Sources of Modelling Error in the Calibration of Flight Detectors Relative to Reference Detectors.

Generally, the relative quantum efficiency measurements are subject to fewer errors, of smaller magnitude than those afflicting the absolute measurements. Nevertheless, the model used to interpret the relative quantum efficiency contains a number of implicit assumptions which are not directly verified by the calibration measurements. Following is a list of some potential ``modelling errors'' that could affect the accuracy of the relative quantum efficiency model. Future work could, in principle, quantify some of these errors more precisely.

1.

Differences between spectral redistribution functions of flight and reference detectors. Our model of the relative quantum efficiency measurements implies that differences in efficiency are due to differences in gate structure thickness or depletion depth. Thus we make no correction for differences in the branching ratios or tail amplitudes of the spectral redistribution function (though differences in the spectral resolution are accounted for). For FI-to-FI device relative measurements, the effects of any such differences are minimized because i) we have chosen an event grade set which is known to be substantially independent of energy in the 0.5 - 2.1 keV band, for any given CCD and ii) the sources used are quasi-monochromatic.

On the other hand, quantum efficiency measurements of back-illuminated flight devices relative to the (front-illuminated) reference detectors are much more sensitive to errors from this source, since the redistribution function is so different for the two types of detector. Indeed, this difference, coupled with the spectral complexity of the X-ray sources used, is believed to cause significant systematic errors in our current analysis of the relative quantum efficiency data.

At present we have no direct estimate of the size of errors introduced by differences in spectral redistribution functions in FI-to-FI relative efficiency measurements. The consistency of relative quantum efficiency measurements made at MIT and XRCF implies that such errors are not large, at least for the front-illuminated devices. See below.

Errors in BI-to-FI device efficiency arising from this source are discussed in some detail in section 4.7.3. Depending on the source spectrum, such errors can range in size from 5% to 25%.

2.

Spectral complexity in the source. The current interpretation of relative detection efficiency measurements presumes that the source is monochromatic. In fact, none of the sources used is monochromatic. As discussed above, the error introduced by complexities in the source spectrum is coupled to differences in the response functions of the flight and reference detectors. This error is certainly more important for measurements of back-illuminated flight detectors relative to front-illuminated reference detectors.

One bound on the magnitude of such errors is provided by a comparison of relative quantum efficiency measurements made at XRCF to those made at MIT CSR, since the ``out of band'' spectra of the sources at the two sites was generally quite different. In general, the agreement for FI-to-FI detector comparisions is quite good (1.1% RMS below 8 keV), while BI-to-FI detector relative efficiencies are not so reproducible.

3.

Differences in channel stop parameters in the the flight and reference detectors. The most reliable measurements of channel stop dimensions are obtained using the mesh technique described in section 4.5, and from (destructive) scanning electron micrographs. Neither of these techniques has been applied to determine the channel stop parameters of the flight or reference detectors themselves. Since differences in channel stop parameters are not included in the relative quantum efficiency model, any such differences would be modelled incorrectly. In principle, measurement of channel-stop parameters on a number of siblings of the flight devices (via mesh experiments) could bound the size of errors due to channel stop variations.