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The Graz system uses a CSPAD detector, thus minimising energy-dependent range variation during calibration. The calibration data were obtained from target board ranging at low return rate (~20%), and the calibration 'fiducial' value determined at Graz from the raw calibration data by computing an iterated mean using a 2.2 sigma rejection level. The range-distribution of these processed observations then represents the whole-system response, including the standard data-treatment (clipping) procedures used at Graz.
We then smoothed the clipped calibration data using Andrew Sinclair's Gaussian smoothing routine, to derive a smooth version of the system response. The process is illustrated in this system plot
The smooth system distribution can now be used to compute the expected range distribution for any satellite whose impulse response is known, strictly for single-photon levels of return. This smoothed system response was convolved about its mean value with the Lageos impulse function derived by Reinhart Neubert. Range-residuals from full-rate data from a pass of Lageos-1 and -2 were used to form a histogram showing the distribution of range values.
The observations were obtained at return levels higher than single-photons, so we might expect to see in the distribution of the range residuals a reduced contribution from the extended array of Lageos; with a large number of photons reaching the detector, photons from the leading edge of the return pulse will preferentially be detected. During the process of forming normal points at Graz, 2.2-sigma clipping is applied to the de-trended range residuals, analogous to the treatment of the calibration data. Thus we consider it valid to compare the model distribution with that of the Lageos range residuals, and estimate the appropriate CoM from the result, as done for the single-photon Herstmonceux data. As before, the model amplitude was adjusted and the mean value of the range residuals altered from zero to give the best fit between the model and the data. This process is shown in this satellite plot
As can be seen, the leading edge of the model fits the data distribution quite well, and the clipping applied to the data is clearly apparent in the poorer fit between the tails of the distributions. The fit of the model to the data implies that the centre-of-mass correction appropriate to the normal observing and processing methods at Graz as represented by these sample data is close to 247 mm. By way of confirmation of this result, a 2.2-sigma iterative solution for the mean and s.d. of the MODEL gives a value of 246 mm with s.d 9 mm.