Circle of Confusion Question

From: Sandy King ^lt;[email protected]>
Date: 08/08/04-05:53:21 PM Z
Message-id: <a0602040dbd3c6d3e1564@[]>

Let me send this again with a proper subject line.

I am at something of a impasse with the following problem and hope
that someone with a better understanding of mathematics can provide
some assistance.

The issues is this. I am trying to figure out how to convert angular
measurements of point discrimination to linear measurements for the
purpose of creating custom Circle of Confusion tables for minimum and
critical thresholds of human vision for 1 minute of arc and 25
seconds of arc. I would like to create the tables for a common
observing distance of 25 cm, or 10 inches.

John B. Williams, in Image Clarity: Theory of High-Resolution
Photography, gives the following formula for the conversion of
angular to linear measurements.

l = Dtana

Where l is the linear measurement, D is the observing distance and a
is the angular size.

He provides the answer for this equation for a distance of 25 cm as a
linear measurement of 0.07mm, or 70 microns, and continues by noting
that the tangent of one minute of arc is roughly 0.00029. I have
worked this problem backwards several ways and still have not been
able to figure out how he determined that the tangent of one minute
of arc is 0.00029.

Help appreciated from all competent persons.

Sandy King
Received on Mon Aug 9 12:16:17 2004

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