"Leonard Evens" wrote in message
...
Richard Knoppow wrote:

What you say below is correct. But there is one minor
problem for
perfectionists. You have to know the actual focal length,
which may be
different from the nominal published focal length.


Its not hard to find the principal points of a lens.
If
you know the focal length its only necessary to focus
the
lens exactly at infinity and measure one focal length
from
the focal plane toward the lens. By definition that is
the
principle point. To measure the front or first principal
point turn the lens around and again focus it for
infinity.
Again, measure from the focal plane toward the lens,
that
will be the first or front principal point and is the
point
to measure object to lens distance to.
If there is no handy target far enough away to
approximate infinity you can focus by autocollimation.
You
need a small mirror and a card with a small hole in it,
and
a flashlight to place behind the card. Place the mirror
over
the lens. Place the card in back of the lens, adjust the
card (or lens) until an image of the illuminated hole is
reflected back to the card. It should be near the hole.
When
this image is sharply focused the lens is exactly at
infinity focus from the card. In a view or press camera
you
can usually get sufficiently good accuracy by placing a
small light source over the ground glass near the center
and
focusing the lens on that.
Since you know the focal length and infinity focus
position you can calculate the amount the lens must be
moved
from infinity focus and use that to adjust for some
closer
distance. Its still necessary to know the location of
the
front principal point so you can measure the distance.

For any lens the distance from the infinity focus point
for
any closer distance is:

X = f^2 / u - f

Whe
X = extension from infinity focus
f = focal length
u = subject distance



Its not difficult in principle to measure the exact focal
length, but it does require some precision, especially for
shorter lenses. With the above formula one can determine the
focal length from the extension required for a known
distance or from magnification. The easiest is the set the
lens for unity magnification since the focus extension from
infintity to 1:1 is exactly one focal length.
It may be easier to measure the extension for a known
distance than it is to set the image for exactly 1:1.
However, knowing the exact distance requires knowing the
location of the princpal points and that requires knowing
the focal length unless one has access to an optical bench
and a nodal slide. So, the unity magnification is perhaps
the most practical method. The lens is focused for infinity
with either a very distant target or by autocollimating as
above. Then the lens is set for exactly 1:1 image to object
size. The displacement of the lens from the infinity focus
point is one focal length. A double check is the total
distance from focal plane (ground glass) to object. At 1:1
it is exactly four times the focal length.
The principal points are found by measuring one focal
length back toward the lens from the focal plane at infinity
focus. The first or front principal point is found by making
the same measurement with the lens turned around. These
points are somtimes useful to know for calculating focus,
depth of field, exposure correction, and magnification.

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Richard Knoppow
Los Angeles, CA, USA