Comparing Models with Data

In order to assess the validity of our models, they must be compared with subassembly and XRCF calibration data. We will concentrate here on the mechanics of comparing the models with XRCF data. We start by using MST-provided SAOsac rays (see the MST Performance Report of June 1997, XRCF Phase 1 Testing: Preliminary Results) as input to the ACIS model.

We must fold in the ACIS focal plane geometry, accounting for chip spacing and tilts, and project the SAOsac rays onto the CCDs. The input spectrum is first modified by the filter transmission function, using both the spatial and spectral filter data. The rays that make it through the filters then provide the input to the CCD simulator described above. This simulator generates an event list that can be ingested by Event Browser, the visualization tool used by the ACIS team at XRCF for real-time analysis, or viewed using other methods. The goal is to process the simulated event list and the actual XRCF event list in exactly the same way, to look for differences between the data and the models.

The real task of calibration, then, is to find ways to improve the models so that they more closely reproduce the data. This is complicated by the fact that several models are involved and we expect to work closely with MST when it is not obvious whether the discrepancies arise from inadequacies in the ACIS model or in the HRMA model. This plan also makes obvious our dependence on the HRMA model - we require rays from an appropriately extended source at the correct (finite) distance, with a good estimate of the input spectrum. The iterative nature of the problem will likely require several runs of SAOsac for each line in the CMDB (each test configuration at XRCF).

In order to test the models, we must find physically meaningful and appropriate metrics to characterize both the simulated and actual event lists. As mentioned above, the HRMA + ACIS PSF depends on the input photon energy (which gets modified due to the ACIS spectral response matrix), the subpixel position of the source, the grade selection scheme used (which implies assumptions regarding the best split event threshold and gain conversion for each of 40 CCD amplifiers), the count rate at ACIS and the degree of pileup, and possibly other quantities.

For on-axis sources, some simple PSF core metrics are the centroid and its second moments, cuts through the centroid pixel, and fits to those cuts. The PSF wings can be characterized by the radial surface brightness and encircled energy, but these quantities yield no azimuthal information. The PSFs of off-axis sources lose the simple centrally-peaked geometry enjoyed by on-axis sources (see the MST Phase 1 report). Other, more complicated metrics must be employed here, such as width of the pincushion caustics and major and minor axes of the extended lobes. Again we must work closely with MST to characterize these features, generating a common set of metrics to facilitate comparison.