Macrostereo formula (2)

[P3D Paul S. Boyer <boyer@xxxxxxxxxxxxx>]

John Bercovitz writes:
>Paul S. Boyer gives us a formula for macro.
>Paul, what is the theoretical or practical basis
>for your formula?
>Thanks,
>John B

I was afraid that someone might ask that!  But here goes:

The source is Kitrosser's formula (1953, Photographic
Society of America Journal, Section B: Photographic
Science & Technique 19B, no. 2, pp. 74-76).  In slightly
modified form, Kitrosser's formula is

(0.0635*w)/(v*W*I) = 1/d-1/D

where w is the width of the diapositive or negative, v
is the lens-to-film distance, I is the interlens
separation, d is the distance to the nearest object,
and D is the distance to the farthest object in the
field of view.  (All distances in meters.)  W is a
constant, set by Kitrosser at 1.52, but in actual practice
(using Realist as a standard) I think that it should
be more like 1.25.

Now M = (v-F)/F

where M is the magnification, v is the lens-to-film
distance, and F is the focal-length of the lens.
Solving for v, we get

v = F*(M + 1)

which can be used as a sustitute for v in the first
formula.

Here comes a slight fudge: the 1/d-1/D part.  If
objects at infinity are in the field of view, 1/D
become 0.  In ordinary Realist-practice the
window would be at d = 2.1 meters, so I used this
value for d assuming that I want the finished slide
to look like a normal Realist stereogram with
the closest object at the window.  I know that
this is an assumption, and that many folks
like things sticking out of the window, so that
protective eyewear is needed to view their
slides.  I am more moderate!  Also, in macro
one does not see things at infinity, really,
because they won't be in focus.  Anyway, here's
what I did, and you can try something else if
you wish: all I ask is that you let us know
how it works.

So,

I(in meters) = (0.0635*w*2.1)/(1.25*(F*(M+1)))

That gets us down to three independent variables,
w for the particular format, F for the lens one
is using, and finally M (read off the lens),
to determine I.

For my spreadsheet I have a cell in which I can set
w (= 36 for full-frame, = 31 for European, or = 23 for
Realist), and another cell for F = focal length of
my macro lens.  I convert the formula for mm as

I = (106.68*w)/(F*(M+1))

so that I can enter w and F in mm, and the I also comes
up as mm.

As I mentioned, my Minolta macro-lens is actually marked
in reciprocals of M, so that my table is arranged to be
read directly from those markings.

The practical basis is that the results look good!
I would like to hear of the experience (and criticisms)
of others.

Final note: When one doubles the focal length of
the lens, the interlens separation is halved,
other things being equal.  That is the reverse of
the advice offered by McKay and others: the
only explanation for McKay's advice that I can
think of is that he was taking into account that
usually the longer lens is used for more
distant objects.  Of course, that is not always
true in macro work.  In macro, I prefer the
approach of working from M because it avoids
having to measure distances (which takes time),
and the M-method keeps the calculations simple.

For my 100-mm macro lens and Realist format,
I can keep a small slip of paper marked thus:
1:1     12 mm
1:1.2  13 mm
1:1.4  14 mm
1:1.6  15 mm
1:1.8  16 mm
to
1:2.2  17 mm
to
1:2.6  18 mm
to
1:3.2  19 mm
to
1:4     20 mm
to
1:5.2  21 mm
to
1:7.2  22 mm
through
1:10

If I wanted, I could tape a scale to the
barrel of the lens!

--Paul S. Boyer   <boyer@xxxxxxxxxxxxx>


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