Satellite Photometry

by D. Tholen

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                             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
        * 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
    * single element detectors can work, with some effort; possible techniques
        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
                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