Real optical systems are usually affected by geometrical distortions whose type and amount varies significantly from barely visible to significant. Furthermore, some characteristics of light propagation in an optical system results in unavoidable effects, such as wide angle lens vignetting. In this section we will look at a few TeMa functions that can be used to simulate geometrical distortions and vignetting effects.
The first step is to get some perfect images. A simple and cheap
way to obtain such images is to generate them using a ray tracing
system. Package TeMa includes some testing images generated using
the Persistence of Vision Ray Tracer (http://www.povray.org).
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As detailed by Equations TM:2.26-27 geometrical distortions can be
considered as image plane effects and can be accurately simulated once
the distortion curves are specified. Detailed distortion information
is often available for high quality lenses directly from the
manufacturer or can be measured using calibration patterns. The
following code snippet shows to curves based on the public data for a
real wide angle lens: the percent distortion and the vignetting are
reported as a function of the distance expressed in millimeters from
the optical center of the lens designed for a standard
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frame. The distortion and vignetting curves are obtained using spline
interpolation given a set of manually measured points.
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Inspection of the distortion curve, reported in
Figure , shows it to be of a complex type,
exhibiting both barrel distortion (up to 15mm from the optical center)
and pincushion distortion (from 15mm onwards).
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[width=10cm]figures/sampleDistortion.jpg |
[width=7cm]figures/vImage.jpg
[width=7cm]figures/vDeltaProfile.jpg |