Redistribution of X-rays by Pileup

Pileup can effect event detection in two ways, event-extinction and event-redistribution. Up to this point, only event-extinction has been modeled since its occurance rate is nearly a factor of ten less than event-redistribution. This difference is nicely displayed by reanalyzing the experimental pileup data from section 3 as follows. For a series of energy spectra at different source fluxes (i.e. different x-ray tube currents), the spectra are normalized to the total exposure time and incident flux. Since the CCD output electronics use an A to D converter, the energy scale is discretized into intervals. For each energy interval, a plot is made of the spectral intensity versus the incident flux. If there was no pileup effect, the points would lie along a horizontal line, that is the normalized spectral intensity would not vary with incident flux at that energy. For weak pileup in the linear regime, the points actually lie on a linear line with a negative slope. In effect, this procedure results in plots similar to Figs.  4.12 -  4.15, except now there is a plot for every energy bin (in our case there were 4096 energy bins). The intercept of this line represents the intensity observed at that energy if pileup effects did not occur. Plotting all 4096 intercepts together versus energy results in a new spectrum which can be considered the spectrum observed if the detector had no pileup effects. Correspondingly, in addition to the intercept, the slope of each line represents a quantitative measure of the pileup effect at that energy. Plotting all 4096 slopes together versus energy results in a new spectrum reflecting the spectral change caused by pileup.

Figures  4.28 -  4.29 show the spectral change for all 12 energies as observed by w203c2 during 7 second exposures. The most prominant feature for each (target) energy is the large negative spike which represents x-ray extinction of the K$_{\alpha}$ peak. For example, in V, the K$_{\alpha}$ line at 4949 eV looses about 0.02 x-rays/$\mu A^2$ in each energy bin. Associated with each K$_{\alpha}$ extinction spike is the K$_{\beta}$ extinction spike, usually about ten times smaller. Small negative spikes also result from the Si escape peak, the fluorescence peak, and the L peak (best seen in spectra from higher Z, e.g. Cu). Aside from negative extinction spikes, there are positive redistribution spikes. The largest such positive peak always occurs at twice the K$_{\alpha}$ energy. This peak represents the pileup of two K$_{\alpha}$ x-rays such that they appear as a single x-ray at twice the energy. One nice example of additive redistribution is the Cl plot which shows a series of three positive peaks, each representing pileup from all three combinations of K$_{\alpha}$ and K$_{\beta}$ x-rays. Redistribution in the continuum can also be seen, but is too small to be observed on the displayed scale. These events represent the slight overlap of two x-rays appearing as one x-ray, but without the total inclusion of the sum all their charges (or energy). The collected energy lies anywhere between that of one memeber of the incident pair of x-rays and that of the sum of the pair. The number of these redistributed ``continuum'' events is a small fraction (about 10%) of redistributed events with no energy loss. This observation forms an important conclusion: the largest effect of spectral redistribution is the simple energy summation of two x-rays.

Other minor redistribution effects are observed around the base of the K$_{\alpha}$ peak. The net effect appears as a slight line shift, caused by pileup moving a few events from the low energy side of the K$_{\alpha}$ peak to the high energy side. However, this detail was not regularly observed under all conditions.

  

Figure 4.28: Redistribution of G02346 events in w203c2 during 7 second exposures due to pileup for Al, Si, P, Cl, Ti, and V HEXS targets

  

Figure 4.29: Redistribution of G02346 events in w203c2 during 7 second exposures due to pileup for Fe, Co, Ni, Cu, Zn, Ge HEXS targets