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Paul Ewins
28-Dec-2005, 14:44
Does anybody know of a formula for calculating the image circle of a lens at closer distances? I'm much more interested in portraits than landscapes, so for me knowing the IC at 2m - 3m is more important than at infinity. It looks like it should be a fairly straight forward calculation, but it has just been too long since High School physics for me to be certain that I could derive the correct formula myself.

thanks,

Paul

Nick_3536
28-Dec-2005, 15:02
You've got a triangle. One side is the distance from the lens to the film plane. Second side is the from the middle of the film plane out to the edge of the image circle. The third side is from lens out to the edge of the film plane. You've got three angles. 90 degrees is at the middle of the film plane. The angle at the lens is 1/2 the coverage angle [I think] The third angle is 90 - 1/2*coverage angle. All three should add up to 180.

Okay you know all three angles. You can figure out the length of the line from the lens to the film plane easy enough.

You then cheat and go here:

http://www.trig.ionichost.com/trig.php

A angle of coverage

B 90 degrees

C 90 -A

Leave side a blank

Side b equals the distance to the film plane

leave side c blank

hit solve. Then double the result for side A.

I'll leave it to the people that remember highschool math to point all the mistakes I'm sure to have made -)

Nick_3536
28-Dec-2005, 15:03
Ooops. A is half the angle of coverage.

Nick_3536
28-Dec-2005, 15:14
Okay let me oops again. Leave b blank to. c is the distance to the film plane.

Michael Gudzinowicz
28-Dec-2005, 15:47

IC@Infinity x ( 1 + Magnification )

Paul Ewins
28-Dec-2005, 16:53
Ok, that makes it fairly clear. The extra coverage is calculated by dividing the focal length by the subject distance. For a 210mm lens at 2m this is approx 10% extra. Not a huge difference, but will increase with focal length and might be important for ULF work.

thanks,

Paul

Michael Gudzinowicz
28-Dec-2005, 17:22
You don't get much more coverage other than at macro distances. For "far" subjects, you can use your estimate for the magnification, but for close distances (d), the focal length (f) should not be ignored:

IC@Infinity x ( 1 + Magnification ) = IC@Infinity x ( 1 + f/(d-f))