The observational basis for this paper is HST imaging
of an off-centre field at 
from the centre
of M 32 taken with the WFPC2 on October 22, 1994
(standard-calibration observations, archive data, ID 5233).
See Grillmair et al. Figs. 1 and 2 for an outline of the M 32 PC field
on the sky.
The 
frames in F555W (V) and F814W (I),
respectively, were co-added through the cosmic-ray removing software of
Groth & Shaya (1992) resulting in two programme frames.
An I-band programme frame of the field at 
was produced in
a similar way from 3 exposures of 400 s each (archive data, ID 5464).
Correction for vignetting was carried out according to
Holtzman et al. (1995a),
and standard magnitudes and colour were derived using
the calibrations in Holtzman et al. (1995b).
We have adopted AI = 0.14 for the galactic absorption
(Burstein & Heiles 1984; Cardelli et al. 1989):
The luminosity functions and CM diagrams have been corrected for this.
The programme frames did not contain sufficiently bright, isolated stars to define a proper point-spread function (PSF). Therefore, model PSFs generated by the program Tiny Tim (Krist 1993) defined the artificial stars added during the completeness tests and the master PSF of the psf-fitting software by Stetson's (1987) DAOPHOT II package.
The completeness tests were carried out by adding stars
distributed according to the observed CM diagram.
The 
star signs
in Fig. 2 (click here) for I and V, respectively,
outline the range of magnitudes and colours.
A total of 7110 artificial stars were added to each
of the two programme frames. When carrying out an addition of stars,
only very few (in principle one, or several laid in a grid)
ought to be added at a time so as to avoid confusion between added stars and
an increase of the image crowding.
As an alternative, we split the addition of the artificial stars into two
and those stars
which happened to be added near another artificial star were removed.
The stars were added using our HST-Sim
routines, which scale and add the required number of PSFs
(the routines are implemented using Interactive Data Language, IDL).
The routines take into account the geometric distortion inherent in the
WFPC2 optical system, and
shifting and rebinning of the subsampled PSFs provide subpixel positioning.
Finally, Poissonian photon noise and Gaussian read noise are added.
The photometry of objects in the programme frames was obtained through
a procedure that included several passes of object identification
and measurement of magnitudes, using DAOPHOT II.
First we worked through the identification of objects in the I-frame.
In order to identify as many objects as possible and
to ease the identification of faint objects we carried out
iterations, successively reaching fainter magnitudes.
For every two iterations we concatenated the lists of hitherto revealed stars,
subtracted those from the original frame, and continued from there.
The iterations ended when we reached a threshold of 4
standard deviations of the background level,
as calculated by DAOPHOT - at that point only a few hundred stars were
identified and successfully subtracted by ALLSTAR and an additional
iteration did not provide more objects.
The final ALLSTAR list of all stars in I was then applied
for star-subtraction in the V frame.
After having calculated flux-averaged positions based on the I and V
list of objects we again ran
ALLSTAR on both frames, now with fixed coordinates.
In this way a total of 19461 stars were found to match in V and I.
The photometry of the star-added frames was carried out in a way
identical to that of the programme frames.
Note, Grillmair et al. applied Stetsons's (1994) photometry package ALLFRAME. They found that the global characteristics of the CM diagram produced using DAOPHOT II/ALLSTAR were essentially identical to those found using ALLFRAME.
We have made no attempts to correct for the M 31 background stars
as none of the conclusions of this paper depend on knowing this accurately.
According to Grillmair et al. about 18% of the 
stars identified
in the programme frames originate in M 31.