Re: Shimming a triplet - 3D camera

[T3D John Bercovitz <bercov@xxxxxxxxxxx>]

> Agnars have front-cell focussing, but it's the first two elements that
> focus, not just the first, which makes me suspect that you could move the
> rear element instead of the front element to achieve the same effect,
> changing the focal length.

That's very interesting about the two front elements moving.  Perhaps Ed
Romney can tell us more about that.  I think you're exactly right - moving
the single rear element should be the equivalent of moving a single front
element.

In a Cooke triplet (I looked this up last night after I posted my earlier 
message), in very rough terms, the front and rear elements are about equal
in power and the center element is about the same power as the sum of the
other two but it's negative.  The front element to the center element is
about half the distance from the center element to the rear element.  The
front element alone has about three times the power of the assembly.

>From this I should be able to make an Excel spreadsheet for this form of
a Cooke.  There are tons of variations, though.

Now since you already have the lens in hand, we don't really have to
guess.  What I need for you to do is to measure how far the lens' front
cell moves when you go from some known distance to an infinity setting.

Let's say that you set the lens for infinity and measure the position 
of the front cell relative to something that won't move like the camera
body.  Now you refocus for 2 meters by screwing the front cell out.
measure the distance of the front cell from the body again.  Subtract 
to get the total movement of the front cell when moving from one distance
to the other.  Let's say you had to move it 0.1 mm (triplets are _very_
sensitive).  If the lens was a 45 mm lens when it was focussed at infinity
and it didn't move (essentially) when it was refocussed to 2000 mm, then
the lens had to have been changed from a 45 mm lens to a higher powered
lens of 44 mm.  So now we know that adding a shim of 0.1 mm thickness
increases the power of the lens by decreasing its focal length 1 mm.
Does this make sense?

OK, so how did I know the lens went from 45 mm to 44 mm?  Easy, from
the Gaussian form of the lens equation:

    1     1     1
    -  =  -  +  -
    f    s1    s2

We know the lens was 45 mm to start with so that's s2 when s1 is infinity.
We also know s2 is still 45 mm when we refocus to 2000 mm.  When we refocus
to 2000 mm, the equation looks like:

    1      1     1
    -  =   -  +  -
    f    2000    45 

If we solve this, we find f is 44 mm.  45 - 44 = 1 mm so we know what
ever adjustment we made cause the lens to change by 1 mm.

John B


------------------------------