From: Loris Medici ^lt;*loris_medici@yahoo.com*>

Date: 08/08/04-07:05:30 PM Z

Message-id: <001001c47dac$f85dcbc0$bd02500a@Loris>

Date: 08/08/04-07:05:30 PM Z

Message-id: <001001c47dac$f85dcbc0$bd02500a@Loris>

1 degree = 60 minutes, when I check for tan(1 / 60) using the calculator

provided with my operating system, indeed the result is 0.00029... I

crosschecked the result by finding arctan(0.00029) * 60 = 0.9960... :) (it's

not exactly 1 because tan(1 / 60) is not exactly 0.00029) So there's no

error in the claim "tangent of one minute of arc is 0.00029".

BUT:

linear measurement 70 microns = 0.07mm = 0.007cm

distance = 25cm

l = d * tan(a)

0.007 = 25 * tan(a)

tan(a) = 0.007cm / 25cm = 0.00028 (<-- I guess this is exactly what raises

the confusion!?)

arctan(0.00028) = 0.016042... * 60 = 0.9625

This is not 1. I guess Williams' definition of "rough" is 3.75% tolerance

range :)

FWIW, I personally use a CoC value according to the planned enlargement

factor. I aim for a final resolution of 8 lpmm on the print because I have

read somewhere (don't remember) that this is the approx. resolution limit

"for most of us" ("at minimum viewing distance"). This is quite

contradictory to the result from Williams (~14 lpmm @ 25cm viewing

distance)! No problem, I'm fine with this figure. So, if I want to make a

20x30cm print from a 35mm film frame, I first find the enlargement factor:

30 / 3.6 = 8.3, then I multiply this with 8 (because I want 8 lpmm in the

print) 8.3 x 8 = 66.4 lpmm. Therefore, the CoC that will use for 8.3

enlargement factor would be 1 / 66.4 = 15microns.

----- Original Message -----

From: "Sandy King" <sanking@clemson.edu>

To: <alt-photo-process-l@sask.usask.ca>

Sent: Monday, August 09, 2004 2:53 AM

Subject: Circle of Confusion Question

*> 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 12:16:28 2004

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