# Talk:Distortion (optics)

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## Merge proposal

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

It would be really nice to have an article image distortion to link to, but since we have barrel and pincushion in separate articles it would require yet one more for the general case. These are both tiny and would fit better as sections of a generic image distortion article. Please support or oppose the merge, with reasons. Dicklyon 23:12, 7 February 2007 (UTC)

• support, of course, since I suggested it, as explained above. Dicklyon 23:12, 7 February 2007 (UTC)
• Support. Sounds like a good idea. Don't forget to adjust Aberration in optical systems accordingly. Is the best title Image distortion, or Distortion (optics)?--Srleffler 01:25, 8 February 2007 (UTC)
As written, it includes CRT distortion, which is image but not exactly optics. But I'm flexible. Dicklyon 01:39, 8 February 2007 (UTC)
Well, it is electron optics, but I agree that your proposed name makes more sense.--Srleffler 05:09, 8 February 2007 (UTC)
There are several types of image distortion. Anything that prevents an image from being a faithful representation of the original subject would qualify. Among pincushon and barrel distortion would be Vignetting and Chromatic Abberation, each of which have their own wiki. Perhaps, instead of titling this article "Image Distortion", a better title would be either 'Geometric Distortion" or "Rectilinear Distortion". Comments?--TCav 13:51, 10 August 2008 (UTC)
No, distortion is not a general term for things that degrade the image quality. Refractive effects that degrade the image are called aberrations. Chromatic aberration and distortion are just two of many types of aberration. Vignetting is not usually considered to be an aberration, since it doesn't arise from the way the lens elements refract light, but rather comes from non-refractive elements affecting which rays get detected.--Srleffler (talk) 16:27, 10 August 2008 (UTC)
Actually, chromatic aberration can overlap the aberration and distortion categories; lateral chromatic aberration is a wavelength-dependent geometric effect that "distorts" different colors differently; corrections for it use the same kind of geometric undistortion algorithms as other distortions, but on a per-color-channel basis. Tradtionally, though, I agree, we don't want to just include chromatic aberration in distortion; it could be worth a mention and a link. Dicklyon (talk) 17:58, 10 August 2008 (UTC)
Aberrations are things that happen to the path of light. Aberrations result in distortion of an image of a subject. And I'm not suggesting that we include aberrations in the "Image Distortion" wiki; I'm suggesting that we rename this wiki to reflect what it actually is: a discussion of "Geometric Distortion" or "Rectilinear Distortion" (pick one) which is more accurate and precise than the simple, and therefore, excessively broad and imprecise, "Image Distortion", which could encompass something outside optics altogether. (Pulling a piece of paper through a photo printer too fast will distort an image.)––TCav 03:01, 13 August 2008 (UTC)
Distortion is one of the third-order (Seidel) aberrations, covered in every optics textbook. You're using the term in a colloquial sense different from the technical sense used here. Aberrations produce aberrated images, not necessarily "distorted" images. This aberration is normally just called "distortion", but is called "Image distortion" on Wikipedia to distinguish it from distortion. If you feel this title isn't good, I would be open to changing it to Optical distortion, or perhaps Distortion (optics). The alternate titles you suggested are not acceptable, because they don't connect it directly to optics.--Srleffler (talk) 03:50, 13 August 2008 (UTC)
OK. Either "Optical distortion" or "Distortion (optics)" are fine with me. --TCav 23:43, 17 August 2008 (UTC) —Preceding unsigned comment added by TCav (talkcontribs)

### Requested move

So, do we have consensus to change the article title? I would prefer Distortion (optics) of all the titles that have been proposed.--Srleffler (talk) 16:32, 19 August 2008 (UTC)

I'm OK with Distortion (optics). Dicklyon (talk) 16:58, 19 August 2008 (UTC)
I'm in. --TCav 23:25, 20 August 2008 (UTC) —Preceding unsigned comment added by TCav (talkcontribs)
So, now that it's done, can't we just scrap this whole "Merge Proposal" section? --TCav 13:41, 2 September 2008 (UTC) —Preceding unsigned comment added by TCav (talkcontribs)

The above discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

## Vignetting

Would I be right to guess that vignetting is related to image distortion? That is, if a region of the image is stretched, the same light is falling on more area and so would appear darker. —Ben FrantzDale 04:09, 4 November 2007 (UTC)

While it seems reasonable that distortion would lead to a slight darkening or lightening at the edges of the image, this is not one of the dominant causes of vignetting. There are several types of vignetting. The dominant one in optical design comes from off-axis rays of light hitting obstructions inside the camera (or the edges of the individual lens elements). While modern optical design software makes it easy to see when and where vignetting will occur, this was not so easy to predict with traditional lens design methods.--Srleffler 05:14, 4 November 2007 (UTC)

## Details

This article needs details about the causes of distortion in optical systems. For example, I've seen a textbook explanation of how an aperture can cause barrel and pincushion distortion. —Ben FrantzDale 00:36, 13 November 2007 (UTC)

The model provided for the lens distortion is very simplistic, and doesn't include any of the tangential/decentering distortion components, which are useful for subpixel accurate distortion and inverse distortion characterization. Anyone opposed to me adding this info, as well as references to the Brown's seminal paper on the topic from 1966? SpoonlessSA (talk) 09:34, 31 August 2009 (UTC)

## Barrel distortion

You say that the distortion from a fish eye lens is due to it imaging a hemispherical scene. I find this a bit confusing. Surely the barrel distortion is due to the lens, not the properties of the scene being imaged or of perspective projection. E.G. If you took an image of a very large flat plane with squares on it using a pin hole camera the image you get would have straight lines. So no barrel distortion would be present due to the pin hole "lens". Only perspective "distortion" creating the foreshortening of the squares seen further away at the side of the image (making the lines appear closer together as they get further away from the centre of the image). An image of the same scene with a fish eye lens would cause barrel distortion due to the lens itself not the geometry of the scene. --Lrussell1 (talk) 15:49, 26 November 2007 (UTC)

If you were to use a lens with a 60 degree angle of view to take a photo of the center portion of a long straight brick wall, the image would contain straight lines. If you were to use the same lens to take a photo of that portion of the same wall that extends off to the left, the image would contain straight lines converging off to the left. Likewise, if you were to take a photo of the wall on the right, you would get a similar image containing straight lines converging off to the right. If you were to put the three photos alongside one another ("stitch" them), you would not have a faithful representation of the entire wall.
If you used a lens with a 180 degree angle of view to take one photo of the entire wall, you would have a faithful representation of the entire wall. What would not be a faithful representation is the reproducing of that image on a small, flat piece of paper. It is that unfaithful representation of the wall that creates the distortion, not the lens.--TCav 14:06, 10 August 2008 (UTC)
I'm not sure if you're confused, mistaken, or if I'm just misunderstanding you. The lens maps the scene to a planar image. It doesn't matter whether the image is a bitmap stored on a chip, an exposed negative, or a print on paper (small or big). The mapping from scene to image is determined by the lens. Your wall example appears to be confusing perspective with distortion. I don't think these are the same thing.--Srleffler (talk) 05:09, 19 August 2008 (UTC)
Yes. Perspective and distortion are different things. And 'Fish Eye' lenses may or may not distort, but the 'Fish Eye' part is perspective, not distortion. --TCav 21:47, 30 August 2008 (UTC) —Preceding unsigned comment added by TCav (talkcontribs)
If one wants to blame the hemispherical scene, that's a possibility, as having barrel distortion is the only to get that scene imaged onto a finite image plane area. But it makes more sense to explain that the fisheye lens utilizes barrel distortion as a mechanism to do so. If you think of an object plane (flat, not hemispherical), then the object plane imaged by a fisheye (with 180 degree angle of view) is infinite; barrel distortion is therefore obviously required to map it to a finite image area. So barrel distortion is a feature, not a bug, of fisheyes. Dicklyon (talk) 05:38, 19 August 2008 (UTC)

## Pincushion Distortion

The use of a pillow to show pincushion distortion is not accurate. Pincushion distortion is seen in the top of a pincushion whee a button often is.

## Distortion correction

I don't have access to Brown's paper, but the model that you have listed for lens distortion is backwards in terms of current practice. Those formulas should take undistorted points and distort them. Undistorting points is done by taking those formulas and solving for the undistorted input by optimization. —Preceding unsigned comment added by 128.36.233.138 (talk) 22:51, 16 February 2011 (UTC)

Is there any objection if I change the formula backward to match the model in the paper listed for lens distortion ? --Nhlevy (talk) 06:55, 10 July 2012 (UTC)
If you have access to the paper that is cited in the article, please do make the formula here match what is in the paper. Adjust the text if necessary to explain it better. Note that you can look at previous versions of this article by going to the article's history page. If one of those versions is better than the current version (such as the previous version), you can restore that version by clicking on its date in the history list, clicking the "edit" button on the old version's page, and then clicking the save button at the bottom just like any other edit.--Srleffler (talk) 03:00, 11 July 2012 (UTC)

I found a copy of the de Villiers paper online.[1] The xu= form of the equations was correct after all. I found another source as well.[2] This restores the original form of the equations, which makes sense because the original author of this passage was the one most likely to have actually looked at the reference he/she cited. I removed the "disputed" tag, as the support of the equations by references has now been verified.--Srleffler (talk) 02:59, 31 August 2012 (UTC)

I found a copy of Brown's paper online, after much searching. It can be found at asprs.org in PE&RS Archive Articles for May 1966. See ASPRS.org, go to past issue archives then go to 2008 and earlier. HTH — Preceding unsigned comment added by 31.151.126.117 (talk) 12:40, 11 December 2012 (UTC)

Thanks! I fixed the reference in the article.--Srleffler (talk) 03:34, 12 December 2012 (UTC)
I believe that the second expression containing an infinite series, i.e. ${\displaystyle (1+P_{3}r^{2}+\cdots )}$, should not be there. The infinite series only occurs in radial distortion, since tangential distortion only has two axes, I think. — Preceding unsigned comment added by 31.151.126.117 (talk) 16:12, 13 December 2012 (UTC)
This seems like a question that should be answered by consulting the references, rather than by speculation.--Srleffler (talk) 02:54, 14 December 2012 (UTC)
You're right, I've checked the Villiers paper, in which this infinite series does occur, as well as in D. C. Brown's paper “Close-range camera calibration”. However, what is incorrect is the first expression: ${\displaystyle (y_{\mathrm {d} }-y_{\mathrm {c} })(1+K_{1}r^{2}+K_{2}r^{4}+\cdots )}$. This should be ${\displaystyle y_{d}+(y_{\mathrm {d} }-y_{\mathrm {c} })(K_{1}r^{2}+K_{2}r^{4}+\cdots )}$, same for ${\displaystyle x}$. Only when ${\displaystyle y_{c}=0}$ can the expression be simplified to ${\displaystyle y_{\mathrm {d} }(1+K_{1}r^{2}+K_{2}r^{4}+\cdots )}$. — Preceding unsigned comment added by 31.223.160.113 (talk) 13:28, 17 December 2012 (UTC)

I can't find the equation in the Brown's paper! can someone give a page number?! — Preceding unsigned comment added by 134.197.40.78 (talk) 19:09, 14 October 2013 (UTC)

I don't think the equations appear in the same form in Brown's paper, but they are equation 1 in de Villiers' paper, and he attributes them to Brown.--Srleffler (talk) 05:28, 15 October 2013 (UTC)

### Remove equations?

The amount of editing happening in the distortion correction equations is a bit disturbing. Today again an editor flipped two more symbols in the equations. All the back and forth editing on these equations is more likely to introduce errors or sign convention inconsistencies than it is to produce correct formulas that have some useful purpose. It seems to me that if there is back and forth editing of equations, they are not sufficiently well cited to satisfy WP:V. I propose that either these equations should be supported by reference to a source that provides them in exactly the form given here, or they should be removed from the article.--Srleffler (talk) 00:42, 17 May 2014 (UTC)

## Barrel distortion = Perspective distortion?

Caption: "Barrel distortion bends the tower and the foundation in this image of a church" — Preceding unsigned comment added by 93.182.190.77 (talk) 00:59, 1 October 2011 (UTC)

You are right: that's a bad example. It includes perspective "distortion" as well as barrel distortion. I'll remove that picture. —Ben FrantzDale (talk) 12:58, 3 October 2011 (UTC)

The sidebar's assertion that distortion is corrected by adaptive optics systems in astronomical telescope is not true. (MCAO systems have some very limited capability to do this, but there are only a couple such systems in the world.) The ESO page referred to in the sidebar is using the word "distortion" in its informal sense, to refer to the effect of the atmosphere upon the image. Normal AO systems simply correct the optical path perturbation introduced by the atmosphere for field positions within the isoplanatic patch surrounding the guide star. In other words, the correction applied by the AO system is the same throughout the image, so it can't possibly correct distortion. I suggest that the sidebar be removed. Lauipala (talk) 10:09, 12 January 2012 (UTC)

## Linear distortion

I have found some information about linear distortion and I recognize the description of the phenomena from own experience, but I cannot find any other sources than the patent I read the term in and some other patents.

A problem using one stigmator for correcting the astigmatism is that Linear Distortion (LD) arises: the magnification in two perpendicular directions may be different.