"jjs" wrote in message ...
"f/256" wrote in message
. rogers.com...
Here is an example based on the Biogon 38mm:

Assuming it has a fall off as good as Cos^3

[...]
There are ONE and a HALF stops of fall off at the corners of the film with
respect to the center of the film!!

Funny, but I don't find the 38mm Biogon that bad in real life.

Richard K. is correct about Biogon types: they are better than cos^4,
but don't expect any better than cos^3. In fact, you'll be lucky if
you're getting as good as cos^3. This amount of falloff can be
surprisingly subtle as long as its gradual. If you want to really
study it you need to photograph a perfectly uniform scene, and then
analyse the negative or transparency with a densitometer.

It is possible to design a distortion free lens which has absolutely
no falloff. In fact, its even possible to have the corner
illumination a little brighter than the center. The key is to use an
extreme reversed telephoto form that is either telecentric or nearly
telecentric. Telecentricity helps to eliminate both the
inverse-square and angle-of-incidence factors that lead to the
conventional cos^4 rule of thumb. Below is a monochromatic 2-element
example which uses conic aspheres on all four surfaces to help correct
aberrations (10mm EFL, 72 degrees FFOV, f/4). Corner illumination is
slightly higher than the center illumination.


Surf Radius Thickness Index Diameter Conic
OBJ Infinity Infinity 0 0
1 103.5259 3 1.500000 76.49878 0.6488538
2 20.94909 167.5245 54.63685 -0.6207915
STO Infinity 33.51543 10.36337 0
4 31.42817 24 1.500000 25.11525 -1.335523
5 -44.96278 38.56207 25.06757 -3.892987
IMA Infinity 14.53115 0

Brian
www.caldwellphotographic.com