The goal of the calibration procedure is to produce a response matrix valid for a given observation. We assume that the response matrix derived from the ground calibration measurements is valid throughout the mission and for all regions of the detector except that the gain has changed. ie. we assume that the redistribution matrix (the probability that a photon of a particular energy will fall in a given channel) is constant. The problem then reduces to shifting the ground based response matrix in channel space to match the gain of the observation.
The gain is derived from Bright Earth (BE) data. The Bright Earth is dominated by scattered solar X-rays at 525 eV, and is effectively a monochromatic flat-field. BE data has been routinely obtained throughout the mission. Hence the BE data can be used to monitor the gain, both as a function of time and position on the detector, by determining the PHA channel corresponding to the maximum of the BE distribution (the ``BE gain''). The relationship between the BE gain and the response matrix shift (ie. the number of PHA channels the ground-based response matrix is shifted) is determined from calibration sources. The PHA distribution of sources with known (from ROSAT PSPC) spectra were fit within XSPEC, changing the gain of the response matrix until the is minimised. This shift (in channels) is then plotted against the BE gain (Figures 2 and 3) to give a linear ``response matrix shift-BE gain'' relationship.
The steps to acquiring a calibrated response matrix are as follows. Determine the BE gain of the source, use the linear relationship in Figures 2 and 3 to calculate the response matrix shift, and create the appropriate response matrix. This is complicated by the wobble, whereby a source may be moved over regions of the detector with different BE gain. In this case, a single response matrix is not appropriate. This problem is solved by de-aspecting and calculating the number of gain states a source experiences during an observation. A response matrix is then created from the mean gain, or constructed from the time-average of several gain states.