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Old July 2nd 04, 07:10 PM
jjs
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Default Image circle versus stopping down?


"f/256" wrote in message
ogers.com...

"jjs" wrote:


Care to help an innumerate? Taking the 38mm Biogon as an example, what's

the
light fall-off in terms of F-stops?


If you consider the light at the center of the image circle to have a
magnitude of 1 (units do not matter because we will be dealing with

ratios),
the number of stops of fall off at an angle Theta degrees off of the

center
of the center of the image would be:

Fall-off in Stops = 3.322 x Log(1 / Cos^4 of the angle Theta)

If you assume the fall off of the lens design is Cos^3 instead, the

formula
would obviously be:

Fall-off in Stops = 3.322 x Log(1 / Cos^3 of the angle Theta)

For instance, the fall off at a point 30 degrees off of the center,
considering a lens with Cos^4 fall off, would be:

Fall-off in Stops = 3.322 x Log(1 / Cos^4 ( 30 ))
Fall-off in Stops = 3.322 x Log(1 / (0.866^4))
Fall-off in Stops = 3.322 x Log(1 / 0.5625 )
Fall-off in Stops = 3.322 x Log(1.77777)
Fall-off in Stops = 3.322 x 0.2498
Fall-off in Stops = 0.83 stops


Very helpful, Guillermo. I'm a bit closer to understanding.

So, finding the Cos power of the lens-design remains problematic. Here's the
lens I'm working with:
http://course1.winona.edu/jstafford/...s1/index2.html There is very
little light fall of even in the corners. In fact there is so little I can
hardly find any. Note the construction of the lens: it covers 4x5" (actually
more than 5x5") and the rear lens is 4.5" in diameter.