Partial Penumbral Eclipse Mathematics

Gents ... and you-know-who,

This is a little project I have had on my mind for some time and which
has failed on the previous two occasions due to the weather.
Fortunately for me, last evening we had pristine transparency.

Partial penumbral eclipses are generally ignored since they are
considered as ho-hum and due to the virtually undetectable difference
in brightness due to earth's penumbral shadow. However, something
which may not be perceivable by the eye can often be a trivial case
for a (sensitive) camera and which takes a no prisoners approach.

For a composite image comprised of last evening's full moon just
before its entry into the penumbra ("Pre-P1"), the full moon at its
maximum penumbral position ("Max") as well as a third image of the
full moon comprised of the difference (ie. "Diff"), I kindly direct
you to http://www.perseus.gr/Astro-Eclipses-2009-08-06.htm . The
latter of the three component images is really the change in the
moon's brightness owing to its entry into the penumbra and, as you can
see, this particular eclipse was comprised of a partial entry into the
penumbra by a portion of the moon's southern hemisphere and, more
specifically, the region around Tycho and below.

In order not to bias this analysis in any way, the camera was set to
RAW mode so that the images written to the memory card would be
untouched by the camera's on-board software (typical of images saved
in JPG format). Also, exposure settings such as sensitivity (ISO),
exposure length, white balance etc were kept identical for the image
at "P1" and "Max".

My "Pre-C1" image was taken four minutes prior to the predicted first
contact of the moon with the penumbra. I do not know if it would have
been better to capture this baseline image much earlier (ex. an hour)
as a precautionary measure.

I hope the result is of interest.

Anthony.