Subject: quick calibration of recent SDSS APO+SPICam run

From: richmond@astro.Princeton.EDU

Submitted: Thu, 5 Jun 1997 20:53:18 -0400 (EDT)

Message number: 49 (previous: 48, next: 50 up: Index)

       Preliminary photometric calibration of SDSS SPICam data
                         Michael Richmond
                           June 5, 1997

Table of Contents
  Reduction of stare-mode frames
  Photometric solution
  Calibration: mag=20 object
  Overall throughput
  Sky Brightness
  Hubble Deep Field

  This is a short note on photometric calibration for the APO SPICam
run on May 29,30,31 and June 1, 1997.  

  It's hard to draw any conclusions from the current set of data,
for several reasons:

    - there were only 4 standard stars observed in total, 
           SA 105_815, SA 109_71 observed once each on May 31
           BD+262606, Ross 711   observed once each on June 1

    - each star was observed once, at a single airmass

    - we do not have really good SDSS magnitudes for these stars;
           the estimates for BD+262606 are likely to be good to
           within a few percent, but those for the other stars
           are probably less accurate, especially in u' and z'

  We can wait for the MT to observe the fields covered by the SPICam
scans ... but that will take a while.  So, I decided to do the best
I could.  This is what I did:

Reduction of stare-mode frames

     1. processed the stare-mode frames:
            - used right-hand overscan cols to estimate a single bias value
            - subtracted that constant value from the entire frame
            - created median twilight stare-mode flats (after subtracting
                    bias from each raw flatfield frame, of course),
                    using May 30 twilight flats
            - for each standard-star frame, subtracted bias and divided by
                    the median flatfield for that filter

     2. estimated the sky value from each stare-frame by fitting a parabola
               to the histogram of pixel values; it agreed to within
               a single count with both the median and mode

     3. measured the flux within a square (yes, square) aperture of "radius"
               30 pixels = 8.4 arcsec around the standard star.
               Note that the flux was still rising outside this radius.

     4. subtracted the sky contribution from the integrated flux

Photometric solution
  At this point, I had too little information to make a real photometric
solution.  So I tried a "cheat".  If we ASSUME

           a. sky was truly photometric on (late) May 31 and June 1
           b. atmospheric extinction was identical on both nights
           c. all instrumental effects were identical on both nights

THEN we can combine the measurements from the two nights into a single
solution.  Doing so gives us 4 measurements, at different airmass,
for each passband.  We know approximate SDSS magnitudes for the 4 stars:

                       u      g      r      i      z
      BD+262606      10.77   9.90   9.60   9.51   9.49
      SA105_805      12.33  11.55  11.37  11.28  11.25
      SA109_71       12.21  11.55  11.44  11.41  11.41
      Ross711        12.29  11.49  11.29  11.20  11.16

Actually, only the values for BD+262606 are likely to be accurate,
since only it has published spectrophotometry; the other values are
based upon UBVRI magnitudes and empirical conversion from Johnson-Cousins
to SDSS systems.  The u' values, in particular, are likely to be 
incorrect by large amounts.

  Blindly proceeding nonetheless, we can define
       instrumental mag = 30 - 2.5*log(counts/sec)
                      m = (instrumental mag) - (SDSS mag)

for each measurement, and then assume that
                      m = C - k*X

where "C" is some arbitrary constant, "k" is the first-order extinction
coefficient, in magnitudes per airmass, and "X" is the airmass of the 
observation.  We have 4 data points in each passband, and can plot
"m" versus "X" to find "C" and "k".  Doing so reveals that our assumptions
are not too badly satisfied in r' and g', a bit worse in i', and pretty
bad in u' and z'.  Here are the values I derived via unweighted linear fits:

        passband        k            C           scatter from line (mag)
           u'          0.4        7.5  +/- 1.0       0.37
           g'          0.21       4.9  +/- 0.2       0.06
           r'          0.12       4.8  +/- 0.1       0.02
           i'          0.09       5.16 +/- 0.15      0.05
           z'          0.13       6.1  +/- 0.3       0.09

Here, I guessed the uncertainties in the value of "C" by looking at the
plots, moving a ruler up and down with as much wiggle as I could reasonably
find in the 4 data, and then looking at the variation in the zero-point
intercept at airmass = 0.

Calibration: mag=20 object
  One can express the zero-point "C" in another manner, by calculating
how many counts per second are detected within a box of "radius" 30 pixels
around a star of magnitude 20, at an airmass of 0 (outside the
atmosphere).  Chris Stubbs used a different 
aperture size and shape, but one can attempt nonetheless to compare
his numbers with mine:

                          Richmond                 Stubbs
                     box radius 30 pixel      circle radius 55 pixel
        passband         counts/sec              counts/sec
           u'               7  (+10 -4)              8.3
           g'              88  (+18 -15)            88
           r'             104  (+10 -10)           106
           i'              79  (+11 -11)            81
           z'              32  (+10 -8)             34

Overall throughput
  My definition of the overall throughput of a telescope + detector 

               number of photons measured in detector
        QE =   ----------------------------------------
               number of photons which enter aperture

  To calculate the number of photons actually measured, I used
a gain factor of 3.38 electrons/ADU in SPICam, supplied by Chris Stubbs,
and the photometric calibration derived above.  I calculated the number
of photons per second which SPICam detected, scaled to a circle of 
diameter 350 cm above the atmosphere: #measured = 5.7 million per second.

  I then took the published spectrophotometry for BD+262606 and integrated
numerically through the SDSS r' passband to find the number of photons
per second which it should produce per square cm per second, and scaled
it to a circle of diameter 350 cm: #entering = 17.5 million per second.

  The ratio yields an overall throughput, or quantum efficiency, of 
about 33 percent -- quite a reasonable number for an imaging instrument
with 3 reflections.


Sky Brightness
  Using my own calibration, I went back and calculated the sky brightness
in frames of three of the standards (Ross 711 was observed during dawn).
I found that, even in these short exposures, the sky was bright
enough that only the u' values were significantly changed by mis-calculating
the frame's sky value by as much as 0.5 counts/pixel.  
I also include the value for one drift-scan frame of the Hubble Deep
Field, taken on June 01.

                      Sky brightness (mag/sq.arcsec)

    star   airmass   altitude  azimuth      u'     g'     r'     i'     z'
 SA105_815  ~2.5        23       253      21.8   21.3   20.5   19.5   18.3
                                       +/- 1.1    0.3    0.1    0.2    0.3

 BD+262606   1.6        41       277      19.7   21.4   20.6   20.1   19.0
                                       +/- 1.4    0.4    0.2    0.2    0.4

 SA109_71    1.2        57       187      21.7   21.5   20.9   19.9   18.7
                                       +/- 1.2    0.3    0.1    0.2    0.3

 HDF         1.23       54       335                    21.1

  Most of the uncertainty quoted in the table above is in the zero-point
of the photometric solution for the double-night; there is a small 
contribution in the u' and g' from the small number of photons collected
per pixel in the short, standard-star exposures.  

  Note that the sky brightness tends to increase with airmass, as one
would expect ... but not always.  Also note that Alamogordo is west of 
APO, so one would expect the western sky (azimuth = 270) to be brighter
than the southern sky of SA109_71.  For every star in the table,
the moon was more than 12 degrees below the horizon, and the sun
more than 26 degrees below the horizon.

  Let us compare these values with those from the Blue/Grey/Black Book;
I'll repeat the SA109_71 values.

    star   airmass   altitude  azimuth      u'     g'     r'     i'    z'
 SA109_71    1.2        57       187      21.7   21.5   20.9   19.9   18.7
                                       +/- 1.2    0.3    0.1    0.2    0.3

 Black Book                               22.1   21.8   21.2   20.3   18.6

  In each case, the measured values are close to the predicted values,
but somewhat brighter (except for z').  Certainly, this crude photometric
calibration has many untested assumptions; but it is possible that the sky
really is brighter than expected.

Hubble Deep Field
  I have done a small amount of work on the HDF scan from June 01,
frames 3-18.  I reduced the data by

        - subtracting a single bias value per frame (as described above)
        - combining 6 frames into a long-long-long region, then taking
               the median of each column to provide a flatfield value
        - dividing each bias-subtracted frame by the median flatfield

The results look very nice -- there is no discernible gradient perpendicular
to the drift direction, and little gradient along it.

  The HDF itself appears in frame jun1.0012.fits, in the western 
half of the frame.  About one-quarter of the HDF falls off the edge
of the frame.  Here are details on the observation:

        - JD 50601.71014
        - filter = r'
        - exposure time 47.8 seconds
        - airmass = 1.23, alt = 54.5 degrees, az = 335 degrees
        - FWHM = 4.7 pixel = 1.3 arcsec
        - sky = 171.2 counts/pixel = 21.1 mag/sq.arcsec
        - sky sigma approx 7 counts/pixel

  There is a bright star at the eastern end of the frame, which appears
in the Guide Star Catalog at V = 15.0.  I calculate r' = 14.99
for this star.  Using it as a reference, I find the following 
magnitudes for some objects which appear in the HDF from our data;
I also include the magnitudes determined by HST, from the U of Hawaii
interactive HDF page:

    type       RA         Dec            counts   r'       F620     F814
    star   12:36:54.65  +62:13:29.0       219    19.76     20.1     18.8
    star   12:36:56.25  +62:12:42.3       440    18.99     19.6     18.6
    star   12:36:53.57  +62:13:09.36       38    21.62     21.9     20.4
    galaxy 12:36:51.00  +62:13:21.5        62    20.19     20.4     19.4
    galaxy 12:36:49.33  +62:13:47.8       362    18.54     18.9     17.6

  Pictures available upon request.  It will take more work to determine
a meaningful "limiting magnitude".

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