The Core of the Point Response Function

  

Figure 6: Marginal distribution in Y and Z directions for image H-IAI-CR-1.001, demonstrating gravity ovalization effects.

  

Figure 7: PSF shape: orthogonal slices through H-IAI-CR-1.001, showing the effects of gravity ovalization.

  

Figure 8: PSF shape: full width half max (in pixels) of Gaussian fits to orthogonal slices through the brightest pixel

In Figures 6 and 7 we plot the marginal distribution and slices for an image of an Al-K 1.486 keV as spot. This image was obtained in staggered readout mode (e.g. Figure 3, test H-IAI-CR-1.001), and has the lowest count rate per frame (~= 0.2 photons per frame), hence the lowest degree of pileup among the ACIS measurements obtained at the XRCF. It should, in principle, have the smallest ACIS spot size obtained at the XRCF. The spot shows obvious asymmetries in shape, and it is broader along the Z axis than along the Y axis. The Z axis is parallel to the gravity vector and the Y axis is parallel to the CCD readout direction. The direction of the readout can be seen by the trail across the summed image shown in Figure 3.

The asymmetries in Figures and are similar to those seen in the two dimensional scan data for the ensemble HRMA (C-IXF-P2-2.001) obtained during XRCF Phase C with a proportional counter and 10 µm diameter pinholes rastered on 10 µm centers (see NAS8-40224), effectively ~=10 µm pixels. By comparison, the ACIS images have 24 µm pixels, and thus have less than half the sampling of the scan data. The full width at half maximum (FWHM) of the Al-K scan data are FW_y(s)=22.6 µm and FW_z(s)=25.3 µm (NAS8-40224, Table 4.4), whereas we find FW_y(A)=47 µm and FW_z(A)=65 µm for the ACIS measurements. The increased spot size of the ACIS data compared to the scan data is consistent with the decreased sampling of ACIS, or ``pixelization.'' The larger width of the spot in the Z direction seen in both data sets is likely to be residual gravity ovalization. However, the origin of the asymmetries in the ACIS spot stem from the HRMA optics, rather than sampling, because the asymmetries, particularly along the Y axis, are seen in both data sets. The 70% encircled energy radii for the ACIS and scan data are 55 µm and 75 µm respectively. The difference in these figures can probably be explained by sampling.

In Figure 8 we examine the width of the on-axis spot as a function of energy for the tests listed in Table 23. Figure 8 shows the FWHMs of slice profiles along the Yaxis, as in Figure 7. The FWHMs were measured by fitting Gaussians to the profiles. The top panel of Figure 8 includes all grade events and the bottom panel includes ASCA grades 0, 2, 3, 4, and 6 (G02346). Measurements in which the degree of photon pileup is less than 10% are shown as triangles, and those with pileup greater than 10% are shown as squares. The degree of pileup is unknown for the low-energy O-Ka data (crosses) because their pileup peaks were indistinguishable from other features in the spectra. Based on the X-ray fluxes, we expect pileup to be less than a few percent. The solid symbols represent measurement with the S3 backside CCD. This figure shows that the spot FWHM is, to the limits of precision, nearly independent of energy and event grade. In addition, the FWHM is not terribly sensitive to pileup for pileup fractions below ~20%. The spot size measured with the backside device appears to be slightly smaller than the measurements obtained with the frontside device. This slight improvement may be due to the smoother surface of the backside device, a slightly improved focus, or some other explanation.

In Figure 9 we examine the properties of the cumulative distribution of counts or energy (we use counts, events, and energy interchangeably) as a function of spot size by plotting the on-axis 70% and 90% encircled energy radii as a function of energy for 20 tests listed in Table 23. The symbol definitions are the same as for Figure 8. The 70% encircled energy radius at Al-K is ~2.3 pixels, whereas the 90% radius increases to about 3.8 pix. The 70% radius shows a weak dependence on energy. The 90% radius shows a pronounced gradient, increasing from 3.8 pixels to about 5.5 pixels at the 6.4 keV Fe-Ka feature, although the gradient is only marginally significant.

In the limit of zero energy, we find EER(70%)=2.28 pix and EER(90%)=3.43 pix. We note again our definition of the central pixel as 1 for purposes of plotting the cumulative distributions on a logarithmic scale. The actual 70% and 90% radii in pixels are 1.28 pixels and 2.43 pixels respectively.

Event pileup sharply increases the 70% and 90% EER, as shown in Figure 7. This is the result of lost events in the PRF's concentrated core relative to the wings. The EER is apparently more sensitive to pileup than the FWHM. A more exhaustive discussion of photon event pileup can be found in Section 7 and in http://asc.harvard.edu/cal/Links/Acis/acis/Cal_prods/pileup/pileup.html

  

Figure 9: On-axis 70% and 90% encircled energy radii as a function of energy