PRINTING CALCULATOR

Inventors:  Roy H. Stratton, Stephen S. Ashley (74017,3376)

Source:     FOTOKING PRODUCTS, P.O. Box 221, Woodland Hills, CA 91365

This file describes a useful darkroom tool called the "Printing
Calculator."  This tool provides the darkroom photographer with the means
to move from one magnifaction level to another when printing black and
white or color pictures without having to run a whole new series of test
strips.  The story behind its development is interesting.

In 1989, my uncle, Roy Stratton, developed a tool for his personal use to
expedite his darkroom photography.  He took the physical formulas that
relate magnification, enlarger height, enlarging lens focal length, and
exposure and subjected them to the necessary trigonometric and logarithmic
transformations to produce a circular slide rule.  Using the angles
generated by these formulas, he laboriously created his slide rule by hand.
During a family visit he showed me his crude but effective tool.  I did
not have the scientific background to appreciate the scientific aspects of
this tool, but I realized immediately that one could produce a highly
refined version of this slide rule using the PostScript printer interface
language, which handles trigonometry and logarithms easily.  Using my
uncle's formulas, I wrote the PostScript code necessary to generate the
various components of the slide rule on any laser printer or typesetting
machine that understands PostScript.  After hundreds of refinements, we
came up with what became the final version of the slide rule, which we
dubbed the "Printing Calculator."

The Printing Calculator is actually two circular slide rules in one.  Each
side consists of a large, static, circular rule and a smaller, rotating
circular rule.  On the front side, the large, static rule denotes the
carrier-to-easel distance, measured in inches.  The small, rotating rule
denotes lens focal length in millimeters.  By rotating the small rule to
match a given focal length to a given carrier-to-easel distance, one can
determine the resulting magnification.  For instance, if you know that your
negative carrier is 30 inches above the baseboard and that your lens has a
focal length of 135 millimeters, you rotate the small rule until the 30
inch mark on the large rule matches the 135 millimeter mark on the small
rule.  A pointer at the bottom of the rule indicates that the magnification
is just over 3.3.

This feature of the Printing Calculator is handy for determining how high
to set the enlarger to enlarge a negative to a given size.  For instance,
to blow up a 4 x 5 negative to 16 x 20, you need a magnification of 4.
(Actually, you need a magnification of about 4.4, because the negative
carrier crops a 4 x 5 negative by a slight amount.)  By placing the
pointer to indicate a magnification of 4, one can read off the large rule
that an enlarger with a 135 millimeter focal length lens should be placed
at a height of 33.25 inches.  (To achieve a magnification of 4.4, place
the enlarger at a height of 35.25 inches.)

This information, by itself, is not that interesting.  Where the Printing
Calculator really comes in handy is when moving from one magnification to
another.  Suppose that one has printed a 4 x 5 negative at 8 x 10.  This
means a magnification of about 2.  Now you want to print the same
negative at 16 x 20, which requires a magnification of about 4.  The front
side of the Printing Calculator tells you that you need to raise the
enlarger head from a height of 24 inches to a height of 33.25 inches.  But
the big question is, if the original exposure was 10 seconds, how much
should the new exposure be?  The back side of the Printing Calculator
provides the answer.

The back side of the Printing Calculator is laid out the same way as the
front side, with a large, static rule and a small, rotating rule.  At the
top of the large rule is a scale that denotes the original magnification.
At the top of the small rule is a scale that denotes the new magnification.
At the bottom of the large rule is a scale that denotes the original
exposure.  At the bottom of the small rule is a scale that denotes the new
exposure.  Line up the original magnification of 2 (for an 8 x 10 print) on
the large rule with the new magnification of 4 (for a 16 x 20 print) on the
small rule.  Then match the original exposure on the bottom scale of the
large rule with the new exposure on the bottom scale on the small rule.  If
10 seconds yielded a correct exposure at the 8 x 10 size, then 28 seconds
will yield a correct exposure for a 16 x 20. The small scale also contains
a pointer, which indicates that a 1.5 stop increase in the aperature of the
enlarging lens will have the same effect. (Intuition might tell you that
the exposure should be quadrupled (i.e., 40 seconds or 2 stops.  This is
not so, because as magnification is increased, bellows travel is decreased
and hence the true f/stop number is also decreased.  The Printing
Calculator takes this effect into account automatically.)

Anyone interested in obtaining a Printing Calculator should write to
Fotoking Products, P.O. Box 221, Woodland Hills, CA 91365 or telephone Roy
Stratton at (818) 348-4449.

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