Re: Data reduction methodology for V-I colors

[Stupendous Man <richmond@stupendous.cis.rit.edu>]

  About two weeks ago, Richard Miles made a suggestion for the 
photometric reduction of the TASS magnitude measurements.  I'm sorry
to be joining the discussion so late....

> it occurred to me that TASS may not be making optimal use of some
> of the data, in particular those pertaining to V-I color index.  The
> thinking goes like this.  (Someone correct me if I have not got the
> methodology right):

> The photometric reductions in V and I are performed separately.
> The last step (step 8) of the data reduction pipeline is to calibrate the
> magnitude of each star.
> Each frame in each color is reduced against a subset of Tycho stars and a
> zero-point for each frame is determined.

  No, not quite.  

  Each individual V frame is turned into a set of instrumental magnitudes
individually -- yes.  Each individual I frame is turned into a set of
instrumental magnitudes individually -- yes again.

  However, the step of converting instrumental magnitudes to the
standard V,I scale (really the Vt, It scale) does not treat each
frame individually.  Instead, it solves simultaneously for the
zeropoints of each frame, a V-band color term and an I-band color term.

  I believe that the current pipeline already does something along
the lines that you are suggesting...

> Now here's my concern.  To calculate V-I for each star and frame, the value
> of I must be subtracted from the value of V.  However, each of these have a
> contribution to their uncertainty contributed by the two independent
> zero-point values determined for each of the frames.
> Surely there is a much better methodology for arriving at a more accurate
> V-I color index whereby the reduction (for V-I only) is carried out by
> always working in terms of the differential instrumental magnitudes, v-i.
> Qualitatively, changes in sky transparency have a significant effect on V
> and I zero-points whereas the equivalent v-i values are relatively immune to
> such changes if each pair of images are made simultaneously.  Therefore, why
> not add an additional step in the pipeline to derive V-I for each star by
> working entirely in color index space?

  I understand what you are saying here -- using color indices rather
than magnitudes.  It's a standard technique in photoelectric photometry.
Let's see .... I think what this would mean is that instead of allowing
the zero-point value of each V-band frame to be a parameter for which
we solve, and the zero-point value of each I-band frame to be a parameter
for which we solve independently (thus, solving for 2*N zero-point
values, where N is the number of exposure pairs), you suggest we force
the V-band and I-band zero-point values of each pair of simultaneous
frames to be linked.  For example, if the V-band zero-point drops
by 0.03 mag on the V-band image of pair 28, then the I-band zero-point
must also drop by some smaller amount (say, 0.02 mag) for the I-band
image of pair 28.  That would reduce the number of parameters for
which we solve to N, rather than 2*N.

  Would this improve our output V and I magnitudes?  Yes, in theory.
In practice, I _suspect_ that it wouldn't help much, for two reasons.
First, we would need to figure out the ratio of V-band to I-band
shift in zero-point, which would be an input to the photometric model.
Not a big deal, just a few days work with several nights or weeks
of data.  Second, we are in an overdetermined situation: each frame
has, typically, 30 or 40 Tycho stars (I believe -- I don't have the
exact number handy, and it varies with galactic latitude); a typical
V,I pair, therefore, has 60 to 80 instrumental magnitudes.  The current
pipeline derives 2 zero-points (plus a fraction of a color term)
from this mass of data.  Richard's method would reduce this to 1 zero-point
(plus a fraction of a color term) from the same amount of data.
I am guessing -- purely guessing, mind you -- that decreasing the 
number of parameters for which we solve from 2 to 1 won't make a big
difference in the accuracy of that output parameter.  If we were
going from, say, 20 to 10 parameters, I'd suspect that the improvement
would be larger.

>  At present no calibration
>  advantage is being derived from the contemporaneous nature of the image
>  pairs (or am I mistaken about this?) 

  You are correct -- we are not using the simultaneous collection of
V and I measurements to help us.

> It might even be possible to arrive at a more accurate estimate of the I
> magnitudes themselves via this approach than by basing this on Tycho Vt and
> Bt data as used at present.

  Hmmm.  I think that if we discard the Tycho data, we might be able
to solve more precisely for magnitudes on the _instrumental_ "I"-band
system, but we would have no idea of the instrumental "I" compared
to the standard Johnson-Cousins I, or even a pseudo-Johnson-Cousins "It"
based on the Tycho Bt and Vt.  So we would have a more precise
measurement of a quantity, but a much larger unknown systematic
error.  It might help us to find low-amplitude variations, but we 
could not compare them to I-band values published elsewhere.

                                           Michael Richmond