The observational material which supports this investigation consists of
four plates of - two in B and two in V - taken at
the RC focus of the National Astronomical Observatory 2 m telescope
(F/8, scale 12.86 arcsec per mm). The B band is realized with ORWO ZU21
behind GG13 emulsion-filter combination, and the V band - via KODAK 103a-D
behind GG11. All plates are taken with very short exposure times
(40 s. in V and 90 s. in B ). This allows good separation of the stars
down to 0.6 arcmin from the cluster center.
On each plate the cluster image out to about 6 arcmin of the center was
divided into nine overlapping square regions (18 mm in size) which were
digitized with the Joyce-Loeble microdensitometer of the NAO. For the simplicity of
the future explanation the digitized cluster regions we call these ``frames".
It was rather time consuming to scan
such a large area (more then ) but our hope was to indentify as many
stars already photometered by other investigators as possible in order to be
used as a reference system. The plates were traced with a 50
m square
diaphragm and a 30
m step in both X and Y directions in agreement
with the fact that the size of the smallest measured image on the plates
was evaluated to be about 2 arcsec. Having no appropriate finding routines,
for the sake of star location, we accepted an approach
close to that described in Stetson (1979) and Chiu et al. (1979),
namely to
process the subframes centered on the star under consideration. The manner in
which subframes were designed is presented below.
Every four frames corresponding to one and the same cluster region
on the different plates were adjusted to make the positions of the stars
coincide with each other. Then displaying one of the plates (frame by frame)
smaller arrays (subframes) relevant to individual star images were formed
by extraction. During this procedure we
prepared a list where all stars in contact were registered. By the help of some
PCVISTA routines arranged in a batch mode, the process of subframes
formation was automatically performed on the other three plates (due to their position adjustment).
In this way about 1000 subframes (
) each centered on an individual star
were obtained from every plate. Our experience showed that the scatter of
the star's centers (according to different plates) in both directions was less than 2 pixels. There are
many reasons for such a scatter: the orientation of the plates on the scanning desk,
the frames adjusting procedure etc. For the purposes of the present
study the achieved accuracy of the star's centering was regarded as good.
As we have mentioned in the introduction our photometric procedure yields two
sets of MI as an output: one based on a Gaussian fit and the other - on a
synthetic aperture. In the former case we used data in photographic densities
since in the fitting routine a term considering the local sky background
variations had been included. But in the second one for the sake of
a correct background evaluation we had to
work in relative intensities. The input data for DAOPHOT (the output magnitudes
of which we used to check the above two sets) also have to be in relative intensities. On the used
plates there was not any additionally exposed photometric pattern - wedge or
spots. To transform photographic densities to relative intensities we applied
an internal calibration method using density profiles of stars with known magnitudes. For this purpose
24 of Arp's electrophotometric standard stars, previously recognized in the cluster
region under consideration, were used. These stars were scanned additionally,
each in a single frame ( pixels), under the same conditions as described in Sect. 2.1. A comprehensive
description of the procedure is given in Markov (1994).
There were two independent reasons for which we find it necessary to use a certain data filtering. First, an inspection to the stellar images revealed that the frames had transposed rows probably due to the inertness of the microdensitometer, and manner of scanning - in order to save time, every scanned row was made in the opposite direction to the previous one. Unfortunately, the observed displacement is not an exact number of pixels - it is less than a pixel. To improve the situation we need some kind of filtering like a running average with normalized weights. The second reason is connected with the reliable determination of the stellar centroid in the crowded central field. Our presumption was: rejecting the high frequencies to symmetrize the PSF, to improve the determination of the PSF and to get more reliable star locations as well. In order to solve both problems using one reduction procedure we found it appropriate to apply the discrete wavelet transformation (DWT) but in different stages of its application. The wavelet transformation is a versatile tool for signal and image processing and it is used very widely. Thanks to this there are many papers which describe the theory, numerical algorithms and applications of the wavelet transformation (Starck 1993; Starck & Murtagh 1994 etc.). In our work we applied the so called trous algorithm of the DWT described in Starck (1993). The physical basis of this transformation is grounded on consecutive filtering of the frames with a low-pass filter - a running average. The difference between two consecutive resolutions yields the discrete wavelet transformation at a given level. To restore frames with transposed rows we used the first smoothing level of the DWT. The resolution losses are expected to be negligible, since on the best plate the PSF has a FWHM of about 5 pixels but the smoothing window chosen is about 3 pixels in diameter. Figure 1 (click here) presents one enlarged rough stellar image (left) and its smoothed version (right). All scanned regions were treated in this manner.
Figure 1: Restoration of an image distorted by the transposition of rows. The left panel
shows one scanned stellar image - the rows' displacement is probably due to
the inertness of the scanning machine. The right panel demonstrates the same
image but treated with the first smoothing level of the wavelet transformation
For solving the second problem we used the zero DWT level - namely its ability for expressing image features with a desired size (for example - stellar peaks) more clearly. The effect of its application is demonstrated in Fig. 2 (click here), right panel, while the left presents the original frame. The improved separation of the stellar images on the right panel which are in a contact on the left is more than evident. The wavelet transformed frames were chosen only as an input for DAOPHOT's star-finding algorithm.
Figure 2: Two frames of one and the same cluster region. On the right hand side
the zero DWT level of the original frame (left panel) is shown. The gain
in resolution is well demonstrated. Improving the separation of the contact
images we aim to get more reliable stellar centroids
Figure 3: a and b)
Illustration of the efficiency of the cleaning algorithm:
a) two dimensional density maps of the stellar images centered on the star
under consideration (the left panel shows the original but the right - the already
cleaned image); b) integrated stellar profile of this star - original (left)
and cleaned (right)
Figure: a and b) The same as Fig. 3 (click here) but for another image