Pair-conversion
Encyclopedia
A pair-conversion instrument detects high-energy gamma rays by providing an environment—generally a thin foil of dense metal, commonly tungsten—in which they tend to generate electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

-positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...

 pairs, and then using standard particle-physics techniques such as a microstrip detector
Microstrip detector
A microstrip detector is a particle detector designed to consist of a large number of identical components laid out along one axis of a two-dimensional structure, generally by lithography...

 to detect these particles.

Usually there are several stacks of conversion foils and particle detectors placed on top of one another, so that the electron-positron pairs can be tracked as they pass through consecutive detectors; and at the bottom of the stack one commonly finds a calorimeter
Calorimeter (particle physics)
In particle physics, a calorimeter is an experimental apparatus that measures the energy of particles. Most particles enter the calorimeter and initiate a particle shower and the particles' energy is deposited in the calorimeter, collected, and measured. The energy may be measured in its...

 capable of measuring the energy of the electron and the positron and inferring the energy of the incoming gamma ray.

An anticoincidence shield of some kind is needed so that charged particles entering the device from outside are not confused with electron-positron pairs generated in the conversion foils.

One of the larger operational pair-conversion telescopes is the Large Area Telescope on GLAST
Gamma-ray Large Area Space Telescope
The Fermi Gamma-ray Space Telescope , formerly referred to as the “Gamma-ray Large Area Space Telescope ”, is a space observatory being used to perform gamma-ray astronomy observations from low Earth orbit...

. Space-based pair-conversion detectors tend to make for rather expensive missions, since they unavoidably contain several hundred kilograms of lead or tungsten.

http://cosmology.berkeley.edu/inpac/inpac_retreat_slides/Hiroshima_3_9.pdf has a slide illustrating the design of LAT.
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