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Old July 2nd 04, 08:06 PM
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Default Image circle versus stopping down?

So, finding the Cos power of the lens-design remains problematic. Here's

lens I'm working with: 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"

more than 5x5") and the rear lens is 4.5" in diameter.

That's a big piece of glass!

As Richard said, and who am I to argue with him!, designs give you not
better than Cos^3, that lens 3" FL give you and angle of 46 degrees at the
corner of a 4x5 negative, still 1.5 stops according to Cos^3 fall off, so it
may not look like there is any fall off but likely there is.

Here is an explanation to the Cosine^4 and how to find the fstops of fall
off, in case it is helpful for you to understand what's going on:

The way Cosine law works is like this: because a point off the center is
farther away by 1/Cosine of the angle, light at that point is dimmer than at
the center, because the InverseSquareLaw light is dimmer by 1/Cos^2 at that
point (that account for 2 times Cos in the cos^4 law), because light falls
on an angle on the film plane, it covers an area 1/cos bigger that at the
center of the film, more coverage with the same light means dimmer light per
unit of area (another Cos in the Cos^4 law) and finally because the aperture
is no seen as a circle but as an oval that has Cosine of the angle less
area, it allows less light thru by a factor of -you guessed it!- cosine of
the angle (yet another Cosine in the cos^4 law), the whole thing combines to

If we assume a light intensity of 1 at the center, the fall off 60 degrees
off of the center would be Cos^4 (60 degrees) = 0.0625, in other words if
you have 100 units of light at the center, at the corners you would have
only 6.25 units of light !! How do you calculate the numbers of stops
between the 6.25 and 100 ? You double 6.25 until you get 100, like this:

6.25 x 2 = 12.5 one stop
12.5 x 2 = 25 two stops
25 x 2 = 50 three stops
50 x 4 = 100 four stops

There are 4 stops fall off with respect to the center at a point 60 degrees
from the center.