Subject: More measurements of 3.5m+DSC overall throughput

From: Stupendous Man

Submitted: Thu, 24 Aug 95 19:10:13 EDT

Message number: 2 (previous: 1, next: 3 up: Index)

            Throughput of the APO 3.5-m telescope + DSC

                         Michael Richmond
                           Aug 24, 1995

  This note supplants earlier calculations of the overall
throughput which appeared in the document, "Results of first run of PHOTO 
on DSC data from May 25, 1995".  Readers will be happy to note
that the efficiency of the instrument is slightly higher than
originally claimed.

  I have analyzed images taken with the Drift-Scan Camera in
the SDSS r'-band on May 25, 1995, in a region near SA 57.
After processing them with the standard PHOTO package --
which does NOT attempt to deal with the known 'spurious charge'
problem -- I measured the flux around a set of stars on known
brightness on several images.   I make the following assumptions:

          - Bessell R passband is equivalent to SDSS r'
                 (my tabulation of Bessell R yields central 
                  wavelength of 6544, equiv width 1521 Angstroms;
                  the documents "The SDSS Photometric System",
                  by Fukugita et al., states that SDSS r' has
                  central wavelength 6250, width 1400 Angstroms)
          - the night of May 25 was clear, and observations at
                 airmass = 1.05 suffered 0.13 mag of extinction
                 in the r'-band
          - the gain of the DSC is 2.0 electrons/DN

  With these assumptions, I compared the fluxes above sky inside
apertures of various sizes around stars which have been observed
by Connolly et al. (private communication) and by Majewski et al.
(PASP 106, 1258 [1994]).  I used several very bright stars
(V < 10) to look at the curve-of-growth of the light from a star
in increasingly large circular apertures.  I found that 
>= 86% of the "total" flux from a star ("total" means as measured
inside a radius of 96-arcsecs) falls within a radius of 5.5 arcsecs.
I used apertures of radius 5.5 arcsec (20 pixels) for most of 
my measurements, checking the results with a smaller, 5-pixel 
radius aperture.

  The main difference between the present result and the earlier
one is that I now correct for the light which falls outside of 
a 5.5-arcsecond aperture.

  I measured fluxes from a set of stars in 4 different frames,
and compared them with the fluxes predicted from the magnitudes
listed in Connolly's catalog as "aperture mag".  If we define
"overall throughput" to mean "the fraction of photons entering
the telescope which register as counts on a DSC image"

      - using 5 stars with 15.95 < R < 17.0, I find
                overall throughput <= 15% +/- 3%

        [where the "less than" occurs because I believe my assumption
         that only 86% of the light falls inside a 5.5-arcsec
         aperture is a very conservative estimate]

      - using 11 stars with 15.95 < R < 18.0, I find

                overall throughput <= 15%  +/- 2%
  I then used a set of stars from two frames which fall within
Majewski's field of standards.

      - using 5 stars with 17.69 < R < 19.75, I find

                overall throughput <= 18%  +/- 4%

  The seeing in these frames, when modelled with a sum of two
gaussians, had an inner gaussian FWHM of 1.3 arcsec.  It may
be of some use to note that, under these conditions, I measure
directly from the images (that is, I don't just assume a true
gaussian profile)

      - 13% of the total flux of a star (after correcting for
            extinction) falls within a radius of 5.5 arcseconds
      - 10% of the total flux of a star (after correcting for
            extinction) falls within a radius of 1.4 arcseconds

  Using these values for the telescope + instrument's sensitivity,
I calculated the quantity "signal-to-noise" (S/N) using 
circular apertures around a set of the same stars.  Here, I 
used the standard deviation from the mean pixel count in "empty"
areas to determine the "readout + sky noise", and added to it
the variance due to counts from each star.  Using a circular
aperture of radius 1.4 arcseconds, I find 

      - S/N ~ 10 for stars with R ~ 20.0

  Nonetheless, when I look at the positions of stars known to be
fainter (from a deep image kindly provided by Connolly), I have
trouble finding stars fainter than 21.0 with my eye on the DSC
images, even though one would expect S/N ~ 5.  PHOTO also fails
to find faint stars: when its "ffo_threshold" parameter is
set to "3" [which ought to mean something like a 3-sigma detection],
it finds 50% of the stars at about R = 20.5.  

  Why are the faint stars so hard to find?  I have not been able to
find a good answer, but my current theory is that the pixels in 
these DSC images may not exhibit true random, gaussian fluctuations,
but instead may feature "clumps".  I measured the mean of pixel
values inside 10x10 pixels boxes placed in "empty" areas in a number
of frames, and compared the distribution of mean values with those
expected from a truly gaussian distribution of pixels.  The
set of measured means had a significantly larger width than expected.
I currently interpret this to mean that there are "features" in 
the images which confuse the eye (and PHOTO) when it attempts
to find faint stars.

  As a further test, I smoothed one image with a gaussian that had
the same FWHM as the typical star.  In the resulting smoothed image,
I was able to pick out several stars with R ~ 21.3, but fainter
stars were either invisible or had "peaks" which were not very
different from spurious peaks in empty areas of the image.

  Tim McKay has told me that he has fixed some of the DSC electronics,
and that the "spurious charge" problem should not occur in future
DSC runs.  I have a run at APO upcoming, and plan to use the DSC
with only a single amplifier in slow-scan mode.  If I manage to
collect useful data, I will subject it to some of the same tests
I have made here.

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