Re: ATM: Measuring pinhole diameter.

[Anthony Stillman <atmer@flash.net>]

Eli,

First I consider this to be totally on topic.  Second, I can measure that
pin hole with one bobby pin, a laser, a card, and two rulers.  To begin,
bend the bobby pin into one of those little bobby pin bombs that spring
wildly when you toss them against something.  Set it, but don't through it.
Next on a long sturdy ruler mount the laser, then pin hole, and then some
distance away, the card as a screen.  Align the laser so that light passes
through the pin hole to strike the screen.  On the screen you will see an
airy disk.  The center to center diameter of the first dark ring is defined
by the diameter of the pin hole and the distance from the pin hole to the
card.  Specifically:

    d_airy = 2.44 * R * lambda / d_pinHole    (1)

Here R is the distance from the screen to the pin hole.

Therefore for a lambda of 670nm (2) and a pin hole to card separation of 1
meter.

    d_pinHole = (2.44 * 1 * 670EEX-9) / d_airy
or
    d_pinHole = 1.6348EEX-6 m^2 / d_airy

where the pin hole and airy disk diameters are measured in meters.

So, for a pin hole 0.0085" in diameter and a card distance of 39.37" with a
670nm wavelength laser pointer, the airy disk would be 0.2981" in diameter.

Measuring center to center the dark ring that surrounds the central spike
of the airy disk can be difficult.  I suggest making several measurements
at several distances, then average the calculated pin hole sizes.  Also,
its unlikely that using a diode laser will produce the classic airy disk
appearence.  Rather, artifacts from the diode junction will be visable
around the center spike.  You can clean this up by using a second pin hole
and/or lens before the pin hole under test, if need be.

Oh, yea don't leave that bobby bomb laying around un-detonated.

Anthony



1) Unless of course you are lactose intolerant.  In which case you will
want to split hairs and note that its not exactly the center of the ring
the airy disk is defined to.
2) Your wavelength may vary.