Internal Consistency of Relative Quantum Efficiency Measurements made at MIT CSR.

As noted above, the flight detector I0 (w203c4r) was calibrated with respect to both w190c3 and w103c4. Since we also cross-calibrated w190c3 and w103c4 with respect to one another, it is possible to check the consistency of these measurements. This comparison is shown in Table 4.56. Excluding the point at 8 keV (which was used in the reference detector cross-calibration), the mean difference is $0.0037 \pm 0.0035$, consistent with zero, where we have taken the standard deviation of the mean as the error. The RMS about the mean is 0.0085. Assuming each of the 3 relative QE measurement sets has the same error, and that the error is independent of energy, then, to a good approximation, the error in any single measurement is $\sigma_{rqe} = 0.0085/\sqrt{3} = 0.0049$.
 

Table 4.56: Reproducibility of Relative Quantum Efficiency Measurement of Detector I0

Flight	Position	Mean Relative Efficiency vs. Energy (keV)							Reference
Device		0.525	0.677	1.740	2.015	4.509	5.894	8.040	Device
		O	F	Si	P	Ti	Fe55	Cu
w203c4r	I0	0.972	0.992	0.996	$\phantom{-}0.982$	$\phantom{-}0.994$	0.977	$\phantom{-}0.933$	w190c3 (meas.)
w190c3	Ref.	0.890	0.767	0.986	$\phantom{-}0.949$	$\phantom{-}1.010$	1.058	$\phantom{-}1.164^{\dag }$	w103c4 (meas.)
w203c4r	I0	0.866	0.760	0.982	$\phantom{-}0.932$	$\phantom{-}1.004$	1.034	$\phantom{-}1.086^{\dag }$	w103c4 (calc.)
w203c4r	I0	0.848	0.756	0.977	$\phantom{-}0.940$	$\phantom{-}1.005$	1.030	$\phantom{-}1.095$	w103c4 (meas.)
Difference	line 3 - line 4	0.018	0.004	0.005	-0.008	-0.001	0.004	$-0.009^{\dag }$
$^{\dag }$Cross-calibration of w190c3 vs. w103c4 uses w203c4r data; see text
Mean Difference, excluding 8 keV point : 0.0037
RMS Difference, excluding 8 keV point : 0.0085

This level of error, while probably acceptable for ACIS calibration purposes, is one order of magnitude larger than the limiting uncertainty imposed by photon counting statistics. A number of factors may contribute to this excess error. The two reference detectors used are known to have slightly different pileup characteristics, but the same pileup model was used in the analysis of both data sets. One reference detector (w103c4) was operated with an older (pre-ACIS) generation of electronics that is somewhat noisier than the ACIS electronics; the slight differences in response function may contribute some error. Finally, relative misalignment between flight and reference CCDs can influence low energy ratios (C, O, F) due to the non-uniformity of these sources. (Some misalignment on order 50 pixels seems evident in a few cases, despite the apparent precision achieved with the alignment system.) This is less important for higher energies, which make use of a commercial X-ray tube and have a flatter illumination pattern at the CCD location (primarily due to a larger source-detector separation).

Systematic errors in the modelling of the relative calibration measurements are discussed in detail in Section 4.8.