can be considered a point source if the resolution of the imaging instrument is too low to resolve the source's apparent size.
There are two sources of light. A point source, an extended source. Mathematically an object may be considered a point source if its angular size, θ, is much smaller than the resolving power of the telescope: θ << λ / D, where λ is the wavelength of light and D is the telescope diameter. Examples: Light from a distant star seen through a small telescope Light passing through a pinhole or other small aperture, viewed from a distance much greater than the size of the hole Light from a street light in a large-scale study of light pollution or street illumination Radio wave sources which are smaller than one radio wavelength are generally treated as point sources. Radio emissions generated by a fixed electrical circuit are polarized, producing anisotropic radiation. If the propagating medium is lossless, the radiant power in the radio waves at a given distance will still vary as the inverse square of the distance if the angle remains constant to the source polarization. Gamma ray and X-ray sources may be treated as a point source.
Radiological contamination and nuclear sources are point sources. This has significance in radiation protection. Examples: Radio antennas are smaller than one wavelength though they are many metres across Pulsars are treated as point sources when observed using radio telescopes In nuclear physics, a "hot spot" is a point source of radiation Sound is an oscillating pressure wave; as the pressure oscillates up and down, an audio point source acts in turn as a fluid point source and a fluid point sink. Examples: Seismic vibration from a localised seismic experiment searching for oil Noise pollution from a jet engine in a large-scale study of noise pollution A loudspeaker may be considered as a point source in a study of the acoustics of airport announcements Point sources are used as a means of calibrating ionizing radiation instruments, they are a sealed capsule and are most used for gamma, x-ray and beta measuring instruments. In vacuum, heat escapes as radiation isotropically. If the source remains stationary in a compressible fluid such as air, flow patterns can form around the source due to convection, leading to an anisotropic pattern of heat loss.
The most common form of anisotropy is the formation of a thermal plume above the heat source. Examples: Geological hotspots on the surface of the Earth which lie at the tops of thermal plumes rising from deep inside the Earth Plumes of heat studied in thermal pollution tracking. Fluid point sources are used in fluid dynamics and aerodynamics. A point source of fluid is the inverse of a fluid point sink. Whereas fluid sinks exhibit complex changing behaviour such as is seen in vortices, fluid sources produce simple flow patterns, with stationary isotropic point sources generating an expanding sphere of new fluid. If the fluid is moving a plume is generated from the point source. Examples: Air pollution from a power plant flue gas stack in a large scale analysis of air pollution Water pollution from an oil refinery wastewater discharge outlet in a large scale analysis of water pollution Gas escaping from a pressurised pipe in a laboratory Smoke is released from point sources in a wind tunnel in order to create a plume of smoke which highlights the flow of the wind over an object Smoke from a localised chemical fire can be blown in the wind to form a plume of pollution Sources of various types of pollution are considered as point sources in large-scale studies of pollution.
Line source Dirac delta function
Betelgeuse designated α Orionis, is on average the ninth-brightest star in the night sky and second-brightest in the constellation of Orion. It is a distinctly reddish, semiregular variable star whose apparent magnitude varies between 0.0 and 1.3, the widest range of any first-magnitude star. Betelgeuse is one of three stars that make up the Winter Triangle asterism, it marks the center of the Winter Hexagon. If the human eye could view all wavelengths of radiation, Betelgeuse would be the brightest star in the night sky. Classified as a red supergiant of spectral type M1-2, the star is one of the largest stars visible to the naked eye. If Betelgeuse were at the center of the Solar System, its surface would extend past the asteroid belt engulfing the orbits of Mercury, Earth and Jupiter. However, there are several other red supergiants in the Milky Way that could be larger, such as Mu Cephei and VY Canis Majoris. Calculations of its mass range from under ten to a little over twenty times that of the Sun.
It is calculated to be 640 light-years away, yielding an absolute magnitude of about −6. Less than 10 million years old, Betelgeuse has evolved because of its high mass. Having been ejected from its birthplace in the Orion OB1 Association—which includes the stars in Orion's Belt—this runaway star has been observed moving through the interstellar medium at a speed of 30 km/s, creating a bow shock over four light-years wide. Betelgeuse is in a late stage of stellar evolution, it is expected to explode as a supernova within the next million years. In 1920, Betelgeuse became the first extrasolar star to have the angular size of its photosphere measured. Subsequent studies have reported an angular diameter ranging from 0.042 to 0.056 arcseconds, with the differences ascribed to the non-sphericity, limb darkening and varying appearance at different wavelengths. It is surrounded by a complex, asymmetric envelope 250 times the size of the star, caused by mass loss from the star itself; the angular diameter of Betelgeuse is only exceeded by the Sun.
Α Orionis is the star's designation given by Johann Bayer in 1603. The traditional name Betelgeuse is derived from the Arabic إبط الجوزاء Ibṭ al-Jauzā’, meaning "the underarm of Orion", or يد الجوزاء Yad al-Jauzā’, meaning "the hand of Orion". In 2016, the International Astronomical Union organized a Working Group on Star Names to catalog and standardize proper names for stars; the WGSN's first bulletin of July 2016 included a table of the first two batches of names approved by the WGSN, which included Betelgeuse for this star. It is now so entered in the IAU Catalog of Star Names. Betelgeuse and its red coloration have been noted since antiquity. In the nineteenth century, before modern systems of stellar classification, Angelo Secchi included Betelgeuse as one of the prototypes for his Class III stars. By contrast, three centuries before Ptolemy, Chinese astronomers observed Betelgeuse as having a yellow coloration; the variation in Betelgeuse's brightness was first described in 1836 by Sir John Herschel, when he published his observations in Outlines of Astronomy.
From 1836 to 1840, he noticed significant changes in magnitude when Betelgeuse outshone Rigel in October 1837 and again in November 1839. A 10-year quiescent period followed. Observers recorded unusually high maxima with an interval of years, but only small variations from 1957 to 1967; the records of the American Association of Variable Star Observers show a maximum brightness of 0.2 in 1933 and 1942, a minimum of 1.2, observed in 1927 and 1941. This variability in brightness may explain why Johann Bayer, with the publication of his Uranometria in 1603, designated the star alpha as it rivaled the brighter Rigel. From Arctic latitudes, Betelgeuse's red colour and higher location in the sky than Rigel meant the Inuit regarded it as brighter, one local name was Ulluriajjuaq "large star". In 1920, Albert Michelson and Francis Pease mounted a 6-meter interferometer on the front of the 2.5-meter telescope at Mount Wilson Observatory. Helped by John Anderson, the trio measured the angular diameter of Betelgeuse at 0.047", a figure which resulted in a diameter of 3.84 × 108 km based on the parallax value of 0.018".
However, limb darkening and measurement errors resulted in uncertainty about the accuracy of these measurements. The 1950s and 1960s saw two developments that would affect stellar convection theory in red supergiants: the Stratoscope projects and the 1958 publication of Structure and Evolution of the Stars, principally the work of Martin Schwarzschild and his colleague at Princeton University, Richard Härm; this book disseminated ideas on how to apply computer technologies to create stellar models, while the Stratoscope projects, by taking balloon-borne telescopes above the Earth's turbulence, produced some of the finest images of solar granules and sunspots seen, thus confirming the existence of convection in the solar atmosphere. Astronomers in the 1970s saw some major advances in astronomical imaging technology beginning with Antoine Labeyrie's invention of speckle interferometry, a pr
Astronomy is a natural science that studies celestial objects and phenomena. It applies mathematics and chemistry in an effort to explain the origin of those objects and phenomena and their evolution. Objects of interest include planets, stars, nebulae and comets. More all phenomena that originate outside Earth's atmosphere are within the purview of astronomy. A related but distinct subject is physical cosmology, the study of the Universe as a whole. Astronomy is one of the oldest of the natural sciences; the early civilizations in recorded history, such as the Babylonians, Indians, Nubians, Chinese and many ancient indigenous peoples of the Americas, performed methodical observations of the night sky. Astronomy has included disciplines as diverse as astrometry, celestial navigation, observational astronomy, the making of calendars, but professional astronomy is now considered to be synonymous with astrophysics. Professional astronomy is split into theoretical branches. Observational astronomy is focused on acquiring data from observations of astronomical objects, analyzed using basic principles of physics.
Theoretical astronomy is oriented toward the development of computer or analytical models to describe astronomical objects and phenomena. The two fields complement each other, with theoretical astronomy seeking to explain observational results and observations being used to confirm theoretical results. Astronomy is one of the few sciences in which amateurs still play an active role in the discovery and observation of transient events. Amateur astronomers have made and contributed to many important astronomical discoveries, such as finding new comets. Astronomy means "law of the stars". Astronomy should not be confused with astrology, the belief system which claims that human affairs are correlated with the positions of celestial objects. Although the two fields share a common origin, they are now distinct. Both of the terms "astronomy" and "astrophysics" may be used to refer to the same subject. Based on strict dictionary definitions, "astronomy" refers to "the study of objects and matter outside the Earth's atmosphere and of their physical and chemical properties," while "astrophysics" refers to the branch of astronomy dealing with "the behavior, physical properties, dynamic processes of celestial objects and phenomena."
In some cases, as in the introduction of the introductory textbook The Physical Universe by Frank Shu, "astronomy" may be used to describe the qualitative study of the subject, whereas "astrophysics" is used to describe the physics-oriented version of the subject. However, since most modern astronomical research deals with subjects related to physics, modern astronomy could be called astrophysics; some fields, such as astrometry, are purely astronomy rather than astrophysics. Various departments in which scientists carry out research on this subject may use "astronomy" and "astrophysics" depending on whether the department is affiliated with a physics department, many professional astronomers have physics rather than astronomy degrees; some titles of the leading scientific journals in this field include The Astronomical Journal, The Astrophysical Journal, Astronomy and Astrophysics. In early historic times, astronomy only consisted of the observation and predictions of the motions of objects visible to the naked eye.
In some locations, early cultures assembled massive artifacts that had some astronomical purpose. In addition to their ceremonial uses, these observatories could be employed to determine the seasons, an important factor in knowing when to plant crops and in understanding the length of the year. Before tools such as the telescope were invented, early study of the stars was conducted using the naked eye; as civilizations developed, most notably in Mesopotamia, Persia, China and Central America, astronomical observatories were assembled and ideas on the nature of the Universe began to develop. Most early astronomy consisted of mapping the positions of the stars and planets, a science now referred to as astrometry. From these observations, early ideas about the motions of the planets were formed, the nature of the Sun and the Earth in the Universe were explored philosophically; the Earth was believed to be the center of the Universe with the Sun, the Moon and the stars rotating around it. This is known as the geocentric model of the Ptolemaic system, named after Ptolemy.
A important early development was the beginning of mathematical and scientific astronomy, which began among the Babylonians, who laid the foundations for the astronomical traditions that developed in many other civilizations. The Babylonians discovered. Following the Babylonians, significant advances in astronomy were made in ancient Greece and the Hellenistic world. Greek astronomy is characterized from the start by seeking a rational, physical explanation for celestial phenomena. In the 3rd century BC, Aristarchus of Samos estimated the size and distance of the Moon and Sun, he proposed a model of the Solar System where the Earth and planets rotated around the Sun, now called the heliocentric model. In the 2nd century BC, Hipparchus discovered precession, calculated the size and distance of the Moon and inven
The apparent magnitude of an astronomical object is a number, a measure of its brightness as seen by an observer on Earth. The magnitude scale is logarithmic. A difference of 1 in magnitude corresponds to a change in brightness by a factor of 5√100, or about 2.512. The brighter an object appears, the lower its magnitude value, with the brightest astronomical objects having negative apparent magnitudes: for example Sirius at −1.46. The measurement of apparent magnitudes or brightnesses of celestial objects is known as photometry. Apparent magnitudes are used to quantify the brightness of sources at ultraviolet and infrared wavelengths. An apparent magnitude is measured in a specific passband corresponding to some photometric system such as the UBV system. In standard astronomical notation, an apparent magnitude in the V filter band would be denoted either as mV or simply as V, as in "mV = 15" or "V = 15" to describe a 15th-magnitude object; the scale used to indicate magnitude originates in the Hellenistic practice of dividing stars visible to the naked eye into six magnitudes.
The brightest stars in the night sky were said to be of first magnitude, whereas the faintest were of sixth magnitude, the limit of human visual perception. Each grade of magnitude was considered twice the brightness of the following grade, although that ratio was subjective as no photodetectors existed; this rather crude scale for the brightness of stars was popularized by Ptolemy in his Almagest and is believed to have originated with Hipparchus. In 1856, Norman Robert Pogson formalized the system by defining a first magnitude star as a star, 100 times as bright as a sixth-magnitude star, thereby establishing the logarithmic scale still in use today; this implies that a star of magnitude m is about 2.512 times as bright as a star of magnitude m + 1. This figure, the fifth root of 100, became known as Pogson's Ratio; the zero point of Pogson's scale was defined by assigning Polaris a magnitude of 2. Astronomers discovered that Polaris is variable, so they switched to Vega as the standard reference star, assigning the brightness of Vega as the definition of zero magnitude at any specified wavelength.
Apart from small corrections, the brightness of Vega still serves as the definition of zero magnitude for visible and near infrared wavelengths, where its spectral energy distribution approximates that of a black body for a temperature of 11000 K. However, with the advent of infrared astronomy it was revealed that Vega's radiation includes an Infrared excess due to a circumstellar disk consisting of dust at warm temperatures. At shorter wavelengths, there is negligible emission from dust at these temperatures. However, in order to properly extend the magnitude scale further into the infrared, this peculiarity of Vega should not affect the definition of the magnitude scale. Therefore, the magnitude scale was extrapolated to all wavelengths on the basis of the black-body radiation curve for an ideal stellar surface at 11000 K uncontaminated by circumstellar radiation. On this basis the spectral irradiance for the zero magnitude point, as a function of wavelength, can be computed. Small deviations are specified between systems using measurement apparatuses developed independently so that data obtained by different astronomers can be properly compared, but of greater practical importance is the definition of magnitude not at a single wavelength but applying to the response of standard spectral filters used in photometry over various wavelength bands.
With the modern magnitude systems, brightness over a wide range is specified according to the logarithmic definition detailed below, using this zero reference. In practice such apparent magnitudes do not exceed 30; the brightness of Vega is exceeded by four stars in the night sky at visible wavelengths as well as the bright planets Venus and Jupiter, these must be described by negative magnitudes. For example, the brightest star of the celestial sphere, has an apparent magnitude of −1.4 in the visible. Negative magnitudes for other bright astronomical objects can be found in the table below. Astronomers have developed other photometric zeropoint systems as alternatives to the Vega system; the most used is the AB magnitude system, in which photometric zeropoints are based on a hypothetical reference spectrum having constant flux per unit frequency interval, rather than using a stellar spectrum or blackbody curve as the reference. The AB magnitude zeropoint is defined such that an object's AB and Vega-based magnitudes will be equal in the V filter band.
As the amount of light received by a telescope is reduced by transmission through the Earth's atmosphere, any measurement of apparent magnitude is corrected for what it would have been as seen from above the atmosphere. The dimmer an object appears, the higher the numerical value given to its apparent magnitude, with a difference of 5 magnitudes corresponding to a brightness factor of 100. Therefore, the apparent magnitude m, in the spectral band x, would be given by m x = − 5 log 100 , more expressed in terms of common logarithms as m x
In optics, the Airy disk 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 and astronomy; the diffraction pattern resulting from a uniformly illuminated, circular aperture has a bright central region, known as the Airy disk, which together with the series of concentric rings around is called the Airy pattern. Both are named after George Biddell Airy; the disk and rings phenomenon had been known prior to Airy. They succeed each other nearly at equal intervals round the central disc.... However, Airy wrote the first full theoretical treatment explaining the phenomenon. Mathematically, the diffraction pattern is characterized by the wavelength of light illuminating the circular aperture, the aperture's size; the appearance of the diffraction pattern is additionally characterized by the sensitivity of the eye or other detector used to observe the pattern.
The most important application of this concept is in telescopes. Due to diffraction, the smallest point to which a lens or mirror can focus a beam of light is the size of the Airy disk. If one were able to make a perfect lens, there is still a limit to the resolution of an image created by such a lens. An optical system in which the resolution is no longer limited by imperfections in the lenses but only by diffraction is said to be diffraction limited. Far from the aperture, the angle at which the first minimum occurs, measured from the direction of incoming light, is given by the approximate formula: sin θ ≈ 1.22 λ d or, for small angles θ ≈ 1.22 λ d, where θ is in radians, λ is the wavelength of the light in meters, d is the diameter of the aperture in meters. Airy wrote this as s = 2.76 a, where s was the angle of first minimum in seconds of arc, a was the radius of the aperture in inches, the wavelength of light was assumed to be 0.000022 inches. The Rayleigh criterion for 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. However, while the angle at which the first minimum occurs depends only on wavelength and aperture size, the appearance of the diffraction pattern will vary with the intensity of the light source; because any detector used to observe the diffraction pattern can have an intensity threshold for detection, the full diffraction pattern may not be apparent. In astronomy, the outer rings are not apparent in a magnified image of a star, it may be that none of the rings are apparent, in which case the star image appears as a disk rather than as a full diffraction pattern. Furthermore, fainter stars will appear as smaller disks than brighter stars, because less of their central maximum reaches the threshold of detection. While in theory all stars or other "point sources" of a given wavelength and seen through a given aperture have the same Airy disk radius characterized by the above equation, differing only in intensity, the appearance is that fainter sources appear as smaller disks, brighter sources appear as larger disks.
This was described by Airy in his original work: The rapid decrease of light in the successive rings will sufficiently explain the visibility of two or three rings with a bright star and the non-visibility of rings with a faint star. The difference of the diameters of the central spots of different stars... is fully explained. Thus the radius of the spurious disk of a faint star, where light of less than half the intensity of the central light makes no impression on the eye, is determined by, whereas the radius of the spurious disk of a bright star, where light of 1/10 the intensity of the central light is sensible, is determined by. Despite this feature of Airy's work, the radius of the Airy disk is given as being the angle of first minimum in standard textbooks. In reality, the angle of first minimum is a limiting value for the size of the Airy disk, not a definite radius. If two objects imaged by a camera are separated by an angle small enough that their Airy disks on the camera detector start overlapping, the objects cannot be separated any more in the image, they start blurring together.
Two objects are said to be just resolved when the maximum of the first Airy pattern falls on top of the first minimum of the second Airy pattern. Therefore, the sma