Progress Report on Bright Star Photometry

                Based on Grand 1d PSFs

                                   CX 7.20.00

This is the third report on the progress of the task of 1-d fitting of
bright stars.  Again a different approach from the previous report has
been taken due to some new findings.

I.  Problem with the previous approach: Previously, I have used the
    Voigt function to fit the 1-d profiles of 5 test stars. The
    fittings to J-band profiles were satisfactory, but to the H and Ks
    band profiles were less so. Then Gene Kopan suggested, based on
    some quantitative analyses of several profiles in all 3 bands, that
    the counts in the wings of the 1-d profiles of bright stars may be
    proportional to the brightness. This is in conflict with the
    results from my Voigt
    function fittings which suggested that the wing increases as the
    square root of the brightness.

    In order to understand what had caused the difference between
    my results and Gene's results, I plotted the normalized J, H,
    and Ks profiles of the 5 bright stars that I had been fitting on
    top of each other, using different colors to distinguish
    profiles of different stars (profiles_j.gif ,  profiles_h.gif ,
    and profiles_k.gif ). On profiles_j.gif, it appears that pixels
    in the annulus next to the saturated core have widely spread
    counts, many of which are less than  40000 DN (the fiducial point of
    saturation), forming a piece of nearly vertical 'profile'.
    These large spreads are likely to be caused by artifacts (e.g. bleeding
    of electrons from adjacent strongly saturated pixels). When I
    did the Voigt function fitting for a given star, I treaded these
    counts as real since they are < 40000DN. This may have
    resulted in over-estimate of the amplitude of the central
    Gaussian in the Voigt function fit. A similar problem is found
    for Ks-band (profiles_k.gif), while the effect is not strong in
    H-band profiles (profiles_h.gif).
 

II. New Approach:
1)  Assumptions:
 i) If the pixels next to the saturated core are indeed
    affected by artifacts and therefore should be neglected in the
    fitting, and
ii) if both the wing and the
    central Gaussian are indeed proportional to the brightness, so the
    normalized profiles are the same for stars of different magnitudes
    (lets ignore the effect of the seeings at the moment), then
    one should be able to build a grand 1d psf for each of the J, H and
    Ks bands by piling-up pieces of normalized 1d profiles of stars of
    different magnitudes. Certainly, for each normalized 1d profile,
    only those 'good pixels' should be selected and included in the
    grand 1d psf.

2)  The following criteria are applied to select the 'good pixels':
 i) Counts > cut_l, where cut_l=min(10rms, cut_b), and rms is
    determined using pixels in r > 30 (i.e. > 60").  For very bright
    stars, the rms so determined may be affected by the gradient and
    therefore overestimated.  Then cut_l=10 rms will be replaced by
    cut=cut_b, where
            cut_b=100 DN for J band,
            cut_b=80 DN  for H band,
            cut_b=40 DN  for K band.
ii) Let n_a be the number of pixels in annulus r1<r<r2, n_s be the
    number of pixels with counts > 40000DN, and frac=n_s/n_a. Set a
    threshold cut_f, when frac > cut_f, all pixels in that annulus
    will be treated as 'bad pixels' and excluded from the profile
    fitting. Currently, cut_f=0.2 is adopted. Further more, since
    in J and K band there is evidence that pixels next to the
    saturated core are also affected, so these pixels are also
    excluded.

3)  Function form of the grand 1-d psf's:
    With some preliminary experiments, I found the following function
    form may give good analytical representations of the grand 1-d
    psfs:
    Function:
       f=f0*exp(-(r/r0)^2) + f1*exp(-(r/r1)) + f2/(1+(r/r2)^2)^q
    where:
       q=1.2 for J and Ks band,
       q=1   for H band.
    Parameters (6): f0,f1,f2,r0,r1,r2.

4)  Preliminary results: The results (including this report)
    can be found at:
    /data/2MASS/docs/supplementary/brtstar/grand_psf/
    Here are some highlights:
 i) Using 5 bright stars (K < 2) and 6
    unsaturated stars for which Raymond has already got the profiles,
    I made preliminary grand 1d psf's for J, H and Ks band. They
    can be found in:
                    grand_j_psf_test.gif ,
                    grand_h_psf_test.gif ,
                    grand_k_psf_test.gif .
ii) As an experiment, I did tentative fittings using the preliminary
    H band grand 1d psf (grand_h_psf_test.gif) for 9 stars
    (3 bright stars and 6 unsaturated stars) that we have profiles
    and the CIO/2mass magnitudes (for unsaturated stars 2mass
    magnitudes are used). The results are in:
                     results_h_test.dat .
    According to this experiment, the deviation is generally less than
    0.1 mag.

5)  Next step: I'm waiting for ~ 100 profiles that Raymond is
    preparing. Once I have those, I'll do the following:
    (1) Bin the profiles in seeing bins and build grand 1d profiles
        (J, H, Ks band) for different seeing bins.
    (2) The zero point corrections will be carried out, which may
        affect particularly the J band results significantly.
    (3) Using the grand 1d psf's to estimate the J, H, Ks magnitudes
        for stars in the profile sample that are used to build
        the 1d psf's.
    (4) Compare the magnitudes from 1d fit to the CIO or 2mass
        (unsaturated stars) mags, and get the standard deviations.
    (5) Exclude the outliers (e.g. (M_fit-M_cio) > 3 sigma),
        which may have erroneous CIO mags, from the sample for
       1d psf building.  And get the final 1d psf's.