Satellite Photometry
by D. Tholen
Entire Article (Postscript format) (RTF format)
Satellite Photometry
David J. Tholen
Saturn Ring Plane Crossing Workshop
Lunar and Planetary Laboratory, Tucson, AZ
1994 May 27
I. Calibration
* timing should be good to better than a second to keep the systematic error
smaller than the likely random error in the midevent time determination
* GPS good to better than a millisecond
* modem synchronization to NIST good to small fraction of a second
* TCP/IP synchronization to NIST good to fraction of a second (not as
good as modem due to irregular network delays
* manual synchronization can be done to fraction of a second using WWV
receiver
* for longer events, be sure to measure clock drift
* use two comparison stars for magnitude calibration
* should be chosen to match colors of satellites reasonably well so that
transformation errors are minimized
* should be faint enough to avoid saturation or nonlinearity problems,
but bright enough to minimize time spent on magnitude calibration
* Titan itself may prove to be a useful calibrator for other satellites
II. Signal to Noise Ratio
* most events are of short duration, so high speed devices are required to
provide suitable time resolution, and large aperture is needed to provide
adequate signal to noise ratio during each integration
* high speed CCD is best
* slow readout CCD might work if image drifted across chip (orthogonal
to Saturn-satellite axis), though saturation may be a problem
* high speed aperture photometer may work, though see below
III. Background Subtraction
* two-dimensional detectors offer best prospects for accurate background
subtraction
* single element detectors can work, with some effort; possible techniques
include:
1. chopping to a point the same distance from Saturn: doesn't work, due
to the complex brightness contours produced by the rings and
diffraction bars
2. measuring the background at several positions surrounding your
object, such as to the north, south, east, and west: doesn't work,
because the average of these is not usually the same as the
background at your object
3. chopping to a point diametrically opposite the center of Saturn: best
bet for those who can't change aperture sizes easily, because there
is some symmetry to the scattered light background, but very
sensitive to positioning errors, especially when working closer to
the planet, where the brightness gradient is steeper
4. chopping between concentric apertures of different sizes: known to
work well for Triton and Deimos, but requires additional
calibration observations;
with n representing the count rate, through the smaller aperture, we
have:
n_total = n_obj + n_back + n_dark
and through the larger aperture, we have:
n_total = n_obj + n_back + n_dark
> the coefficient is not unity because of nonzero light in
the wings of the PSF; for aperture sizes of 6.6 and 9.4
arcsec and arcsec seeing, experience suggests a value of about 1.02;
can be measured by performing standard photometry through both
apertures on a bright star
> the coefficient is essentially the area ratio of the larger
and smaller apertures; can be measured by determining the brightness
of a blank region of sky through both apertures; best to measure it
observationally, rather than relying on measurements of the aperture
diameters (apertures may not be perfectly round, or may have burrs
around the edges); a value close to 2 is good, because if too close
to 1, then the determination of the background is poor, and if too
large, then the value of (see below) becomes too large and
therefore sensitive to modeling errors
> the coefficient represents the ratio between the average
sky brightness through the larger and smaller apertures; it is not
unity because of the complex background brightness distribution; can
be determined by numerically integrating over the two apertures using
either a model background brightness distribution, or better yet, one
provided by an observer using a two-dimensional detector; note that
the function that describes the brightness variation caused by the
planet sits on top of a variable bias caused by other essentially
flat sky brightness contributions, such as moonlight, so the value of
changes from observation to observation due to both this
effect and the changing radial distance from the planet, and
therefore must be remodeled each time; the closer to the planet, the
larger the value of
> this concentric aperture technique is essentially a variant on the
second one mentioned above, namely sampling the background in a
variety of positions surrounding the object; however, in this case
the background brightness in the smaller aperture is determined from
the background brightness in the annulus surrounding the smaller
aperture, but inside the larger aperture; this annulus is much closer
to the region of interest than in the second technique mentioned, is
more continuous than in the second technique, and much less sensitive
to the background model
IV. Data Format
* time invariant information (telescope, observer, instrument, etc.) kept in
header file
* time variable information stored in data file; sample format used for
Pluto-Charon mutual event data (expressed using FORTRAN edit descriptors):
* F13.5 midtime of observation, expressed as Julian Date
* 1X,A2 filter code
* 1X,F7.4 apparent magnitude
* 1X,F6.4 one-sigma uncertainty in apparent magnitude
V. Know Your Field
* one percent photometry requires knowledge about other light sources in
your object or background fields that are five magnitudes fainter than
your object
</pre>
