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

The agreement between XRCF and CSR is not as good for the backside devices. At 525 eV, both S1 and S3 appear to have been 10-12% more efficient relative to S2 in the XRCF data compared to the CSR data. Discrepancies at the 5% level are also apparent at several other energies. Here we discuss possible origins for these discrepancies.

We have investigated the effects of windowing and spatial variation in the charge transfer inefficiency of the backside devices by averaging the relative efficiency uniformity maps at 525 eV over all columns and plotting the average relative efficiency versus row number. This analysis indicates that the peak-to-peak variation in the relative efficiency of the backside devices, averaged over regions of 1024 columns by 24 rows (similar to the windows used at XRCF), is only$\sim$2-3%. This is too small to account for the differences between the CSR and XRCF relative efficiencies at 525 eV, although this level of variation would constitute a significant fraction of the discrepancies measured at the higher energies.

The spectral redistribution functions of the front- and back-illuminated detectors are significantly different. Moreover, the X-ray sources used at both MIT and XRCF emitted significant and differing continuum fluxes in addition to the intended line flux. In principle, therefore, proper analysis of BI-to-FI relative QE measurements must account for response function differences. Our analysis to date has ignored these response function differences, and so is subject to several systematic errors as a result. In an effort to bound these errors, we have begun to examine the line-to-continuum ratios of the various sources. We find, for example, that the continuum level of the XRCF source was stronger relative to the emission line at 525 eV than was the case in the CSR source (see Figures 4.87 and 4.88).

We estimate that neglect of the continuum biases the BI-to-FI QE ratio at 525 eV, measured at XRCF, by as much as 15% above the true value. In the CSR measurements, the lower continuum produces a substantially lower bias (about 5%). We also note that one would expect this error to be most serious at the lowest energies, where the BI and FI response functions differ in width by as much as a factor of two; at higher energies, the response function widths differ by 30% or less. Figures 4.89 and 4.90 show that differences in the line-to-continuum ratios at XRCF and CSR were negligible at higher energies.

We conclude that our heretofore inadequate treatment of the redistribution functions and source spectra may well account for the XRCF-to-CSR discrepancies in BI-to-FI relative quantum efficiency measurements. A corollary conclusion is that the CSR measurements of these quantities may be in error by $\sim5\%$ at low energies.

We have some confidence that suitable modelling of the BI redistribution function and the source spectra will provide us with more accurate estimates of the BI response. The excellent repeatability of the FI results demonstrates that our fundamental measurement procedures are sound. Moreover, each BI measurement was accompanied by a simultaneous or nearly simultaneous measurement of the same source with an FI device. These FI data, and our sound FI models, will provide independent constraints on the source spectra used to characterize the BI detectors. These constraints, in turn, should improve our understanding of the BI-to-FI relative quantum efficiency data.
 

Figure 4.87: O-K spectra for S3 (upper panel) and S2 (lower panel) from XRCF Phase I. The bar in each plot marks the range of channels within 3 sigma of the peak.

Figure 4.88: O-K spectra for S3 (upper panel) and w203c2 (lower panel) from CSR Subassembly Calibration The bar in each plot marks the range of channels within 3 sigma of the peak.

Figure 4.89: Ti-K spectra for S3 (upper panel) and S2 (lower panel) from XRCF Phase I. The bar in each plot marks the range of channels within 3 sigma of the peak.

Figure 4.90: Ti-K spectra for S3 (upper panel) and w203c2 (lower panel) from CSR Subassembly Calibration The bar in each plot marks the range of channels within 3 sigma of the peak.