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Science Forum Index » Optics Forum » Distortion Correction Math
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| Tom Hubin |
 Posted: Sun Mar 09, 2008 7:02 pm |
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Hello,
I can scale a distortion free camera CCD image by a constant to get an
accurate representation of the object plane. That constant would be the
reciprocal of the magnification.
If I use an inexpensive short focal length (f<10mm, f/2) wide angle lens
I get distortion. I would guess that the magnification is a function of
the radial distance from the optical axis.
But before I start deriving equations I thought I would ask here how
distortion calibration and correction are usually handled mathematically.
Tom Hubin
thubin@earthlink.net |
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| James R (Jim) Lynch III |
| Posted: Sun Mar 09, 2008 10:20 pm |
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I've used linear least squares to fit image height [y(i)] versus half-fov
angle [theta(i)] data to the following polynomial:
y(i) = f*tan(theta(i)) + T*tan(theta(i))**3 + F*tan(theta(i))**5 +
S*tan(theta(i))**7 + N*tan(theta(i))**9
The f coefficient is the calibrated EFL, the T coefficient is the third
order distortion term, and so forth.
I could get the ordered pairs by analysis since I had designed the lens, so
I had accurate values to work with.
If I had relatively inaccurate, measured data, I doubt I could have fitted
terms much beyond the third order distortion term.
James R (Jim) Lynch III |
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| Richard J Kinch |
| Posted: Mon Mar 10, 2008 12:09 am |
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Tom Hubin writes:
Quote: But before I start deriving equations I thought I would ask here how
distortion calibration and correction are usually handled mathematically.
You could take samples by shooting a calibrated linear scale under
magnification, fit a curve to the non-linear image of that, and then invert
the curve mathematically against the future images. |
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