Note 3: The first constant term in the equation, above, is
somewhat dependent upon the signal circle size. If the circle is
smaller than the size used for the annual calibration (and that's a
temptation, since your SNR for a faint object is best for smaller
signal apertures), then you'll have to determine the response ratio.
This is done using a bright, nearby star, where you note the ratio of
intensities for a large aperture that captures >99% of the star
light, and the intensity corresponding to the smaller aperture you want
to use for the faint asteroid. Use this response ratio to adjust the
asteroid's intensity before using the above equation.
Note 4: Notice that your asteroid magnitude will be more
accurate when observing at high elevations, where air mass is small and
the extinction term is smallest. It is difficult to know the
exact value of your extinction coefficient on a particular night, and
greater the air mass the greater the systematic error this uncertainty
will produce. At my site the clear sky extinction at zenith probably
varies from 0.12 to 0.15 during the year. An observer at a lower
altitude than my 4700 feet will have slightly higher extinction. For my
site extinction values for the filters BVRIC (where C = unfiltered) are
typically 0.28, 0.16, 0.13 and 0.09 magnitude per air mass.
Procedure for Annual System Calibration
The calibration observing session is meant to evaluate the first
the above equation, and possibly to check your assumed extinction per
air mass coefficient. Whenever I conduct a system calibration I cycle
through my 5 filters, BVRIC. Probably most
asteroid searchers observe unfiltered, so you may ignore references to
changing filters in the following description.
For the system calibration choose only a completely cloudless night
with no greater than calm winds. When these two conditions are met the
night is referred to as "photometric."
Start the night with dusk flat frames near zenith. I use a double
T-shirt "diffuser" placed in front of the telescope aperture to
eliminate the possibility of stars showing up on the flat frames.
Choose exposure times that produce a maximum counts value for the
entire image of no more than ~30,000 counts (in order to avoid
saturation). Don't use images with
exposure times <1 second (because shutters can introduce their own
component of vignetting for short exposures). I use only flat
frames with exposure times between 1 and 20 seconds. Using dark frames
is a good idea, but some people consider this optional. Don't use a
cooler for the CCD chip (or if you do, be sure the chip temperature is
very stable). After the flats are complete for all filters, turn on the
CCD cooler to a vlue that the TEC can reach in a reasonable time (a few
minutes) and start focus observations.
Select Landolt areas to observe that are at low and high air mass.
Try to position your FOV so that several Landolt stars are present. (As
a convenience, I've produced a TXT-file of the Landolt stars for import
into TheSky. During the import process TheSky creates a SDB-file for
fast loading on subsequent uses of the program. Whenever TheSky is run
it automatically includes the Landolt stars and displays their
magnitudes when a star is clicked.) Choose exposure times that avoid
saturation for all Landolt stars. For me 10 seconds works well. Make at
least 4 exposures of each Landolt area, and make at least that many
dark frame exposures. Calibrate the light images using many darks
(median combined) and your flats (averaged).
In theory you can stop after obtaining exposures of a Landolt area
at high air mass and another at low air mas, but it's prudent to repeat
the pairing to be sure temporal trends of extinction are not present.
Two pairs of Landolt area observations should take no more than 4
Analysis of these observations might be considered difficult by
observers not used to the joys of spreadsheets. I make manual readings
of intensity for all Landolt stars using a carefully chosen set of
photometry dimensions. The signal circle must be large enough to
accommodate >99% of the photons registered by the largest FWHM
Landolt star for the night. Each image must be inspected to assure that
nearby stars are not present in the sky reference annulus. If
interfering stars can't be avoided, then edit them away! Don't be
afraid of pixel editing, but be careful in using this tool to
select new pixel values that are representative of the sky background
level for that part of the image.
Record all intensities, and mid-exposure UT times, and use a
planetarium program to determine air mass values for each image. Enter
these data into a spreadsheet, and also enter the Landolt magnitudes.
To veiw a sample spreadsheet layout, click SampleSpreadsheet.
concept to be implemented in the spreadsheet is to perform a least
squares solution for that first term, unique to the telescope system,
such that the equation produces magnitudes that agree with the Landolt
magnitudes. With this as a guiding concept you are invited to create
your own spreadsheet to solve for the best value for this one
constant. You are also invited to solve for your site's extinction
coefficient, making use of the fact that you have high and low air mass
measurements of known stars. If you're ambitious, you can also try to
detect a temporal trend for extinction for this calibration
When the results of this telescope system calibration are used for
the analysis of images taken on other nights there may be systematic
errors of 0.1 magnitude. I don't understand these changes yet, but
beware of systematic changes that might be even larger for unknown
reasons. It is always prudent to use another method to check the
magnitude determinations from this method if you want to be assured of
0.15 magnitude accuracy.
Return to Photometry for Dummies
This site opened: January 1, 2005. Last Update: January 4, 2005