# What is mFT FoV?

Started 4 months ago | Question thread
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 Re: Effects of Pin-cushion Distortion Correction on FOV In reply to Detail Man, 4 months ago

Detail Man wrote:

gollywop wrote:

Detail Man wrote:

However, since correcting for barrel-distortion has the apparent effect of "squeezing" image-data outwards (beyond the horizontal borders of some given aspect-ratio), could it be that the inverse operation of correcting for pincushion-distortion (pincusion-distortion correction) would have an effect of "squeezing" image-data inwards (within the horizontal borders of some given aspect-ratio) - thus having the effect of actually decreasing the horizontal (and thus the diagonal) FOV existing in (pincusion-distortion corrected) image ?

Well, the pin-cushion correction could also be by pulling data outwards, but along the middles of the borders rather than the corners. If that's what happens (and it's my suspicion that it is), the "pulled-out" portion can simply be discarded and the original aspect and size retained. But I have no examples to analyze.

But have a look at the example mathematical identities set forth in this information source:

http://en.wikipedia.org/wiki/Distortion_%28optics%29#Software_correction

Radial distortion ... [is] ... primarily dominated by low order radial components ...

where:

(xd, yd) = distorted image point as projected on image plane using specified lens;

(xu, yu) = undistorted image point as projected by an ideal pin-hole camera;

(xc, yc) = distortion center (assumed to be the principal point);

Kn = Nth radial distortion coefficient;

and r equals the following:

Barrel distortion typically will have a positive term for K1 whereas pincushion distortion will have a negative value.

I take it from the above statement that barrel-distortion correction coefficients will have negative terms for Kn, and that pincusion-distortion correction coefficients will have positive terms for Kn.

Thus, it seems that the x-axis locations of corrected pixel-locations are shifted in opposite directions in the corrected images - causing pincushion-distortion corrections to push the x-axis location of pixels inwards, and rectilinear-distortion corrections to push the x-axis location of pixels outwards. Upon having a look at the above-quoted information, does that make sense to you ?

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This matter seems potentially quite relevant to your original question posed in this thread.

With respect to some fixed reference aspect-ratio of output images, it seems that camera body manufacturers must cover the specified FOV in the case of zero rectlinear distortion, and we have found that additional FOV can only be realized (in the case of the existence of finite amounts of barrel-distortion) when one is willing to increase the magnitude of the numerical value of the output image aspect-ratio (such that the horizontal dimension of the output image is allowed to increase relative to the vertical dimension).

However, it seem (to me) that a different situation appears to exist in the case of the existence of pincushion-distortion. In those cases, what I am thinking is that additional FOV can only be relalized (in the case of the existence of finite amounts of pincushion-distortion) when one is willing to decrease the magnitude of the numerical value of the output image aspect-ratio (such that the horizontal dimension of the output image is allowed to decrease relative to the vertical dimension).

Given that today's preferential trends for image-presentation seem to in many cases be moving towards higher valued (as opposed to lower valued) aspect-ratios ("wider" displays and screens), it seems that RAW-images recorded using a telephoto zoom lens that (over some range of Focal Lengths of adjustment) exhibits pincusion-distortion appear to operate at a relative disadvantage (where realizable FOV is concerned) relative to the situation where (over some range of Focal Lengths of adjustment) barrel-distortion is exhibited.

(Perhaps) this is one reason why (at least to my limited knowledge regarding such leneses) fixed Focal Length lenses do not exhibit pincushion-distortion in their un-corrected image output ?

DM...

A touch of casual empiricism:

If I open an image of a rectangular item (in this case a CC24 card) whose edges closely border the edge of the frame in ACR and apply negative rectilinear distortion (pincushion) correction, it bows the edges out at their center at a much greater rate than it moves the corners. In fact, the corners barely move, even when the edges bow out considerably. That's what I would expect. The corner-to-corner (both vertically and horizontally) and the diagonal pixel count remains unchanged, but a horizontal (vertical) line in the center is stretched considerably outside the frame.

And, if one now crops the resulting "corrected" figure, the pixel dimensions are exactly the same as the initial (uncorrected) image.

This contrasts to the case of barrel distortion, where the corners again remain fixed, but the edges are bowed inwards. An "interior" crop now is necessarily smaller than the original in both dimensions, and, ﻿pari passu﻿, the diagonal.

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gollywop

Edited 4 months ago by gollywop
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