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     THE NEAR-IR SCATTERING PHENOMENON IN THINNED SITe CCDs

                    J. E. Gunn 
                   20 July 1997


Some time ago Don York was told about an alarming result discovered by
Rich Reed at NOAO during tests of thinned SITe CCDs like ours for STIS. 
In these tests, Reed saw extended scattering wings in the near infrared,
which he attributed to light going through the thinned device and
scattering from the indium solder interface behind the translucent
ceramic substrate which supports the thinned membrane in these chips. 
In what follows we shall call this phenomenon, whatever the cause, rear
scattering (because it is certainly associated with the return of flux
from the rear of the device.)

Reed kindly sent me his data in graphical form, and I have finally
gotten around to analyzing it in the context of the SDSS.  It would
appear that the data are well described by the phenomenon which Reed
proposed; light scattering in a translucent medium is attenuated by a
factor 1/r due to the 2-dimensional geometry and by an exponential
optical depth factor due to scattering and losses (into the ccd or
absorption by the indium or the ceramic).  The data are well fit by
the radial function

Bs/F = (f/2*pi*r0) * exp(-r/r0)/r, 

where Bs is the surface brightness of the scattering wing, F is the
total flux, and f is the fraction of the total which is scattered.  Reed
studied the phenomenon at several wavelengths using what was essentially
a line source, and his curves are well represented by the projection of this
function in one dimension. 

The parameters f and r0 are reasonably well represented by the 
interpolation formulae

r0 = 50 lam^2, lam = wavelength in microns

f = exp(11.51*(lam-1.05)), lam < 1.05
    1                      lam > 1.05

representative values are

     lam    r0(pix)    f
    
    6000      18     .006
    7000      25     .016
    8000      34     .065 
    9000      41     .18
   10000      48     .56

Here r0 is in pixels for the 24u pixel device; it presumably scales with
the inverse of the pixel size and in some complex way which depends on
the exact details of the transport upon the thickness and opacity of the
ceramic substrate, the thickness of the silicon membrane, the
reflectivity of the indium film, and the efficiency of the
antireflection coating on the CCD.  The scattered fraction f presumably
goes to unity at the wavelength of the bandgap of silicon, about 10500 A
(at which wavelength the quantum efficiency goes essentially to zero
anyway.) and the behavior, in which the log of f is almost linear with
wavelength, supports this conjecture.  It is perhaps curious that the
relation is more nearly exponential with wavelength than frequency, and
the interpolation formula for it is to be regarded as just that.  There
in reality will be a small thermal tail extension to 1-f to longer
wavelengths, which we ignore here. 

As one can see from the table, at 1 micron the effect is catastrophic,
with nearly 60 percent of the flux in the scattering halo; by 9000, the
fraction is still 18 percent, 8000, six percent, and 7000, only 1.6
percent.  The effective wavelengths of the Sloan filters for this effect
are considerably longer than the flux effective wavelengths because of
the very strong wavelength dependence; the effective wavelengths,
scattering lengths, and scattered flux fractions are approximately

  fil    lameff(u)   r0      f
  
   r'      0.64      20    .009     
   i'      0.78      32    .049
   z'      0.95      44    .31

The photometric camera is, of course, not using thin chips in the z
band, but the monitor telescope is.  The effect is likely to be worse,
in fact, for the MT chip because its UV-optimized coating is less
efficient in the red and infrared than the normal vis-AR coatings and
more reflective for the scattered flux returning to the device from
below.  Preliminary estimates for the MT throughput confirm this, with
the u', g', r', and i' efficiencies pretty close to the estimates, but
the z' efficiency about a factor of 2 low.  This will not be a problem
provided the effect is sufficiently uniform over the chip.  This is, in
fact, likely to be the case, because the primary QE is not dependent on
the effect, but if the rear scattering is not uniform one must be very
careful in the interpretation of flat fields for calibration, which
measure in effect the total PSF including the rear scattering wings.  It
may be necessary to use stars to calibrate the "flat field" in z' with
the MT, and perhaps in i' as well, though probably not.  The use of
aperture magnitudes for the MT, necessary because of the undersampling,
makes the operational consequences of the phenomenon negligible; the
measurement of fluxes can proceed exactly as it is being done now. 

The consequences for the survey imaging data are a little more severe
and may have some software impact.  The z' chips are not affected at
all, since they are thick.  In u' and g' the effect of rear scattering
is negligible; in r', the small-angle scattering wings of the PSF
generated by the atmosphere and optics dominates the wings of the PSF
everywhere, but if the amplitude of the rear scattering is as Reed
measured it, the wings are significantly modified at radii of 20 pixels
or so.  In i' the rear scattering dominates the PSF from 10 to over 100
pixels radius, and the simple power-law model for the PSF wings which
the pipeline uses currently will not work.  This has little or no impact
for photometry, but severly affects the subtraction of the wings of
bright stars; in brightness, the range is from about 5.e-4 to 3.e-7 of
the central intensity; the flux, again, is about 5 percent of the total. 

In the following table is presented some expected radial profiles of
stars including Kolmogorov seeing and observed small-angle scattering,
and the rear scattering wings as calculated here.  The first column is
the radius in units of the half width at half maximum, here assumed to
be 1.25 pixels (0.5 arcsec); the next column, kolpsf, is the Kolmogorov
seeing psf of unit central intensity, including observed small-angle
scattering wings (from Racine).  The next three columns, rscatt, iscatt,
and zscatt, are the expected rear-scattering wings in r', i', and z',
respectively, for a thinned device in this seeing.  These wings are to
be compared with the Kolmogorov psf decreased by the unscattered
fraction, 0.99, 0.95, and 0.68, respectively, for the parameters
discussed here.  The pixel scale assumed here is that for the imaging
camera with 1 arcsecond seeing, and so the z' column is of academic
interest only, but the severity of the effect we would have to live with
had we chosen thin chips for the z' band is properly frightening.

      r     kpsf     r'scatt    i'scatt    z'scatt

   0.100 9.909e-001 1.542e-003 5.260e-003 2.501e-002
   0.126 9.870e-001 1.533e-003 5.231e-003 2.488e-002
   0.158 9.807e-001 1.519e-003 5.188e-003 2.468e-002
   0.200 9.705e-001 1.498e-003 5.122e-003 2.438e-002
   0.251 9.543e-001 1.468e-003 5.025e-003 2.393e-002
   0.316 9.295e-001 1.424e-003 4.882e-003 2.327e-002
   0.398 8.920e-001 1.362e-003 4.677e-003 2.231e-002
   0.501 8.358e-001 1.276e-003 4.394e-003 2.098e-002
   0.631 7.541e-001 1.165e-003 4.024e-003 1.924e-002
   0.794 6.423e-001 1.030e-003 3.572e-003 1.711e-002
   1.000 5.014e-001 8.793e-004 3.063e-003 1.470e-002
   1.259 3.435e-001 7.248e-004 2.540e-003 1.223e-002
   1.585 1.973e-001 5.797e-004 2.047e-003 9.888e-003
   1.995 9.173e-002 4.529e-004 1.615e-003 7.836e-003
   2.512 3.505e-002 3.481e-004 1.256e-003 6.129e-003
   3.162 1.237e-002 2.642e-004 9.682e-004 4.756e-003
   3.981 4.668e-003 1.983e-004 7.407e-004 3.671e-003
   5.012 1.943e-003 1.470e-004 5.625e-004 2.818e-003
   6.310 8.743e-004 1.073e-004 4.232e-004 2.150e-003
   7.943 4.082e-004 7.675e-005 3.146e-004 1.626e-003
  10.000 1.964e-004 5.352e-005 2.302e-004 1.216e-003
  12.589 9.713e-005 3.612e-005 1.651e-004 8.966e-004
  15.849 4.929e-005 2.339e-005 1.154e-004 6.488e-004
  19.953 2.557e-005 1.437e-005 7.803e-005 4.584e-004
  25.119 1.352e-005 8.260e-006 5.064e-005 3.143e-004
  31.623 7.257e-006 4.369e-006 3.120e-005 2.075e-004
  39.811 3.942e-006 2.080e-006 1.799e-005 1.306e-004
  50.119 2.161e-006 8.675e-007 9.555e-006 7.741e-005
  63.096 1.193e-006 3.062e-007 4.572e-006 4.253e-005
  79.433 6.621e-007 8.761e-008 1.918e-006 2.124e-005
 100.000 3.687e-007 1.924e-008 6.823e-007 9.404e-006

For the MT pixel scale, the star image is more concentrated than in the
case of the camera, so the effect on the psf is somewhat smaller; the
fraction of light lost to scattering is the same, but it is spread out
over a much larger area compared to the star image (though the profile
of the scattered light is the same in PIXELS, modulo a trivial change in
convolution due to seeing).  The table above for the MT becomes (the
unit of radius is still 0.5 arcsec) :


      r     kpsf     r'scatt    i'scatt    z'scatt

   0.100 9.909e-001 3.794e-004 1.294e-003 5.960e-003
   0.126 9.870e-001 3.771e-004 1.287e-003 5.929e-003
   0.158 9.807e-001 3.737e-004 1.276e-003 5.882e-003
   0.200 9.705e-001 3.686e-004 1.260e-003 5.810e-003
   0.251 9.543e-001 3.612e-004 1.236e-003 5.703e-003
   0.316 9.295e-001 3.504e-004 1.201e-003 5.545e-003
   0.398 8.920e-001 3.350e-004 1.151e-003 5.317e-003
   0.501 8.358e-001 3.140e-004 1.081e-003 5.001e-003
   0.631 7.541e-001 2.867e-004 9.899e-004 4.586e-003
   0.794 6.423e-001 2.535e-004 8.787e-004 4.077e-003
   1.000 5.014e-001 2.163e-004 7.536e-004 3.504e-003
   1.259 3.435e-001 1.783e-004 6.249e-004 2.914e-003
   1.585 1.973e-001 1.426e-004 5.036e-004 2.357e-003
   1.995 9.173e-002 1.114e-004 3.973e-004 1.867e-003
   2.512 3.505e-002 8.564e-005 3.091e-004 1.461e-003
   3.162 1.237e-002 6.500e-005 2.382e-004 1.133e-003
   3.981 4.668e-003 4.878e-005 1.822e-004 8.748e-004
   5.012 1.943e-003 3.616e-005 1.384e-004 6.716e-004
   6.310 8.743e-004 2.639e-005 1.041e-004 5.124e-004
   7.943 4.082e-004 1.888e-005 7.740e-005 3.876e-004
  10.000 1.964e-004 1.317e-005 5.664e-005 2.899e-004
  12.589 9.713e-005 8.886e-006 4.061e-005 2.137e-004
  15.849 4.929e-005 5.753e-006 2.838e-005 1.546e-004
  19.953 2.557e-005 3.534e-006 1.920e-005 1.093e-004
  25.119 1.352e-005 2.032e-006 1.246e-005 7.491e-005
  31.623 7.257e-006 1.075e-006 7.675e-006 4.946e-005
  39.811 3.942e-006 5.117e-007 4.427e-006 3.113e-005
  50.119 2.161e-006 2.134e-007 2.351e-006 1.845e-005
  63.096 1.193e-006 7.533e-008 1.125e-006 1.013e-005
  79.433 6.621e-007 2.155e-008 4.719e-007 5.061e-006
 100.000 3.687e-007 4.734e-009 1.679e-007 2.241e-006

It is seen here that scattering has little effect on the psfs except in
z', dominating only between about 30 and 60 pixels in i' and even so not
dominating by very much.  In z', the scattering dominates beyond about 8
units, 4 arcsec, 5 pixels, radius.  For a just saturated star, the
annulus between 12.5 and 25 pixels (10 and 20 arcsec) has a signal which
is enhanced by 14 and 5 DN, respectively, at its inner and outer
boundaries.  Using such an annulus for the sky signal would depress the
measured flux by about 2.5 percent; it happens that about 2.5 percent of
the flux is also scattered within 5 pixels, so the net result of using a
disk of 5 pixels radius for the stellar aperture and determining the sky
from an annulus with inner and outer radius 12 and 25, which is a
reasonable set, is that the scattering roughly cancels, and leaves one
measuring the unscattered fraction, about 70 percent of the total. 

Recall that it would appear from the preliminary MT data that the
UV-coated chip suffers rather more than these parameters would indicate
in z', but until better data are available, detailed calculations of the
form of the psf and the effect on the shape of the z' band cannot be
done.  We CAN calculate the effects if the current paramters were
correct, and in that case the 'vital statistics' of the MT passbands
are, with no scattering, (these are slightly different from those last
distributed because the MT mirror coatings have changed since then to
bare aluminum on the secondary and a quartz-overcoated aluminum film on
the primary.)

MT FILTER QUANTITIES, NO ATMOSPHERE 1 bare 1 230nm SiO2, no rear scatt. 
 fil     lbar     wid        qt         qtdll       sig     efwhm
  u'     3505     630  1.919e-001    3.220e-002   0.0569     469
  g'     4744    1415  4.348e-001    1.207e-001   0.0899    1003
  r'     6217    1385  4.945e-001    1.065e-001   0.0653     955
  i'     7626    1533  4.406e-001    7.921e-002   0.0588    1055
  z'     9061    1392  2.396e-001    3.689e-002   0.0573    1221

MT FILTER QUANTITIES, 1.2 AIRMASSES 1 bare 1 230nm SiO2 no rear scatt.
 fil     lbar     wid        qt         qtdll       sig     efwhm
  u'     3547     584  9.758e-002    1.513e-002   0.0536     447
  g'     4772    1379  3.619e-001    9.458e-002   0.0885     994
  r'     6227    1374  4.495e-001    9.412e-002   0.0649     951
  i'     7629    1530  4.079e-001    7.161e-002   0.0591    1061
  z'     9038     984  2.254e-001    3.175e-002   0.0584    1242

MT FILTER QUANTITIES, NO ATMOSPHERE 1 bare 1 230nm SiO2, 'std' rear scatt. 
 fil     lbar     wid        qt         qtdll       sig     efwhm
  u'     3505     630  1.919e-001    3.220e-002   0.0569     469
  g'     4744    1415  4.338e-001    1.205e-001   0.0899    1003
  r'     6216    1384  4.911e-001    1.057e-001   0.0652     954
  i'     7616    1522  4.304e-001    7.584e-002   0.0585    1048
  z'     8955    1194  2.100e-001    2.818e-002   0.0506    1067

MT FILTER QUANTITIES, 1.2 AIRMASSES 1 bare 1 230nm SiO2 'std' rear scatt.
 fil     lbar     wid        qt         qtdll       sig     efwhm
  u'     3547     584  9.758e-002    1.513e-002   0.0536     447
  g'     4772    1380  3.610e-001    9.443e-002   0.0885     993
  r'     6225    1374  4.449e-001    9.334e-002   0.0649     951
  i'     7618    1519  3.993e-001    6.855e-002   0.0588    1054
  z'     8927     968  1.980e-001    2.435e-002   0.0506    1063

For contrast, the quantities for the photometric camera are

DSS FILTER QUANTITIES, NO ATMOSPHERE 2 shiles Al bare, 'std' rear scatt.
 fil     lbar     wid        qt         qtdll       sig     efwhm
  u'     3501     619  2.394e-001    3.956e-002   0.0564     464
  g'     4741    1419  5.425e-001    1.508e-001   0.0902    1006
  r'     6220    1385  6.110e-001    1.318e-001   0.0653     955
  i'     7613    1519  5.267e-001    9.258e-002   0.0585    1047
  z'     9150    1348  1.374e-001    2.166e-002   0.0640    1377

DSS FILTER QUANTITIES, 1.2 AIRMASSES 2 shiles Al bare, 'std' rear scatt.
 fil     lbar     wid        qt         qtdll       sig     efwhm
  u'     3543     567  1.237e-001    1.853e-002   0.0530     442
  g'     4770    1387  4.501e-001    1.181e-001   0.0887     996
  r'     6229    1373  5.569e-001    1.164e-001   0.0649     952
  i'     7615    1513  4.924e-001    8.370e-002   0.0588    1053
  z'     9134     950  1.291e-001    1.867e-002   0.0659    1417

Note that though the bands for the MT and the camera match very well for
u', g', r', and i', the z bands do not match well; this was always the
case, but the mismatch now is much worse than before; there was roughly
a 100A mismatch in the effective wavelengths before, and with scattering
taken into account the mismatch is 200 A.  The calculated effect on the
total throughput, qtdll, is a bit smaller than we estimated, about 25
percent vs 31, doubtless because of the extreme assymetry of the z'
passband. 

The z' response (system DQE, in these tables with no atmosphere) with 
wavelength for the camera, MT with no scattering and MT with scattering,
with the scattering model employed here, is

    DSS z' response functions
  lam    camera   MT_noscatt  MT

 7800   0.00001   0.00001   0.00001
 7900   0.00009   0.00019   0.00018
 8000   0.00073   0.00158   0.00149
 8100   0.00447   0.00973   0.00912
 8200   0.01856   0.04024   0.03739
 8300   0.04607   0.09775   0.08998
 8400   0.07862   0.16013   0.14585
 8500   0.10580   0.20480   0.18430
 8600   0.12359   0.22716   0.20166
 8700   0.13326   0.23310   0.20374
 8800   0.13715   0.23044   0.19787
 8900   0.13639   0.22408   0.18855
 9000   0.13266   0.21609   0.17764
 9100   0.12671   0.20614   0.16499
 9200   0.11904   0.19429   0.15078
 9300   0.11021   0.18105   0.13555
 9400   0.10047   0.16632   0.11943
 9500   0.09021   0.15027   0.10274
 9600   0.08001   0.13345   0.08609
 9700   0.07039   0.11668   0.07022
 9800   0.06171   0.10028   0.05548
 9900   0.05428   0.08437   0.04208
10000   0.04773   0.06876   0.03009
10100   0.04174   0.05384   0.01987
10200   0.03596   0.04002   0.01168
10300   0.03008   0.02779   0.00572
10400   0.02411   0.01820   0.00198
10500   0.01846   0.01159   0.00000
10600   0.01344   0.00722   0.00000
10700   0.00943   0.00433   0.00000
10800   0.00675   0.00249   0.00000
10900   0.00527   0.00141   0.00000
11000   0.00463   0.00075   0.00000

The systematic shift to the blue is seen clearly in this set
of tables.

Thus it would appear that the net result of the effect is that we will
be driven to complicate the form of the model psf used for fitting for
purposes of star subtraction in the photometric pipeline in i' and
perhaps in r' as well, and may have to complicate the flat-fielding
calibration for the MT in z' and perhaps i'.  Parenthetically, it would
appear that the choice of thick chips for z', which was an entirely
economically driven one, was fortuitously the best one as well; the real
quantum efficiency (for stars) of the thick chips is roughly as high as
that for the thinned ones and the lost light does not wander to other
places in the device.  It is also unfortunately the case that the
dependence of quantum efficiency on wavelength through the z' band has
been grossly incorrectly measured, because the measurements include both
the primary (which is all that is relevant for stars) and rear-scattered
components and the rear-scattered fraction is large and very
wavelength-dependent.  To calculate the correct effective stellar
passband for the MT in z' will require observations of bright stars with
the telescope to determine the scattering amplitude. 

The already large and now larger difference between the MT and the
camera passbands in z' raises the issue of how the z' magnitude should
be defined; for the other bands there should be no systematic
differences of any important magnitude, but in z' it would appear that
it might be best to define a synthetic z' magnitude which fits the
instrumental response of the camera better, so that z' and i' images
from the camera will have measured flux ratios which are on the
`system'.  The lever arm in i'-z' for the camera is about 1500A, and for
the MT is about 1300A, so a color

(i' - z')_syn = 1.15(i'-z')_MT

would approximately match the camera instrumental colors for
not-too-complex spectra. 

I would like to thank Rich Reed for access to the rear scattering data
and some very helpful information on its quantitative properties and
method of acquisition. 

