A number of HST WFPC2 exposures were made of the central part of the LMC Bar for an ongoing investigation of the chemical composition and star formation history of the Large Magellanic Cloud (LMC) (Ardeberg et al. 1997). Among those, a total of 16 Strömgren y exposures of the same field are available. A single exposure was used to test the method on a real image. The combined exposures allowed the LF to be measured with classical methods to a fainter limit than possible in a single exposure. This way, the results of LUMINOUS were checked against the LF determined from counts of individually measured stars of the same field, serving as the "true'' LF. For this exposure, the detection of faint stars is mainly limited by the signal to noise ratio of the stars, not the degree of crowding. The simulations in the previous section are similar to the HST exposure, both in crowding and noise properties.
The assumptions mentioned in Sect. 2.3 are not completely fulfilled. The test with the WFPC2 image shows the combined effect of the errors in the assumptions.
Only stars are present. DAOPHOT photometry of the combined images showed that nearly all objects could be described well using star-like objects. Visual inspection suggested the same.
Distribution of stars. The visible stars were distributed randomly, the field of view was small and located in the centre of the LMC. There was no reason to assume any special distribution for the faint stars. Any clustering of faint stars near bright ones was assumed absent.
Constant PSF. This assumption was not correct. The PSF varies over the image (Linde & Snel 1997; Biretta et al. 1996). The current version of the software used did not allow for a variable PSF. However, the LF derived from the central 25% of the image did not differ from that derived from the central 60%.
Read-out noise. Investigation of WFPC2 bias images showed that the read-out noise could accurately be described by a Gaussian distribution. Since the read-out noise was about 0.7 ADU, few bins with information about the shape of the noise distribution were available.
Diffuse sky background. Visual inspection of the image showed no gradients or large scale structure in the sky background.
The pipeline calibration of WFPC2 images corrects for a large number of effects (Biretta 1996). Standard calibration files for these effects are available in the HST archive, and were used for the simulation of the effects as well. These included modelling of effects of the flat field, dark-image and bias-image.
A variable effect of the bias image has been observed (Holtzman et al. 1995), resulting in different bias levels for the odd and even columns in the image. These levels, and the difference between them, differ from exposure to exposure. This odd-even effect has been included in the model.
Measured ADC effects for WFPC2 are available from the HST data archive. There has been no demand for an accurate description of these effects, so no update of the information has been made (Stiavelli 1997). The standard ADC effect calibration file from the Space Telescope Science Institute was modified with the help of exposures from the HST archive, and used to model the effect.
WFPC2 images can contain bias jumps, changes in the bias level within a single image. Linde & Snel (1997) have detected small bias level jumps in WFPC2 images, undetectable without heavy smoothing to suppress read-out noise. Such effects, if present in the image, would have the same effect as an error in the bias image, or an increase in the read-out noise, combined with a change in the distribution of the read-out noise.
The LF of the images was determined in four different ways: direct detection in a single exposure, direct detection in an average of 16 exposures, derived with LUMINOUS from a single exposure using a 4.5 pixel PSF radius, and using a Tiny Tim (Krist 1995) model PSF (Fig. 9 (click here)).
Figure 9: LFs measured in an average of 16 WFC exposures of the LMC Bar
and corrected for completeness,
measured in a single WFC exposure and corrected for completeness,
smoothed derived LF for a single exposure using a model PSF,
and measured in a single WFC exposure
The LF from the averaged image was corrected for incompleteness and was used to check the validity of the derived LF. The correction was done by estimating completeness of detection using artificial stars. The detected LF from the single image was also corrected for incompleteness and is shown as a comparison in Fig. 9 (click here).
Both solutions using LUMINOUS were sensitive to the adopted value of the
read-out noise. This value was adjusted to obtain lowest 
, and
was within one sigma of the value tabulated by
Biretta (1996). For both
the extracted and model PSF it was possible to obtain a of about 1.2.
The corresponding LFs were nearly identical for all but the
faintest magnitudes, but deviated somewhat
from the LF derived from the average image.
The slightly high value for indicated that the fit to the
histogram was less than optimal.