At 02:56 1/19/01, John Prosper wrote:
Rectilinear means the lens has been corrected for barrel distortion: this
is unlike fisheye lenses which lack this cvorrection.
A technical correction to promote better understanding about the dfference
between a fisheye and a rectilinear lens . . .
Neither a theoretical fisheye nor a theoretical rectilinear lens has
"distortion." In particular, a theoretical fisheye lens does not have
"barrel" distortion. This is a popular myth. In practical lenses, they
may have detectable distortion of one type or another, but that is a
deviation or aberration from the theoretical definition of what they are.
A rectilinear lens, by definition, maps a flat plane in space to a flat
plane of film by preserving angles at the expense of preserving
areas. This is why, if you aim a rectilinear lens at a flat surface with
lens axis perpendicular to both the surface and the film plane, parallel
lines in space remain parallel on the film. It is also why there are
practical design limits on their vertical angle of view beyond about
100-105 degrees. It is impossible to even theoretically achieve a 180
degree or greater horizontal or vertical angle of view.
A fisheye lens, by definition, maps a portion of a spherical surface in
space to a flat plane of film by preserving areas, not angles. Any
detectable "distortion" is some deviation from these definitions. It is
why one can achieve angles of view in practical designs of them that are
180 degrees and greater. A fisheye lens image appears distorted because
our eyes and brains see the world around us in rectilinear terms, or very
nearly so until you are at the limits of peripheral vision. However it's
not distortion from reality; It _is_ reality mapped to a flat surface
differently from the method our eyes and brains use.
Think of the two lens types like a cartographer does in making maps on a
flat piece of paper. It's how points in space are mapped to a flat surface
that defines them. The mapping is different between a "Mercator"
projection and a "polar" projection because the mapping mathematics differ
between the two.
-- John
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