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The I array achieves better performance than a single monolithic planar detector, because the four CCD chips comprising the array have been tilted to approximate a sphere. As each single CCD is planar, and the blur performance is a function of off-axis angle, and the mirror's relative contribution is weighted by the effective area of that mirror shell (which is energy dependent), it becomes intractable to attempt any analytic prediction of the ACIS imaging response.
Instead a computer program has been developed, (available from Penn State or the ASC) which predicts the ACIS imaging properties. The prediction is based on a HRMA off-axis behavior model (SAO-AXAF-83-014) which describes the ideal rms blur performance. To this is added in quadrature an error term of 0.5 to account for alignment and manufacturing errors. Then the resulting blur is combined for all four shells, weighted by effective area.
This program can be iterated at each CCD pixel in the imaging array to produce a histogram of the number of pixels per blur circle increment, as shown in Fig. 2.13 & 2.14. The dotted histogram in each case arises from the use of the inner two chips of the S array to enlarge the imaging field of view. (These two chips provide degraded spatial resolution because there are located substantially off-axis and not along the optimum imaging surface.)
Note that the S array chips provide some locations with blur performance worse than 20 radius, but the plots have been cut off for scaling convenience. Also note that the two imaging aim points have been chosen at symmetric locations on the I array. This means that the predicted performance of the I array chips is identical for the two aim points. The sole change is that the two active chips in the S array are farther off axis at IP#1 than at IP#2, thus the broken line histogram reflects the degraded imaging performance for the S array chips active during imaging.