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An effective area measurement entails determining the ratio of the x-ray line count rate RFP measured by the ACIS focal plane detector to the x-ray line flux FBND incident on the HRMA as measured by a beam normalization detector.
We define as the effective area Aeff of the HRMA/ACIS combination the quantity:
where ABND is the area of the BND normalization detector.
The effective area measurements performed at the XRCF were made in a defocused mode with ACIS moved approximately 40 mm away from the optimal focus position in the direction of the x-ray source. Operating in the defocused mode resulted in the reduction of pileup by means of spreading the x-ray image over many CCD pixels. In several measurements the image was defocused onto 2 adjacent segments of a CCD that were read out by different CCD amplifiers. Because of slight differences in the properties of the CCD amplifiers, the spectra corresponding to each amplifier were analyzed separately and the results combined to produce the total detected ACIS event rate over the selected spatial region of interest (ROI). Each estimate of the ACIS/HRMA effective area presented here is accompanied by the computed centroid location of the defocused image and the spatial region of interest used.
The analysis technique used for determining the detected x-ray line count rates from the spectra obtained with ACIS are based on a region of interest approach. Incident spectra produced by the electron impact point source (EIPS) combined with the double crystal monochromator (DCM) contain a narrow x-ray line at the selected energy with a minimal amount of contamination from higher orders. For the present analysis we have in most cases, unless mentioned otherwise, considered the DCM spectra to be monochromatic. The extraction of the x-ray line count rate detected by ACIS simply entails determining the number of counts in a region of interest around the x-ray line. The incident x-ray flux levels were high enough to produce noticeable pileup in the ACIS spectra despite defocusing. Pileup occurs whenever 2 or more photons are incident within 0 or 1 CCD pixels and are detected between successive CCD frame readouts. In such an instance the ACIS electronics will regard these as a single event with an amplitude given by the sum of the charge in the 3x3 neighborhood of the pixel with the maximum detected charge. The manifestation of pileup in the ACIS spectra is the appearance of ``pileup lines'' at energies that are multiples of the incident line energy. In addition to these lines a portion of the charge from the multiple events will not be recorded in the 3x3 island resulting in tails below the pileup lines. Another consequence of pileup is grade migration, which results when the presence of more than one photon per readout interval causes the recognized grade of the event to change from the value expected for single photon events.
For the analysis of ACIS spectra we have considered ROI's that include the Si escape peak (if present), the main x-ray line and pileup lines. The number of events, Npileup,n detected in the n'th pileup line are multiplied by n+1. We estimate the detected ACIS count rate with the expression: