[This article will soon appear on my web page in the articles
section at - www.donferrario.com/ruether/articles.html, but
I include it here since there has been so much recent discussion
(and misconception...) here on the topic...]
"On Lenses and Perspective Types"
There are various types of perspectives. Some are rectangular,
spherical, reverse spherical, orthographic, cylindrical, and
isometric.
The pure rectangular perspective type can be defined as one in
which straight subject lines remain straight in the image regardless
of how the lens is turned (but, in common with most other
perspective types, subject element sizes in the image will not
remain constant as the lens is turned). An example of a camera
that makes perfect rectangular perspective images is the pinhole
camera.
The pure spherical perspective type can be described as one in
which small subject elements remain the same size in the image
regardless of how the lens is turned on its axis, and all subject
straight lines off axis of the lens will curve away from the image
center, progressively more the further they are from the lens axis.
A lens with moderate spherical perspective (or it may be full, but
with only a small part of the full perspective area being used to
make the image) is said to have "barrel distortion", but this may
not truly be distortion (it may be just unwanted). This is most
common in many wide angles, some fast normal lenses, and most
zooms toward the shorter FL ends of their zoom ranges.
A rectangular perspective lens will show the same magnification
of a small distant subject element placed in the image center as a
spherical perspective lens (fisheye) of the same FL will (this is
also true for the other perspective types), but as one looks away
from the lens image centers (without rotating the lenses) at a series
of identical objects placed in planes perpendicular to the axes of
the lenses, the fisheye will show progressively decreasing off axis
subject magnification and the rectangular perspective lens shows
constant magnification of these same subject elements. Therefore,
there is more included subject area (a greater angle of view) with
the fisheye compared with a rectangular perspective lens of the
same FL. Or, a fisheye of longer focal length can have a wider
angle of view than a rectangular perspective lens with an even
shorter focal length.
A reverse spherical perspective type of lens will show straight
subject lines as straight lines in the image only so long as they
pass through the optical axis of the lens and image center (of an
unshifted lens - but this characteristic of showing straight image lines
of subject lines that cross the image center is true for all perspective
types). Otherwise, the image centers of off-axis subject straight
lines will curve inward toward the image center, progressively more
the further they are from the image center. Image edge magnification
of subject elements will increase, reducing the angle of view. This
type of perspective is most often seen in modest amounts (called
"pincushion distortion") with some telephotos and most zooms
toward the longer FL ends of their zoom ranges.
An orthographic perspective type of lens shares many of the
characteristics of the spherical type, but its off-axis curvature is
somewhat more mild over most of the image area, and then more
extreme toward the image edge.
Panoramic cameras that use a swinging lens shooting through a slit
(which is generally used as a focal-plane type of shutter) produce
a cylindrical type of perspective, defined as one that shows straight
subject lines that are perpendicular to the direction of the lens swing
as straight in the image, but as curved lines in other axes. These
can produce very wide but natural-looking landscape and cityscape
photographs if handled well. In digital, stitching of several images
shot in a sequence along one axis can approximate this perspective
type.
Isometric projection has essentially no perspective. The effect
can be approximated by the use of VERY long telephoto lenses,
which appear to "smash" everything together into one plane, with
no differentiations due to distance size relationships (everything
appears to be in the same scale, regardless of distance). This can
also be seen in old Japanese paintings and drawings of buildings,
often viewed from above.
The various perspective types may cause straight lines of subjects
running off axis of the image center (of an unshifted lens relative to
the sensor) to be curved, which causes a shift in image magnification
away from the center of the image, permitting a greater (or lesser)
angle of view to be photographed using some lens perspective types.
In all images, made by all lenses, the focal lengths are rated similarly
(by the distances of the lens' optical centers from the sensors at
infinity focus). This number, in millimeters, is used in combination
with the sensor format diagonal dimension and perspective type to
get an idea of what the resultant angle of view is. Complicating
this, though, is that many lenses are not accurately rated for FL,
may change FL with focus (many zooms and macro lenses do this),
and/or do not accurately follow their perspective types. Sometimes
perspective types may be combined in one image, as with the
"wavy-line" or "moustache" rendering of straight lines (combining
spherical and reverse-spherical perspectives) toward the image edges
of some wide angles and zooms.
On Lenses and Perspective Types 
Linear Mode
