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In order to obtain a quantitative estimate of the accuracy and reliability of
our data reduction procedures and results, we have performed a data reduction
pipeline based on the following steps: i) define a set of simulated HST-like
images with synthetic globular cluster stellar distributions, which provide the
``true'' data for comparison; ii) convolve these images with appropriate
assumptions of PSF and noise in order to construct simulated ``observed'' data;
iii) deconvolve the ``observed'' images using some of the most widely adopted
techniques and assumptions; iv) reduce the ``deconvolved'' frames in a totally
independent way, and compare with the initial ``true'' data. Specifically, for
steps i) and ii) we used the set of HST-simulated images prepared by Hanisch
(1993) (namely the files in the directory star_cluster),
in order to be able to compare our results also with the work of other
researchers in the field, while steps iii) and iv) were performed by two
different teams of our group who ignored the assumptions made by the other team
in order to assure the complete independence of each step. Since this work was
started in September 1993, we adopted the version of Hanisch files then
available, which is different from the revised version released on October 6,
1993. The characteristics of our files are then: (i) intensity-normalized PSF
peak; (ii) stars centered on the pixels; and (iii) zero-point = 9.0 mag.
In summary, using a special version of the package ROMAFOT (Buonanno et al.
1983, Buonanno &Iannicola 1988), we have then reduced the following set of
files:
- a)
- ``Truth'': input star cluster with a globular cluster-like
luminosity function (LF) and spatial distribution (Hanisch 1993). It contains
470 stars.
- b)
- ``Observed'': HST-simulated ``star_cluster'' (Hanisch 1993) with
470 stars, old WFC (sim2.fit), new WF2 (sim2c.fit), size = 256
256,
space invariant PSFs (psf12.fit, psfc12.fit), filter F555W, center of image,
where ``sim2'' stands for the HST images uncorrected for spherical aberration,
and ``sim2c'' are the HST-corrected frames, and hereafter label the two
separate families of adopted simulations.
- c)
- ``R-L deconvolved'': deconvolved with the Richardson and Lucy
method (R-L) (Richardson 1972, Lucy 1974, 1992), using a variable number of
accelerated iterations (50, 150, 250).
- d)
- ``MEM deconvolved'': deconvolved with the Maximum Entropy Method
(MEM), adopting two different versions, i.e., MEM-IDL (with 50, 150, 250
iterations; this routine was written by F. Varosi based on Hollis et al. 1992)
and MEM/MemSys5 (with ICF = 0, 1; Weir 1991).
- e)
- ``Wiener'': deconvolved with a Wiener-based routine (IRAF, package
restore; Busko 1993).
In the reduction of all frames the star detection threshold has been set always
at 5
, the value calculated on the background empirically determined in
the ``observed'' frames (i.e., 8 counts). Note that, due to the combination of
the systematic centering of the stars in the pixel centers and the crowding
effects, only 373 stars are actually detectable as independent objects on the
``observed'' frame listed in Table 1. The second column, labelled ``Detected'',
contains the total number of identified peaks, including those which could not
be fitted by the ROMAFOT stellar profile fitting routine and are interpreted as
noise. Finally, note also that the two original ``observed'' images (Hanisch
1993) were PSF peak-intensity normalized, therefore the data obtained from the
two families (Table 1 and Table 2) are not directly comparable as the
corresponding stars have actually different S/N values.
Tables 1 and 2 and Figs. 1 and 2 report the summary of the results for
the uncorrected and corrected images ``sim2''and ``sim2c'', respectively.
The main conclusions one can draw from the tables and figures are:
- With ``sim2'' (uncorrected HST), the number of detected ``true'' stars in
the ``observed'' frame is about 20%smaller than the number of stars that
could in principle be detected (302 vs. 373), and the number of ``fitted''
stars includes about 10%of spurious identifications. Overall, the
completeness factor (i.e., ``true''/470) is about 65%, and it would presumably
be somewhat larger if the stars were not assumed to be centered in the pixels
(further tests are in progress using a revised version of the simulation where
the stars are not centered in the pixel matrix). These numbers increase in the
deconvolved images and with increasing the number of iterations, however, the
number of ``spurious'' objects also increases steeply, correspondingly. The
behavior of these quantities as a function of magnitude can be seen in Fig. 1.
- With ``sim2c'' (corrected HST), the number of stars detected in the
``observed'' frame (before deconvolution) is almost coincident with the maximum
attainable (369 vs. 373). The search on the deconvolved images (at a fixed
threshold of 8 counts, as derived from the ``observed'' frame) yields a smaller
number of detected objects. The stars lost are faint objects with peak
intensities just over the threshold in the ``observed'' frame, which fall just
below the threshold after deconvolution. This is due to the fact that all
deconvolution methods tend to enhance the contrast, namely to increase slightly
the peak intensity of the brightest stars at the expense of the weakest peaks
which are damped as noise. Finally, it is remarkable to note the difference in
number of detected objects obtained adopting ICF = 1 or 0 with MEMSYS.
- The impact of these effects on the LFs consists in a ``deformation'' of
the differential LF, with a shift of some objects to the adjacent brighter bin
and a lack of stars close to the detection limit. The detection limit is of
course defined by the adopted threshold, which was selected in order to
optimize the number of detected ``true'' stars with respect to the spurious
identifications.
- Concerning the linearity, the internal photometric accuracy, and the
zero-point checks, additional tests are in progress. In general, the photometry
of safely uncrowded stars yields magnitudes accurate to better than 0.1 mag,
including any systematic zero-point shift. In particular, the use of a
Gaussian fit to the PSF plus a look-up table to map the systematic residuals
already yields satisfactory results.
Next: Surface Brightness Profiles
Up: Photometric and Surface Brightness
Previous: Introduction