Repeatability and Estimated Errors in Relative Quantum Efficiency Measurements of Front-Illuminated Detectors

In Table 4.61 we have computed the fractional difference (1-XRCF/CSR) between the relative QE measurements made at each site. The relative QE ratios at XRCF for the frontside devices are in excellent agreement with the ratios obtained at CSR. Indeed, averaged over seven FI chips and the lowest three energies, the mean difference in relative quantum efficiency is $0.27\% \pm 0.24\%$, where the error is the standard deviation about the mean, and the RMS deviation about the mean is 1.1%. If we assume that the CSR and XRCF relative QE measurements in this energy range each have the same random error, and account properly for the normalization of the CSR measurements by the efficiency of S2 required to make this comparison, we infer that the error on a single relative QE measurement is (very nearly) $\sigma_{rqe} = 0.011/\sqrt{3} = 0.006$. This estimate is only slightly larger than the value obtained from internal consistency of the MIT CSR measurements alone ($\sigma_{rqe} = 0.0049$; see section  4.7.2) For purposes of QE model fitting, to be discussed in Section 4.8, we will adopt the larger value as the uncertainty in the relative QE measurement.
 

Table 4.61: Fractional Difference (1-XRCF/CSR) between Relative Detection Efficiencies at CSR and XRCF--Referenced to S2

Flight	Position	Frac. Rel. Eff. Diff. vs. Energy (keV)
Device		0.525	1.740	4.509	8.040
		O	Si	Ti	Cu
w203c4r	I0	0.019	-0.003	0.009	-0.006
w193c2	I1	0.011	-0.002	0.006	-0.004
w158c4r	I2	-0.003	-0.013	0.005	0.013
w215c2r	I3	0.019	-0.015	0.002	-0.014
w168c4r	S0	0.029	0.001	-0.010	-0.026
w182c4r	S2	0.000	0.000	0.000	0.000
w457c4	S4	0.004	-0.003	-0.010	$^{\ast}$
w201c3r	S5	0.012	0.001	-0.003	-0.042
FI Mean		0.013	-0.005	-0.000	-0.013
FI Std Dev.		0.011	0.006	0.008	0.019
w140c4r	S1	-0.124	-0.001	0.080	-0.010
w134c4r	S3	-0.097	-0.010	0.055	-0.050
BI Mean		-0.111	-0.006	0.068	-0.030
BI Std Dev.		0.019	0.006	0.018	0.028
$^{\ast}$ This data point was excluded because the XRCF bias
for this point was peculiar.

The data at 8 keV require special comment for two reasons. First, the bias obtained from ACIS telemetry for S4 for the 8 keV measurement (ACIS XRCF Science Run 93, TRW ID's I-IAS-SG-1.032 and I-IAS-EA-2.043 through I-IAS-EA-2.048) is peculiar, showing excess charge of order 5 electrons/pixel. The spectral resolution in S4 is severely compromised (FWHM $\sim 200$ eV) by the bias error, and this in turn affects the measured quantum efficiency. As a result, a replacement (telemetry) bias was used (taken from ACIS Science Run 89) to compute the relative efficiency listed in Table 4.59. Even with the replacement bias, the spectral resolution was not quite as good as measured at MIT. For this reason, we regard this measurement as suspect, and have quoted statistics in Table 4.61 with this point excluded. The cause of the bias error is not understood. The high-speed tap data obtained for S4 during (a subset of) ACIS XRCF Science Run 93 show no obvious anomalies.

Second, as noted above, the cross-calibration of the two reference detectors w190c3 and w103c4 at MIT is rather uncertain at 8 keV. We require this cross-calibration to compute the response of S2 relative to reference detector w190c3, since S2 was only measured with respect to reference detector w103c4. Formally, the RMS uncertainty of this cross-calibration (derived from the reproducibility of three measurement sets) is about 0.03 (1-sigma). This uncertainty is expected to dominate other errors in the QE, relative to S2, of the five devices (I0, I3, S0, S4 and S5) for which w190c3 is the primary reference standard.

Nevertheless, excluding the S4 point, we find a mean relative quantum efficiency difference of $-0.013 \pm 0.008$, where the error is the standard deviation of the mean, and the RMS deviation of measurements about the mean is 0.019. Thus, whatever the source of the uncertainty in the CSR measurements of the w190c3 vs. w103c4 cross-calibration, the value we have adopted for this cross-calibration is just consistent, at 90% confidence, (i.e., within 1.3%) with the XRCF relative quantum efficiency data.

A related comparison between the best-fit quantum efficiency models and the XRCF data is presented in Section 4.8.