Finite detector thresholds, energy resolutions, and spatial resolutions produce systematic biases in the imaging capabilities of Compton telescopes. These limitations have been discussed in detail elsewhere in context of two-layer, low-Z converter and high-Z absorber, scintillation detector designs (von Ballmoos et al. 1989), and the conclusions can be directly applied to GCTs. However, GCT designs will introduce additional complications which significantly alter the event reconstruction techniques. Historical Compton telescope configurations make two assumptions about the events which do not generally hold in GCTs: (i) the events are a single Compton scatter in the converter, followed by photoelectric absorption in the absorber, and (ii) the time-of-flight (TOF) between the photon interactions is measured to determine their order.
The distributions of number and type of interaction sites in a GCT for
normally incident, fully-absorbed photons ranging from 0.2-10 MeV are
shown in Fig. 3, for the instrument configuration discussed in Appendix A.
Here we distinguish three event types: a single photoelectric absorption,
one or more Compton scatters followed
by a single photoabsorption, and one or more pair productions.
Compton scatters followed by pair production could potentially be
reconstructed; however, here we include these events with other
pair productions.
These distributions account for the finite spatial resolution of the detectors, so
that interactions occurring too closely together are not resolved. From these
distributions it is clear that events with 8 or more interaction sites can be
immediately rejected as probable pair production events, with little effect on
the Compton photopeak efficiency. For incident photon energies above 0.5 MeV,
3-7 interaction site Compton scatter events dominate the photopeak.
To accurately reconstruct a Compton scatter event, the first and second
interaction sites must be spatially resolved, and their order correctly
determined. The need to determine the proper ordering of
three or more (3+) interaction sites is
complicated by the timing capabilities of GeDs. In the scintillation detectors of
COMPTEL/CGRO the interaction timing can be performed to 0.25 ns
(Schönfelder et al. 1993), which is adequate to determine the TOF between two
interactions in the separate detector planes. With the slower rise time of GeDs one
can reasonably expect event timing to
10 ns, which is inadequate for TOF
measurement in reasonably-sized instruments. While Pulse Shape
Discrimination methods have been proposed to push the interaction timing in GeDs to
1 ns (Boggs 1998), even this timing would be unreliable for determining TOF
among three or more interaction sites. A method of reliably determining the photon
interaction order without timing information must be developed.
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