This notes reports my test to use a Meade DSI to derive the rough
magnitudes per square arcsec (mpsas) photometry for the night sky
above and dark carter floors on a 71% illuminated Moon. In general
the idea crashed and burned, but here is what I was able to salvage.
In addition to other technical problems that I need to work through, I
used the wrong procedure and the signal ratio was too low to be able
to derive confirmable good photometric magnitudes from images of the
south pole and Alcyone taken on the morning of Sept. 9. This note is
to extract what data and conclusions that can be recovered from the
effort.
While I am not going to vouch for the scientific accuracy of the
magnitudes in the above presentation, it at least provides some
differential magnitude information for the lunar south pole at 77%
illuminated fraction. It also illustrates how other amateurs, more
experienced in photometry than I, might develop techniques for amateur
absolute photometry of the Moon.
This note discusses a photometric colorgram of the south lunar pole
contained in a summary info panel of five slides at:
http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090909_1154UT_111W_41N_SP_photometry_panel_kaf.jpg
http://tinyurl.com/r4x9fx
On Sept. 9, I took normal tone images of the south lunar pole through
a Johnson V filter at a high f-ratio more suitable for topographic
resolution, see:
Sept. 9 image in info panel format
http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090909_1154UT_111W_41N_SP_panel_kaf.jpg
http://tinyurl.com/nlf58f
Imaging particulars are: ETX 125mm, MeadeDSI Pro, Johnson V filter,
0.0625 secs, approx. 4500mm efl. by negative projection; dark frame
substraction only.
Then I swung over, without changing exposure settings and imaged part
of the Alcyone multiple. Alcyone was only a few degrees lower in
altitude than the Moon. The three applicable stars imaged were:
Star Johnson V* Pixel_value mpsas
Alcyone 2.9 12223 16.5
HD23629 6.3 596 21.3
HD23607 8.7 81 n/a
* Per Hauck (1997)
Analysis done in AIP4WIN indicated good sigmas for the three stars
based on 70 individual images and the FWHM pixel value that
corresponds to each reference object was obtained. Sigma values
looked good: 0.019, 0.0021, 0.09, respectively. The S/N ratio was
not. Mag. 8.7 HD23607 was just barely visible in the raw images -
having only a few pixel values above background.
I was unable to build a consistent single coefficient transform to
relate the three reference magnitudes (due to poor signal to noise
ratios). I was unable to relate the reference pixel value for Alcyone
and the pixel values in a raw south pole image to mpsas within a
reasonable range of normal values for the lunar surface by converting
them to mpsas. See Cavadore for an algorithm to convert a reference
stellar magnitude and pixel values to magnitudes per square arcsec.
http://www.astrosurf.com/cavadore/articles/pollution/index.html
Nonetheless the raw pixel values for Alcyone and HD23629 can be used
to extract some provisional differential photometry information from
the corresponding raw image of the south lunar pole. It is a
reasonable assumption that pixels in the south lunar polar image that
have the same pixel values as Alcyone and HD23629 have the same V
magnitudes.
A raw south polar image (file: author's file Moon50001-0008.fts) - a
crisp lunar image - was selected and image was dark flat
subtracted.
First, with respect to 6.3 V magnitude HD23629, there are no pixels in
raw image below a pixel value of 596. The minimum pixel value for the
image is 611.
The implication of this is that single point stars of less than 5.8
magnitudes cannot be seen in the sky immediately above the dark limb
due to insufficient contrast.
This is consistent with Schaefer's articles and Qbasic program for the
limiting magnitude of a grazing or occulting star. Recently, we
discussed here the September 9 graze of ZC387, a V magnitude 6.9 star,
whose ground path ran through Utah to California. The IOTA's Occult
4.0 program returned the following limiting magnitudes by aperature
and distance from the terminator's intersection with the lunar
(negative cusp angles are on the sunlit side):
Occult 4.0 limiting magnitude report excerpt for
ZC387 graze on 9-9-2009
---------------------
Librations Long -5.58 Lat -6.16
Illumination of moon 77%-
At longitude -112.50:
Limiting Magnitudes for various
telescope apertures (in mm)
CA\Tdia 250 300 350
-1.1 5.8 6.1 6.3
0.9 5.8 6.1 6.3
2.9 7.6 7.9 8.1
4.9 7.9 8.2 8.4
6.9 8.2 8.5 8.7
---------------------
Even having 14 inches of aperature, as compared to 10 inches, gets you
only a small additional limiting magnitude reach. The lack of
contrast between the background sky and the object controls.
This 1000 to 2000 pixel value clip (5.75 to 5.0 V mags) picks up the
dark sky above the lunar limb at Faustini.
Using some basic differential photometry, the following range of pixel
values and magnitudes were defined:
Pixel Value V mag
596 6.3
1000 5.75
2000 5.0
5000 4.0
7000 3.5
9000 3.23 ~3.25
11000 3.0
12223 2.9
14000 2.75
For pixel value ranges less than 2000, 6.3 V mag HD23629 was used as
the reference star. For pixel value ranges above 5000, 2.9 V mag
Alcyone was used as the reference star.
For discussion purposes, these magnitudes are divided into the
following ranges that are color coded into the summary information
panel in an image panel at (url:
http://tinyurl.com/r4x9fx ):
V mag rng mpsas rng Color Pixel value
5.75-5.0 20.4-19.3 Red-brwn 1000-2000
5.0-4.0 19.3-18.0 Magenta 2000-5000
3.5-3.25 17.5-17.2 Aqua 7000-9000
3.25-3.0 17.2-16.9 n/a 9000-11000
3.0-2.75 16.9-16.6 Yellow 11000-14000
Although I was unable to use direct computation using pixel values and
the pixel size in arcsecs to reasonable values of apparent brightness
in mpsas, Schaefer provides an algorithm to prepare a "cheat" indirect
computation. Schaefer's algorithm provides an method to convert V
steller magnitudes to mpsas for stars above magnitude 6.6. The results
of that conversion are included in the table above. See discussion
url:
http://members.csolutions.net/fisherka/astronote/plan/tlmnelm/html/NELM2BCalc.html
Using AIP4WIN's MinMix math function, a black/white fits image was
created by replacing all pixels below 1000 with 0 and all pixels above
2000 (5.75 to 5.0 V mags) with 0.
The next MinMax threashold clipped image is for pixel values bewteen
2000 and 5000 - corresponding (I hope) to predicted V magnitudes 5.0
to 4.0. This pixel value clip picks up the shadowed area in the
Malapert dark hole, the interior shadowed area of craters Caebus, part
of the shadowed area in Haworth, but not any shadowed portion of
Caebus A and B.
The next pixel value clip is for 7,000 to 9,000 pixel values ( 3.5 to
3.23 V mags). The clip picks up the shadowed floors in Caebus A and
B.
The final pixel value clip is for 11,000 to 14,000 ( 3.0 Vmags to 2.75
V mags) which encompasses the 12,223 pixel value for Alcyone (2.9 V
mags).
Next, the RGB channel combine function of the image processing
software AIP4WIN was used to create a three colorgram of these limited
magnitude ranges. A three-color colorgram is the maximum that you can
create using AIP4WIN. A second piece of freeware available on the
internet - iMerge (url:
http://www.geocities.com/jgroveuk/iMerge.html
) - was used to add a fourth color layer using two bmp images. The
assembly of multiple color layers is, of course, trivial for owners of
the expensive Photoshop application.
Finally, a second more detailed color gram was prepared of the Cabeus
region. See the info panel (url:
http://tinyurl.com/r4x9fx ). An
additional range clip of pixels was added into to cover the ADU pixel
value ranges found in Cabeus A.
The detailed colorgram suggests that the shadowed portion of Cabeus A
at 77% illuminated fraction was an apparent brightness equal to
between 3.5 to 3.25 magnitudes. But again, this is one of my first
photometry tests, so the result may be way off.
The next opportunity to experiment with this technique at illuminated
fractions similar to a 71% illuminated fraction is will be 9-28-2009
3:00UT (68% illumination). This will be an east illumination at very
low horizon altitude of about 30 degrees, considering the Moon's
position in the ecliptic.
This amateur work product. Comments and criticisms of the above are
welcomed.
Clear Skies - Kurt
P.S. A zipped file of the dark subtracted raw image of the Moon and
Alycone and the individual clipped magnitude channels in fits format
is available online at url:
http://members.csolutions.net/fisherka/astronote/observed/LCROSS/20090909Photometry_fts.zip