Calibration Strategy

The quantum detection efficiency of each ACIS flight CCD was calibrated relative to one or more reference CCDs at the CCD Laboratory in MIT's Center for Space Research. The reference CCDs used as calibration transfer standards for the flight CCDs are of the same design and are essentially identical to the flight CCDs except for small manufacturing variations. The reference CCDs were previously calibrated using the facilities of the Physikalisch-Technishe Bundesanstalt (PTB) laboratory at the Berlin Electron Storage ring BESSY[Arnold and Ulm1992], as well as via comparison to a Si(Li) solid state detector at energies above 3 keV. The calibrations performed at PTB-BESSY are described in Section 4.6.1.

The strategy adopted to measure the relative quantum detection efficiency of flight CCDs vs. reference CCDs consisted of alternately moving one flight CCD and one reference CCD into a stable quasi-monochromatic X-ray beam at each of several energies, spanning the spectral range of 0.3-10 keV. Two special vacuum chambers were built for this purpose, containing mounts for two CCDs attached to X-Y translation stages, X-ray sources, and alignment systems employing LEDs and pinholes[Jones et al.1996]. The pinholes illuminated the CCDs with small spots, coaxial with the X-ray sources, whose centroids were determined to the nearest pixel in order to alternately position each CCD at the same X-Y location for the calibration measurements.

Both radioactive (⁵⁵Fe) and fluorescent X-ray sources were used to illuminate the CCDs, providing a range of discrete emission lines to cover the energy band. Two fluorescent sources were used, one with a tritium source whose beta particles excite low-Z targets (for C, O, and F lines), and one employing a Mo-anode commercial X-ray tube to excite higher-Z targets (Al, Si, P, K, Cl, Ti, V, Fe, Co, Ni, Cu, Zn, and Ge targets were available). These sources have been described in detail elsewhere[Jones et al.1996]. The carbon source was only used with back-illuminated (BI) CCDs, as front-illuminated (FI) CCDs have very poor efficiency at 277 eV. The sources used for relative QE calibration and the energies of their $K_{\alpha}$ lines are shown below:

Element	(C)	O	F	Si	P	Ti	Mn	Cu
Energy (keV)	.277	.525	.677	1.74	2.02	4.51	5.89	8.04

To analyze the relative quantum efficiency (QE) data, a Gaussian fit to the main X-ray line was made to the cumulative spectra (for each CCD quadrant); then all counts within 3 sigma of that peak were counted towards the detected flux rate in that line. Both the flight and reference CCDs (containing $1024\times1024$ pixels) were divided into 1024 ``superpixels'' ( $32\times32$ pixel square regions). The calibration measurements collected approximately 10000 counts per superpixel for 1% accuracy (in counting statistics) at the superpixel level. This goal required collecting over ten million counts in each CCD for each energy of interest, a process requiring typically 10 days, with two shifts of data operators per day, per flight CCD candidate. [Counting re-flexed CCDs, almost 40 devices have undergone this process since Jan. 1996.] Smaller sets of data were also taken at the energies not used for quantum efficiency analysis in order to fully characterize the spectral response (gain and FWHM vs. energy).

The alignment process ensured that each reference CCD superpixel viewed the same X-ray flux as the corresponding flight CCD superpixel, even for non-uniform source radiation patterns (C, O, and F were most sharply peaked on axis--the higher energies were relatively flat). It is estimated that the flight and reference CCDs were positioned at the same location in the X-Y (translation stage) plane to within two pixels. The raw relative QE (uncorrected for pileup) for each superpixel pair was taken to be the ratio of the flight CCD count rate (counts/sec/superpixel) to the reference CCD count rate.

This yielded 1024 values of the QE ratio, with typically a Gaussian distribution. By fitting a Gaussian to this histogram of ratios, we obtained a fitted centroid, representing the nominal QE ratio for the two CCDs, and a width (sigma) which represents the spatial variations. A simple average of the 1024 ratios was also calculated, along with the standard deviation. The standard deviation is quite sensitive to outlying values that can originate from bad pixels, hot columns, or edge effects (particularly shadows along one edge attributed to the framestore covers attached to each CCD).

Images and histograms of the spatial uniformity of the superpixel ratios at each energy are presented in Figures 4.77-4.86 in section 4.7.2.