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Date: Thu, 13 Mar 1997 09:59:32 -0800 (PST)
From: henningw@portal.ca (Henning J. Wulff)
Subject: Fishy lenses

There have been a number of posts recently about fisheye lenses and
wideangles, with some misconceptions evident.

Maybe the following will clear some of this up (maybe it won't).

Most lenses are designed to image straight lines as straight lines on film,
wherever they might appear. So generally, 'distortion' (ie, the imaging of
straight lines as slightly bowed on the film) is supposed to be kept to a
minimum. Most SLR wideangle and telephoto lenses cannot do this perfectly,
so compromises come into play. However, for most purposes they do a good
job and we don't object (too much) to the slight curves we see, mostly near
the edges, when we look at pictures of objects we know are blessed with
straight edges in real life. These are normal, or 'rectilinear' wideangles.
Even if we had a lens with essentially no 'distortion' in this technical
sense, we would still perceive an imaging distortion in wideangles which
causes close-up portraits to look hideous, causes round objects to look
like ovals in the corners of pictures, and causes the members of a group
photo who stand at the ends to look like prime candidates for Weight
Watchers. These types of distortion are unavoidable due to the fact that we
are trying to reproduce an image of the three dimensional world on a two
dimensional surface, and then are trying to view the picture from the wrong
distance (for correct perspective, and no distortion, we should view the
picture from a distance so that the photo we are looking at covers the same
angle of view that the taking lens did). Anyways, the lens is doing the job
it was designed to do.

I won't go into the math here, but it can be easily shown that a
rectilinear wideangle cannot cover 180 degrees. Wideangles with focal
lengths equivalent to 10mm or so on 35mm film have been produced, and Nikon
makes a 13mm lens.

To make a single picture which includes, side-to-side, 180 degrees or more,
a different lens or camera design is needed. One is the swing-lens camera,
which in some forms can take a single picture encompassing 360 degrees (or
more), and which produces pictures that many people consider the most
distortion free extreme wideangle. But it cannot take instantaneous photos,
ie, not all of the image gets exposed at the same time, and it cannot show
180 degrees vertically and horizontally at the same time. If you want that,
you need a fisheye.

Most fisheyes produce their very wide angles of view by making the location
of an image point directly proportional to the angle that the object is
away from the optical axis of the lens. So... If an object is straight in
front of you, and you point the fisheye lens directly at the object, the
image of the object will be in the center of the film frame. With a 180
degree fisheye, if an object is at 45 degrees off to the side, to the top,
bottom, etc., the image will appear 1/2 way to the edge of the image on the
film. All fisheyes produce circular images, whether the film format, say
35mm, is large enough to cover the entire image (7.5 or 8mm lenses
commonly), or can only use the middle, so that the edges of the cirle and
the corners of the frame coincide (15 to 18mm lenses, usually). The above
also applies to fisheyes that cover 220 degrees (6mm) and 170 degrees (the
old 16/3.5 MF lens). All use the 'equidistant' projection to produce their
image. One lens that was different was the Nikon 10mm OP lens, where OP
stands for orthographic projection. The primary aim with this lens was to
produce a whole-sky image where the image density was directly proportional
to the object light value. In other words, _no_ light falloff, ever, under
any circumstances. Other lenses, of whatever type, just do not do that.
While regular, equidistant fisheyes produce their images through the
formula Y = c * (Zenith angle), where the zenith is considered the lens
axis, orthographic projection lenses use a formula Y = c * sin(Zenith
angle), where Y is the distance of the image point from the picture center
and c is a constant, dependant on the focal length. All fisheyes, by
definition, curve lines that do not run through the zenith (lens axis), but
the OP produces a more irregular pattern of curves.

You may now hit the delete key, since if you read this, you obviously
missed your opportunity at the beginning of these ramblings.


*
/|\ Henning J. Wulff
/###\ Architecture
|[ ]| henningw@portal.ca
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