On Lens Perspective Types

There are several types of lens and image perspectives.
Some of the more familiar types are rectangular, spherical, cylindrical, and orthographic. 

The pure rectangular perspective type (example
here) 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.

Orthographic projection images (example
here) have essentially no perspective, with no parallel line convergence in the image (and no curvature of subject straight lines in the image), but may be taken from any angle. 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 imaging type can also be seen in old Japanese paintings and drawings of buildings, often viewed from above, and in architectural drawings. For more, go here.

Isometric projection images also have no perspective, but
they do have equally angled projection angles of 120 degrees. This type is most often used for mechanical, and sometimes architectural, drawings. For more, go

The pure spherical perspective type (example here) 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 focal length ("FL") ends of their zoom ranges.

A rectangular perspective lens will show the same
magnification of a small subject element placed in 
the image center as will a spherical perspective lens
(fisheye) of the same FL with the same object placed
at the same distance from it (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 will show constant magnification of these same
subject elements. Therefore, there must be more included
subject area (a greater angle of view) with the fisheye
compared with a rectangular perspective lens of the 
same FL. A fisheye lens can easily have a wider angle 
of view than a rectangular perspective lens with a 
shorter focal length, and a fisheye lens can even have 
an angle of view greater than 180 degrees, which no 
rectangular perspective lens can have (although some
swing lens cylindrical perspective cameras can also
have this).

An orthographic fisheye 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.

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 (with an unshifted lens) - but
this characteristic of showing straight image lines of
straight subject lines that cross the image center is
true for most of the perspective types. Also, 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 with most zooms toward the longer FL ends of their
zoom ranges.

Panoramic cameras that use swinging lenses shooting 
through slits (which are generally used as a focal plane
type of shutter) onto curved film produce a cylindrical
type of perspective, defined as one that shows straight
subject lines as straight in the image that are parallel
with the slit, 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.

These various perspective types may cause straight lines 
of subjects running off axis of the image center (of 
an unshifted lens relative to the sensor or film) to be
curved, which results in a shift in image magnification
away from the center of the image. This results in
greater or lesser angles of view being photographed under
the same conditions with different lenses of the same
FLs (but with different lens perspective types) on the
same camera. Usually the angle of view differences are
subtle (with the visible curvature of straight subject
lines being perhaps not so subtle) except with fisheye
lenses. Using the same lens on different formats and/or
camera types will result in different angles of view
being photographed (i.e., a 65mm FL lens is a super wide
on a 4x5 camera and on a 120 swing-lens panorama camera; 
a moderate wide angle on a 2 1/4 square format; a longish
normal lens on 35mm; a short tele on most dSLRs; and a
long tele on many compact digital cameras and most 
consumer camcorders). 

In all images, made by all lenses, the focal lengths are
rated similarly (by the distances of the lens' optical
centers from the film or sensor 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. For more on this, see "
On Lens Angles Of View,
Magnification, And Perspective
". 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 - and 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. 

For more, see my articles, "
On Seeing and Perspective
and "
On Lens Distortion Types".

David Ruether (d_ruether@hotmail.com)

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