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| {{dablink|Not to be confused with [[spherical aberration]], a loss of image sharpness that can result from spherical lens surfaces.}}
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| {{Optical aberration}}
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| In [[geometric optics]] and [[cathode ray tube]] (CRT) displays, '''distortion''' is a deviation from [[rectilinear projection]], a projection in which straight lines in a scene remain straight in an image. It is a form of [[aberration in optical systems|optical aberration]].
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| Although distortion can be irregular or follow many patterns, the most commonly encountered distortions are radially symmetric, or approximately so, arising from the symmetry of a [[photographic lens]]. These ''radial distortions'' can usually be classified as either ''barrel'' distortions or ''pincushion'' distortions. See van Walree.<ref name="van Walree">{{cite web| url= http://toothwalker.org/optics/distortion.html |title= Distortion |author= Paul van Walree |work= Photographic optics |accessdate=2 February 2009}}</ref>
| | == Cheap Gucci Scarf Wear Outlet == |
| {{clear}}
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| {|
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| |valign="top"|[[Image:Barrel distortion.svg|100px]]
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| |valign="top"|'''Barrel distortion'''<br/>
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| In barrel distortion, image [[magnification]] decreases with distance from the [[optical axis]]. The apparent effect is that of an image which has been mapped around a [[sphere]] (or [[barrel]]). [[Fisheye lens]]es, which take hemispherical views, utilize this type of distortion as a way to map an infinitely wide object plane into a finite image area. In a [[zoom lens]] barrel distortion appears in the middle of the lens's focal length range and is worst at the wide-angle end of the range.<ref>{{cite web |url=http://www.cnet.com.au/tamron-18-270mm-f3-5-6-3-di-ii-vc-pzd-339323047.htm |title=Tamron 18-270mm f/3.5-6.3 Di II VC PZD |accessdate=20 March 2013}}</ref>
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| |valign="top"|[[Image:Pincushion distortion.svg|100px]]
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| |valign="top"|'''Pincushion distortion'''<br/>
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| In pincushion distortion, image magnification increases with the distance from the [[optical axis]]. The visible effect is that lines that do not go through the centre of the image are bowed inwards, towards the centre of the image, like a [[pincushion]].
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| |}
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| {|
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| |[[Image:Mustache distortion.svg|100px]]
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| |'''Mustache distortion'''<br/>
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| A mixture of both types, sometimes referred to as ''mustache distortion'' (''moustache distortion'') or ''complex distortion'', is less common but not rare. It starts out as barrel distortion close to the image center and gradually turns into pincushion distortion towards the image periphery, making horizontal lines in the top half of the frame look like a [[handlebar mustache]].
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| |}
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| Mathematically, barrel and pincushion distortion are [[quadratic function|quadratic]], meaning they increase as the ''square'' of distance from the center. In mustache distortion the [[quartic function|quartic]] (degree 4) term is significant: in the center, the degree 2 barrel distortion is dominant, while at the edge the degree 4 distortion in the pincushion direction dominates. Other distortions are in principle possible – pincushion in center and barrel at the edge, or higher order distortions (degree 6, degree 8) – but do not generally occur in practical lenses, and higher order distortions are small relative to the main barrel and pincushion effects.
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| ===Occurrence=== | | == Cheap Tell Real Gucci Scarf Fake Outlet == |
| [[File:globe effect.gif|thumb|Simulated animation of globe effect (right) compared with a simple pan (left)]]
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| In photography, distortion is particularly associated with [[zoom lens]]es, particularly large-range zooms, but may also be found in prime lenses, and depends on focal distance – for example, the [[Canon EF 50mm lens|Canon EF 50mm]] {{f/}}1.4 exhibits barrel distortion at extremely short focal distances. Barrel distortion may be found in wide-angle lenses, and is often seen at the wide-angle end of zoom lenses, while telephoto distortion is often seen in older or low-end [[telephoto lens]]es. Mustache distortion is observed particularly on the wide end of some zooms, with certain [[Angenieux retrofocus|retrofocus]] lenses, and more recently on large-range zooms such as the [[Nikon]] 18–200 mm.
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| A certain amount of pincushion distortion is often found with visual optical instruments, e.g., [[binoculars]], where it serves to eliminate the [[globe effect]]. | | A rules college move on and exists to principal missouri. back in seminole florida. my friend was initially imprisoned and so your sweetheart motor impounded. A shape baring all becoming a press reporter to gain Croatian television shows plucked a prank on Serbian prime minister,[http://www.orphanage.org/asia/go.asp?id=298 Cheap Tell Real Gucci Scarf Fake Outlet], Ivica Dacic, every last snail mail report january. 31. typically the lady deceiving will probably be correspondent came to be pantyless furthermore accomplished a "Sharon pound splash" of uncrossing the actual hip and legs along with one point truth speaking to the country's Socialist collection tops, <br><br>tend to be realize an individuals 50th birthday there was clearly valid reason to positively observe. if your main fundamental male is starting to become fifty,[http://www.orphanage.org/asia/go.asp?id=94 Silk Gucci Scarf Outlet], He is owed the finest surprise. it does not matter the birthday particular is the daddy, your government, great or possibly partner, such 50th birthday presents results in construct a unique day memorable, <br><br>persons complete ones own holiday gifts buying things the first gain a majority of benefits. initially they do not need to handle congested gifts hunting grounds as hordes of a number of customers are as well trying to do a late holiday. people people who complete these holiday season gift very early include more time unwind while keeping your focus on other items include things like styling, covering creates,[http://www.orphanage.org/asia/go.asp?id=670 Gucci Jacquard Scarf], making xmas crackers or spending a little slightly high time by domestic. |
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| [[File:Archery Target 80cm.svg|thumb|Radial distortions can be understood by their effect on concentric circles, as in an archery target.]]
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| In order to understand these distortions, it should be remembered that these are ''radial'' defects; the optical systems in question have [[rotational symmetry]] (omitting non-radial defects), so the [[didactic]]ally correct test image would be a set of [[concentric]] circles having even separation—like a shooter's target. It will then be observed that these common distortions actually imply a nonlinear radius mapping from the object to the image: What is seemingly pincushion distortion, is actually simply an exaggerated radius mapping for large radii in comparison with small radii. A graph showing radius transformations (from object to image) will be steeper in the upper (rightmost) end. Conversely, barrel distortion is actually a diminished radius mapping for large radii in comparison with small radii. A graph showing radius transformations (from object to image) will be less steep in the upper (rightmost) end.
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| ===Chromatic aberration===
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| {{Further|Chromatic aberration}}
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| Radial distortion that depends on wavelength is called "[[lateral chromatic aberration]]" – "lateral" because radial, "chromatic" because dependent on color (wavelength). This can cause colored fringes in high-contrast areas in the outer parts of the image. This should not be confused with ''axial'' (longitudinal) chromatic aberration, which causes aberrations throughout the field, particularly [[purple fringing]].
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| ===Origin of terms===
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| The names for these distortions come from familiar objects which are visually similar.
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| <gallery widths="150" heights="180">
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| File:Barrel (PSF).png|In barrel distortion, straight lines bulge ''outwards'' at the center, as in a [[barrel]].
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| File:Cushion.jpg|In pincushion distortion, corners of squares form elongated points, as in a [[cushion]].
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| File:Villianc transparent background.svg|In mustache distortion, horizontal lines bulge up in the center, then bend the other way as they approach the edge of the frame (if in the top of the frame), as in curly [[handlebar mustache]]s
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| </gallery>
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| ==Software correction==
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| Radial distortion, whilst primarily dominated by low order radial components,<ref name="devilliers">{{cite conference |last1 = de Villiers | first1 = J. P. | last2 = Leuschner | first2 = F.W. | last3 = Geldenhuys| first3 = R. | title = Centi-pixel accurate real-time inverse distortion correction| booktitle = 2008 International Symposium on Optomechatronic Technologies | publisher = SPIE | date = 17–19 November 2008 | url = http://researchspace.csir.co.za/dspace/bitstream/10204/3168/1/De%20Villiers_2008.pdf |doi=10.1117/12.804771}}</ref> can be corrected using Brown's distortion model.<ref name="brown">{{Cite journal| last=Brown |first=Duane C. |title=Decentering distortion of lenses |journal=Photogrammetric Engineering. |volume=32 |issue=3 |pages= 444–462 |date=May 1966 |url=https://eserv.asprs.org/PERS/1966journal/may/1966_may_444-462.pdf}}</ref> Brown's model corrects both for radial distortion and for tangential distortion caused by physical elements in a lens not being perfectly aligned. The latter is also known as ''decentering distortion''. See Zhang <ref name="zhang">{{cite techreport |first=Zhengyou |last=Zhang |title=A Flexible New Technique for Camera Calibration |number=MSR-TR-98-71 |institution=Microsoft Research |year=1998 |url=http://research.microsoft.com/en-us/um/people/zhang/Papers/TR98-71.pdf }}</ref> for radial distortion discussion.
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| :<math> x_\mathrm{d} = x_\mathrm{u} + x_\mathrm{u}(1 + K_1r^2 + K_2r^4 + \cdots) +
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| (P_1(r^2 + 2x_\mathrm{u}^2) + 2P_2 x_\mathrm{u}y_\mathrm{u})(1 + P_3r^2 + P_4r^4 \cdots)
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| </math>
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| :<math>
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| y_\mathrm{d} = x_\mathrm{u} + y_\mathrm{u}(1 + K_1r^2 + K_2r^4 + \cdots) +
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| (P_2(r^2 + 2y_\mathrm{u}^2) + 2P_1 x_\mathrm{u}y_\mathrm{u})(1 + P_3r^2 + P_4r^4 \cdots)
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| </math>
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| where:
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| :<math>(x_\mathrm{d},\ y_\mathrm{d})</math> = distorted image point as projected on image plane using specified lens,
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| :<math>(x_\mathrm{u},\ y_\mathrm{u})</math> = undistorted image point as projected by an ideal pin-hole camera,
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| :<math>(x_\mathrm{c},\ y_\mathrm{c})</math> = distortion center (assumed to be the [[principal point]]),
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| :<math>K_n</math> = <math>n^{\mathrm{th}}</math> radial distortion coefficient,
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| :<math>P_n</math> = <math>n^{\mathrm{th}}</math> tangential distortion coefficient,
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| :<math>r</math> = <math>\sqrt{x_\mathrm{u}^2 + y_\mathrm{u}^2}</math>, and
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| :<math>...</math> = an infinite series.
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| Barrel distortion typically will have a positive term for <math>K_1</math> whereas pincushion distortion will have a negative value. Moustache distortion will have a non-[[monotonic]] radial [[geometric series]] where for some <math>r</math> the sequence will change sign.
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| Software can correct those distortions by [[image warping|warping]] the image with a reverse distortion. This involves determining which distorted pixel corresponds to each undistorted pixel, which is non-trivial due to the [[nonlinear|non-linearity]] of the distortion equation.<ref name="devilliers"/> Lateral chromatic aberration (purple/green fringing) can be significantly reduced by applying such warping for red, green and blue separately.
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| An alternative method iteratively computes the undistorted pixel position.<ref>{{cite web|title=A Four-step Camera Calibration Procedure with Implicit Image Correction |url=http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=609468 |accessdate=19 January 2011}}</ref>
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| ===Calibrated===
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| Calibrated systems work from a table of lens/camera transfer functions:
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| * Adobe Photoshop Lightroom and Photoshop CS5 can correct complex distortion.
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| * PTlens is a Photoshop plugin or standalone application which corrects complex distortion. It not only corrects for linear distortion, but also second degree and higher nonlinear components.<ref>{{cite web |url=http://epaperpress.com/ptlens/ |title=PTlens |accessdate=2 Jan 2012}}</ref>
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| * [http://lensfun.berlios.de/ Lensfun] is a free to use database and library for correcting lens distortion.<ref>{{cite web |url=http://svn.berlios.de/wsvn/lensfun/trunk/README?rev=246 |title=lensfun - Rev 246 - /trunk/README |accessdate=13 Oct 2013}}</ref>
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| * [[DxO Labs]]' Optics Pro can correct complex distortion, and takes into account the focus distance.
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| * The [[Micro Four Thirds system]] cameras and lenses perform automatic distortion correction using correction parameters that are stored in each lens's firmware, and are applied automatically by the camera and RAW converter software. The optics of most of these lenses feature substantially more distortion than their counterparts in systems that don't offer such automatic corrections, but the software-corrected final images show noticeably less distortion than competing designs.<ref>{{cite web|last=Wiley |first=Carlisle |url=http://www.dpreview.com/articles/distortion/ |title=Articles: Digital Photography Review |publisher=Dpreview.com |date= |accessdate=2013-07-03}}</ref>
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| ===Manual===
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| Manual systems allow manual adjustment of distortion parameters:
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| * [[Photoshop]] CS2 and [[Photoshop Elements]] (from version 5) include a manual Lens Correction filter for simple (pincushion/barrel) distortion
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| * [[Corel Paint Shop Pro Photo]] include a manual Lens Distortion effect for simple (barrel, fisheye, fisheye spherical and pincushion) distortion.
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| * The [[GIMP]] includes manual lens distortion correction (from version 2.4).
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| * [[PhotoPerfect]] has interactive functions for general pincushion adjustment, and for fringe (adjusting the size of the red, green and blue image parts).
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| * [[Hugin (software)|Hugin]] can be used to correct distortion, though that is not its primary application.<ref>{{cite web|title=Hugin tutorial – Simulating an architectural projection |url=http://hugin.sourceforge.net/tutorials/architectural/en.shtml |accessdate=9 September 2009}}</ref>
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| ==Related phenomena==
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| Radial distortion is a failure of a lens to be [[rectilinear lens|rectilinear]]: a failure to image lines into lines. If a photograph is not taken straight-on then, even with a perfect rectilinear lens, rectangles will appear as [[trapezoid]]s: lines are imaged as lines, but the angles between them are not preserved (tilt is not a [[conformal map]]). This effect can be controlled by using a [[perspective control lens]], or [[Perspective control|corrected]] in post-processing.
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| Due to [[Perspective (visual)|perspective]], cameras image a cube as a square [[frustum]] (a truncated pyramid, with trapezoidal sides)—the far end is smaller than the near end. This creates perspective, and the rate at which this scaling happens (how quickly more distant objects shrink) creates a sense of a scene being deep or shallow. This cannot be changed or corrected by a simple transform of the resulting image, because it requires 3D information, namely the depth of objects in the scene. This effect is known as [[Perspective distortion (photography)|perspective distortion]]; the image itself is not distorted, but is perceived as distorted when viewed from a normal viewing distance.
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| Note that if the center of the image is closer than the edges (for example, a straight-on shot of a face), then barrel distortion and wide-angle distortion (taking the shot from close) both increase the size of the center, while pincushion distortion and telephoto distortion (taking the shot from far) both decrease the size of the center. However, radial distortion bends straight lines (out or in), while perspective distortion does not bend lines, and these are distinct phenomena. [[Fisheye lens]]es are wide-angle lenses with heavy barrel distortion and thus exhibit ''both'' these phenomena, so objects in the center of the image (if shot from a short distance) are particularly enlarged: even if the barrel distortion is corrected, the resulting image is still from a wide-angle lens, and will still have a wide-angle perspective.
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| ==See also==
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| * [[Anamorphosis]]
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| * [[Angle of view]]
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| * [[Cylindrical perspective]]
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| * [[Distortion]]
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| * [[Texture gradient]]
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| * [[Underwater vision]]
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| * [[Vignetting]]
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| ==References==
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| {{Commons category|Distortion}}
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| <references/>
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| ==External links==
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| *[http://www.ipol.im/pub/algo/ags_algebraic_lens_distortion_estimation/ Lens distortion estimation and correction] with source code and online demonstration
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| *[http://gearoracle.com/articles/lens-distortion-correction-on-post-processing/ Lens distortion correction on post-processing]
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| | |
| {{DEFAULTSORT:Distortion (Optics)}}
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| [[Category:Optics]]
| |
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