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PS reprint
A. J. Penny
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX,
U. K.
R. Leese
Physics Department, University of Leeds, Leeds, LS2 9JT, U. K.
An enhanced version of Starman, a profile fitting stellar photometry package, has been used to analyze the effect of such variations.
When the seeing drops below one pixel FWHM, photometry errors can rise to the 1--5 percent levels, depending on the nature of the sub-pixel variations. By using suitable software which allows for the sub-pixel pattern, the measuring errors can be reduced to the millimag level.
This paper is concerned with the effects sub-pixel sensitivity variations on stellar photometry measures.
The variation of sensitivity within a pixel of a CCD can be substantial and also substantially the same for each pixel of the CCD. Jordan et al. (1993) found 10% variations for a CCD used on ground-based telescopes, and Burrows et al. (1995) found a similar range for WFPC2 on the HST. Such variations can lead to photometric errors of the order of a few percent, dependent on seeing and pixel phase.
A version of Starman (Penny 1995), a profile fitting stellar photometry package, has been written to incorporate software to deal with such variations. The WWW page contains further information on the standard form of the software.
Figure 1 shows the intra-pixel variations over one pixel measured by Jorden et al. (1995) for a GEC P8603 CCD chip, and given by the manufacturer for an IR PtSi chip.
Figure 1: The intra-pixel variations over one pixel (left) for an optical
CCD (measured by Jorden et al. for a GEC P8603 CCD chip), and
(right) for an IR chip (PtSi chip---manufacturer's specification).
Figure 1 (left): PS 27 Kb, Figure 1 (right) PS 22 Kb
The Starman photometry package fits a profile which is a rotated elliptical Lorentzian, with a low wide circular modified Gaussian and an empirical correction map. In this study, only the Lorentzian part of the profile was used.
where
If a profile has a FWHM less than 6 pixels, the Starman software takes account of the pixel undersampling. In the calculations, at each step of the iterative least squares process of the profile fitting, the profile value at each pixel is calculated by sub-dividing the pixel into small enough sections that the profile is linear across each section. The profile value is then calculated for the centers of these sections, and averaged over the pixel.
A new part of the software, still in development and not yet installed in the Starlink release version, has been used both to create simulations of star light falling onto such pixels, and then to analyze the resultant stellar images.
The principle used is to take the method of dealing with undersampled profiles, that of sub-dividing the pixels, one step further.
For this, the pixel is divided into sections appropriate to the scale of the sensitivity variations inside the pixels. Then for each of these sections the profile is multiplied by the appropriate sensitivity value, and the resultant average profile value for that pixel made, and applied in the iterative least squares process.
This process is computationally tractable if all the pixels have the same pattern of variations, which seems to be the case for the chips measured so far.
Figure 2: The errors introduced by ignoring the effects of the intra-pixel
variations. The horizontal axis is the FWHM of the stellar image in pixels.
The vertical axis shows the standard deviation of the error in
the measured magnitude, for stars whose profile centers are placed at
many random positions relative to the pixel centers. The crosses are for the
CCD chip variations and the circles are the IR PtSi chip
variations of Figure 1.
Figure 2: PS 35 Kb
Figure 3: As for Figure 2, except that here is shown the range
of errors introduced by ignoring the variations. This range is that
from the true magnitude to the largest positive or negative error.
Figure 3: PS 18 Kb
Figures 2 and 3 show the errors introduced by ignoring the intra-pixel variations. It can be seen that, as expected, the effect only becomes significant if the profile width is small, that is if the profile changes significantly on the scale of the intra-pixel variations.
Using the development version of Starman to allow for a known pattern of pixel variations, tests have shown that the errors are removed almost entirely, to the millimag accuracy.
Thus if high-precision photometry is desired and the profile width is small, then these effects both must and can be taken into account.
At present, the intra-pixel variations must be known and input into the software. This is usually possible, as the laboratory measurements are straightforward. However, the possibility exists of using observed stellar profiles to invert the problem, and determine the variations by a least-squares analysis, in much the same way that the stellar profiles are found themselves. Simulations are in process to test this concept.
We are grateful to P. Jorden for communicating the sub-pixel CCD sensitivity measures, and W. K. Griffiths for illuminating discussions.
Jorden, P., et al. 1993, Gemini, 41, 1
Penny, A. J. 1995, Starlink User Note 141, (Didcot, RAL)