Parallax

trigonometric parallaxsolar parallaxmotion parallaxdiurnal parallaxannual parallaxlunar parallaxparallax errorstellar parallaxspatial scanningdaily parallax
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.wikipedia
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Parallax (disambiguation)

Astronomers also use the word "parallax" as a synonym for "distance measurement" by other methods: see parallax (disambiguation)#Astronomy.
A parallax is the difference in the angular position of two stationary points relative to each other from different viewing positions.

Coincidence rangefinder

stereoscopic rangefinderoptical rangefindercoincidence
In computer vision the effect is used for computer stereo vision, and there is a device called a parallax rangefinder that uses it to find range, and in some variations also altitude to a target.
A coincidence rangefinder (stereoscopic, parallax, or split-image rangefinder) is a type of rangefinder that uses mechanical and optical principles to allow an operator to determine the distance to a visible object.

Stereopsis

stereoscopic visionstereo visionhorizontal disparity
Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception; this process is known as stereopsis.
The perception of depth and 3-dimensional structure is, however, possible with information visible from one eye alone, such as differences in object size and motion parallax (differences in the image of an object over time with observer movement), though the impression of depth in these cases is often not as vivid as that obtained from binocular disparities.

Cosmic distance ladder

standard candlestandard candlesdistance
These distances form the lowest rung of what is called "the cosmic distance ladder", the first in a succession of methods by which astronomers determine the distances to celestial objects, serving as a basis for other distance measurements in astronomy forming the higher rungs of the ladder.
The most important fundamental distance measurements come from trigonometric parallax.

Friedrich Bessel

BesselFriedrich Wilhelm BesselBessel, Friedrich
The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.
He was the first astronomer who determined reliable values for the distance from the sun to another star by the method of parallax.

Hipparcos

HIPTYCHipparcos satellite
In 1989, the satellite Hipparcos was launched primarily for obtaining improved parallaxes and proper motions for over 100,000 nearby stars, increasing the reach of the method tenfold.
This permitted the accurate determination of proper motions and parallaxes of stars, allowing a determination of their distance and tangential velocity.

Wiggle stereoscopy

WiggleWiggle stereogram
The motion parallax is exploited also in wiggle stereoscopy, computer graphics which provide depth cues through viewpoint-shifting animation rather than through binocular vision.
The sense of depth from such images is due to parallax and to changes to the occlusion of background objects.

Tycho Brahe

BraheTycho1572 supernova
It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed entirely implausible: it was one of Tycho's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn (then the most distant known planet) and the eighth sphere (the fixed stars).
His precise measurements indicated that "new stars" (stellae novae, now known as supernovae), in particular that of 1572, lacked the parallax expected in sublunar phenomena and were therefore not tailless comets in the atmosphere as previously believed but were above the atmosphere and beyond the moon.

Parsec

Mpcpckpc
The parsec (3.26 light-years) is defined as the distance for which the annual parallax is 1 arcsecond.
Named as a portmanteau of the parallax of one arcsecond, it was defined so as to make calculations of astronomical distances quick and easy for astronomers from only their raw observational data.

Depth perception

depthdepth cuesmonocular cues
Many animals, including humans, have two eyes with overlapping visual fields that use parallax to gain depth perception; this process is known as stereopsis.
Binocular cues include stereopsis, eye convergence, disparity, and yielding depth from binocular vision through exploitation of parallax.

Proxima Centauri

Alpha Proximaits host starProxima
The nearest star to the Sun (and thus the star with the largest parallax), Proxima Centauri, has a parallax of 0.7687 ± 0.0003 arcsec.
He suggested that it be named Proxima Centauri (actually Proxima Centaurus). In 1917, at the Royal Observatory at the Cape of Good Hope, the Dutch astronomer Joan Voûte measured the star's trigonometric parallax at 0.755 ″ and determined that Proxima Centauri was approximately the same distance from the Sun as Alpha Centauri.

61 Cygni

61 Cyg61 Cygni A61 Cyg A
The first successful measurements of stellar parallax were made by Friedrich Bessel in 1838 for the star 61 Cygni using a heliometer.
His observations led to the conclusion that binary stars were separated enough that they would show different movements in parallax over the year, and hoped to use this as a way to measure the distance to the stars.

Astronomical unit

AUastronomical unitsAUs
To ascertain the scale, it is necessary only to measure one distance within the Solar System, e.g., the mean distance from the Earth to the Sun (now called an astronomical unit, or AU).
In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, defining times and places for observing the largest parallax (apparent shifts of position) in nearby stars.

Transit of Venus

transits of VenusVenus1761 transit of Venus
Although Aristarchus' results were incorrect due to observational errors, they were based on correct geometric principles of parallax, and became the basis for estimates of the size of the Solar System for almost 2000 years, until the transit of Venus was correctly observed in 1761 and 1769.
Observations of the 1639 transit, combined with the principle of parallax, provided an estimate of the distance between the Sun and the Earth that was more accurate than any other up to that time.

Single-lens reflex camera

SLRsingle-lens reflexSLR camera
This problem is addressed in single-lens reflex cameras, in which the viewfinder sees through the same lens through which the photo is taken (with the aid of a movable mirror), thus avoiding parallax error.
This is not problematic for pictures taken at a middle or longer distance, but parallax causes framing errors in close-up shots.

Viewfinder

finderviewfindersoptical viewfinder
Parallax error can be seen when taking photos with many types of cameras, such as twin-lens reflex cameras and those including viewfinders (such as rangefinder cameras).
Most viewfinders are separate, and suffer parallax, while the single-lens reflex camera lets the viewfinder use the main optical system.

Light-year

light yearlight yearsly
The parsec (3.26 light-years) is defined as the distance for which the annual parallax is 1 arcsecond.
In those terms, trigonometric calculations based on 61 Cygni's parallax of 0.314 arcseconds, showed the distance to the star to be 660000 astronomical units (9.9 km or 6.1 mi).

Apparent place

apparent positionsapparent motionapparent places
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight, and is measured by the angle or semi-angle of inclination between those two lines.
Annual parallax — the apparent change in position due to the star being viewed from different places as the Earth orbits the Sun in the course of a year. Unlike aberration, this effect depends on the distance of the star, being larger for nearby stars.

Heliocentrism

heliocentricheliocentric modelheliocentric theory
The fact that stellar parallax was so small that it was unobservable at the time was used as the main scientific argument against heliocentrism during the early modern age.
Aristarchus presumably took the stars to be very far away because he was aware that their parallax would otherwise be observed over the course of a year.

Aristarchus of Samos

Aristarchus
This yields for the Earth–Moon distance 60.27 Earth radii or 384399 km This procedure was first used by Aristarchus of Samos and Hipparchus, and later found its way into the work of Ptolemy.
Aristarchus suspected the stars were other suns that are very far away, and that in consequence there was no observable parallax, that is, a movement of the stars relative to each other as the Earth moves around the Sun.

Image stitching

stitchingstitchedpanorama stitching
Parallax is also an issue in image stitching, such as for panoramas.
In general, the major issues to deal with are presence of parallax, lens distortion, scene motion, and exposure differences.

433 Eros

Eros433 Eros AsteroidEros Station
Much later, the Solar System was "scaled" using the parallax of asteroids, some of which, such as Eros, pass much closer to Earth than Venus.
During the opposition of 1900–1901, a worldwide program was launched to make parallax measurements of Eros to determine the solar parallax (or distance to the Sun), with the results published in 1910 by Arthur Hinks of Cambridge.

Reflector sight

reflex sightreflector gunsightReflector (reflex) sight
Non-magnifying reflector or "reflex" sights have the ability to be theoretically "parallax free."
Since the reticle is at infinity it stays in alignment with the device the sight is attached to regardless of the viewer's eye position, removing most of the parallax and other sighting errors found in simple sighting devices.

Celestial sphere

celestialcelestial hemispherehemisphere
It is clear from Euclid's geometry that the effect would be undetectable if the stars were far enough away, but for various reasons such gigantic distances involved seemed entirely implausible: it was one of Tycho's principal objections to Copernican heliocentrism that in order for it to be compatible with the lack of observable stellar parallax, there would have to be an enormous and unlikely void between the orbit of Saturn (then the most distant known planet) and the eighth sphere (the fixed stars).
This effect, known as parallax, can be represented as a small offset from a mean position.

Twin-lens reflex camera

twin-lens reflexTLRtwin lens reflex
Parallax error can be seen when taking photos with many types of cameras, such as twin-lens reflex cameras and those including viewfinders (such as rangefinder cameras). Parallax also affects optical instruments such as rifle scopes, binoculars, microscopes, and twin-lens reflex cameras that view objects from slightly different angles.
Because the photographer views through one lens but takes the photograph through another, parallax error makes the photograph different from the view on the screen. This difference is negligible when the subject is far away, but is critical for nearby subjects. Parallax compensation may be performed by the photographer in adjustment of the sight line while compensating for the framing change, or for highly repeatable accuracy in tabletop photography (in which the subject might be within a foot (30 cm) of the camera), devices are available that move the camera upwards so that the taking lens goes to the exact position that the viewing lens occupied. [Mamiya's very accurate version was called the Para-mender, and mounted on a tripod.] Some TLRs like the Rolleiflex (a notable early example is the Voigtländer Superb of 1933 ) also came with - more or less complex - devices to adjust parallax with focussing.