Hi-- I have no background, formal or otherwise, in this sort of thing
(but, when did that ever stop me [I also do audio electronics and speaker
design, and a whiz friend of mine, who has worked out the theory on a
speaker enclosure design I use, insists that the performance characteristics
that I observe don't happen.... But I just keep enjoying my 10-20 cycle bass
out of an efficient speaker with great damping {and flat bass impedence
curve} and pretend he is wrong...]), so I will jump in, sort of....
>With ordinary lenses and flat film, the illumination of the film falls
>off with cos(theta)^4, where theta is the angle of a subject point off
>the optical axis. One power of cos(theta) comes from the apparent
>foreshortening of the aperture as seen from the subject point.
O.K.
>Now, considering only rectilinear lenses, let us imagine the subject being
>on the inside of a sphere
Why a sphere, and not a flat plane?
>and descibed in phi (distance around from,
>say, horizontal) and theta (distance from axis) coordinates, and
>consider a little patch,
>of the patch is dtheata*dphi*sin(theta), but as rendered on the film,
>its tangential dimension is f*dphi*tan(theta), and its radial
>dimension is f*dphi*sec(theta)^2. Multiplying this out and dividing
>by the original size, doing some simple trig substitutions, and
>dumping the f^2, since it is taken care of by the convention of using
>f-stops, we see that the magnification increases with 1/cos(theta)^3,
>contributing the other 3 powers of cos(theta).
>Obviously the cos(theta)^3 that comes from magnification can't be
>directly eliminated, even by retrofocus designs that make the light
>strike the film at a more more normal angle such as would be the case
>with a normal design.
Seems to me some of it could - the projection distance differences
across the film are sure reduced when the optics are moved further from
the film.
>(It's not the angle of the light striking the
>film that is the problem, it is the fact that a equal sized patches of
>subject area get spread out over more film if they come from the edge
>than from the center.)
Makes sense, but again, the retro design would appear to present the
image to the film in a way that is closer to the way a longer focal
length lens would do it, thus some light falloff advantage.
>But the lens designer can compensate by two
>possible means. 1. The apparent iris can "tip" toward the subject
>when viewed from the side. (If it weren't for the this effect,
>fisheye lenses seeing 180 degrees or more would be impossible.) 2.
>The apparent iris can be larger when viewed from the side.
>So my question is this. Just how effectively can rectilinear lenses
>be compensated for cos(theta)^4 falloff? Is there any fundamental
>limitation? What is achieved in practice?
Try either 15mm Nikkor - they both render even tones across the frame
evenly with B&W prints and slides (I should try Tech Pan at 200 or so
[high contrast] to push the test) - seems to me that for all practical
purposes, these lenses do the "impossible": they eliminate the effects
of the cosine law.
>If this can be done
>without the introduction of too much aberration, why is it that
>compensating neutral density filters are available for large-format
>wide-angle lenses?
The large-format lenses do play funnies with the aperture, but being
non-retro designs, they can't go far enough (though I sold my center
filter for the 90mm f8 Nikkor, since it wasn't much needed, even for
shifted 5x7 [the Schneider 90mm f8 shows serious falloff, even in
shifted 4x5]). The 21mm Leitz early version had more light falloff
than the later somewhat retro version (to clear the meter arm).
Methinks retrofocus design helps with wide angle illumination.
Looking at it the other way, telephoto (not long focus) design
presents more of a problem with illumination than a simple lens
design of equal length (remember those unique tele designed wide
angles in the Olympus XA's, where flatness in the package was
traded for greater than normal illumination rolloff?).
David
> -- David Jacobson
>
>P.S. to sci.optics: This is been crossposted from rec.photo.moderated,
>which (obviously) is moderated, to sci.optics. Replies will go to our
>moderator and may not appear for a few days. But please go ahead and
>reply. Pete Bergstrom, our moderator, is a nice guy.