Thomas Bryhn wrote:
At 04:33 04.12.02, John A. Lind wrote:
The rest of the effect, a cos^3(theta) falloff is the spreading of
light gathered from a solid angle to a flat piece of film. The light
gathered by the lens over a solid angle spreads out more (is magnified
more) nearer the edge and in the corners than in the center. The
farther from the center, the greater the spreading. It is how a
rectilinear lens maps flat planes in space to a flat film plane from a
position that is effectively a point in space, or at least very nearly
a point. This is the effect that making the image circle somewhat
larger than the minimum required can mitigate. Make it too large
though, and the lens suffers from loss of contrast and risk of flare
from the extra light bouncing around inside the light box (region
between lens rear element and film plane).
OK, we agree about where the cos^3(theta) term come from. If we stick to
the simple lens approximation, how is theta defined and found? It's all
defined by focal lenght and the film format, image circle doesn't enter
into the equation at all. So for *this approximation* any lens of a
given focal length will show the same falloff, because the angles are
always the same.
For complex lenses I'm sure the lens designer can do all sorts of funny
things to circumvent cos^4 - but you argue that a larger image circle
will give less falloff. To me this also implies that a smaller image
circle would give more falloff. So I make up an example where I reduce
the image circle by vignetting, and I have at least managed to convince
myself that this doesn't do anything to the rate of falloff.
I think you're both arguing the same thing. John is not saying that a
larger image circle has less fall-off - just that the smaller your film
format the less of the falloff you record on film. By only recording on
film the centre of the image circle you eliminate obtrusive light
falloff towards the edge of the recorded image, although of course the
light falloff towards the edge of the image circle is the same.
Roger
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