Magnitudes of Modelling Errors in the Absolute Calibration of Reference Detectors

We have identified several lines of evidence that can supply quantitative bounds on systematic measurement errors, and on some kinds of modelling errors. Taken together, these checks furnish some confidence that, for front-illuminated devices, the absolute quantum efficiency errors are no larger than 5% in the 0.4 - 4 keV band.

1.

Plausibility of best-fit model parameters. The best-fit values for synchrotron radiation flux normalizations, relative to the expected value, for three reference detectors discussed in section 4.6.1 are 1.000,0.994, and 0.956, respectively; these numbers each have 90% confidence intervals of approximately $\pm 0.005$. The simplest interpretation of these results is that any residual systematic errors in the broad-band quantum efficiency amount to less than 5%. Moreover, the inferred mean gate structure parameters are in the range (within $\pm 50\%$) expected given the device fabrication process, suggesting that the slab and stop model is providing a reasonable, and therefore probably reliable, representation of the gate structure.

2.

Internal consistency of reference detector quantum efficiencies. The quantum efficiency models derived for the reference detectors from synchrotron radiation data can be compared to relative efficiency measurements made at MIT CSR. The ratio of the two models agrees quite well with the relative quantum efficiency data: for the five energies measured at MIT within the BESSY passband (0.525 to 4.5 keV), the residuals (measured ratio minus modelled ratio) have a mean of -0.008 and a standard deviation of 0.01. Thus the mean is consistent with 0 at the 2-sigma level, provided the standard deviation is taken to be measure of the random errors in the residuals. The latter assumption is a good one, given that the errors in the relative quantum efficiency measurements are thought to have a standard deviation of 0.6%.

This result suggests that, although it cannot be ruled out at present, it is unlikely that broadband errors as large as 5% could remain in the absolute quantum efficiency models of the reference detectors, at least in the BESSY passband.

Of course our internal consistency check cannot rule out all systematic errors. For example, this check would not reveal a geometry error that affected every BESSY measurement identically (though the normalization results described above suggest such an error is highly unlikely.) It is noteworthy, however, that the synchrotron measurements in question were made on different runs separated in time by about a year, and with different sets of electronics.

3.

Comparison to other absolutely calibrated detectors An extremely valuable check on ACIS absolute efficiency models will be provided by comparisons to absolutely calibrated beam normalization detectors at XRCF. The most suitable detector for this purpose, the solid-state detector (SSD), has been calibrated at the same PTB beamline that was used to calibrate the ACIS reference detectors. As of this writing, the absolute response of the SSD is not yet available, however, so this important check remains to be done.

Nevertheless, since the SSD detector is thought to be fairly well understood at higher energies, and since we have no other external check on our high-energy absolute calibration, we have compared the ACIS flight detector model predictions to ACIS-to-SSD relative QE measurements made at XRCF. The XRCF phase-I results used for this purpose are detailed in table 4.36 in section 4.6.6. If we use the ACIS detector model quantum efficiencies, together with these relative QE data, to infer the detection efficiency of SSD5 at 8.040 keV, we obtain ten estimates of the SSD5 efficiency. The mean value of these estimates is 0.966, and the standard deviation of the estimates is 0.033. For the FI detectors alone (for which the QE model is based on the branching ratio technique), the mean is 0.952, and the standard deviation is 0.018. The a priori expected quantum efficiency of the SSD5 at this energy is 0.997 (according to R. Edgar). This comparison is thus consistent with the supposition that systematic errors in the absolute efficiency of our models for the FI detectors are no more than 5%.

We emphasize that a more precise characterization of ACIS systematic errors, especially at energies above 4 keV, awaits absolute calibration of the XRCF BNDs to an accuracy of order 5% or better. The calibration of SSD5 would be the most useful for this purpose.