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# Single Photon Calorimeters

## Energy Resolution

Single photon calorimeters work by the low-noise conversion of absorbed energy to heat. Such a device consists of an X-ray absorber and a thermistor that is linked through a load resistor to a low-noise amplifier. The temperature rise induced by the absorption of an X-ray produces a voltage pulse from which energy information can be extracted. The trick is to measure a small increase in temperature on top of a background noise of intrinsic thermal fluctuations and Johnson noise. Johnson noise is a fundamental noise associated with any resistance. The limiting energy resolution is given by the equation delta E = 2.36 x Eta x sqrt(k T0 2C) where C is the heat capacity (in joules per Kelvin) of the detector at a heat sink temperature T0, k is Boltzmann's constant, and Eta is a detector constant dependent primarily on the properties of the thermistor. Typically, Eta has a value in the range 1-3 for silicon thermistors. Non-ideal effects make the realized resolution somewhat worse than this. Other thermometer technologies, such as superconducting transition edge sensors, make lower values for Eta attainable.

## Spatial Resolution

In order to keep the heat capacity low, yet use an absorber that is opaque to X-rays, individual calorimeters tend to be small. For example, the area of the calorimeter pixels on XRS, an instrument to be part of the Astro-E satellite, is 0.625 mm x 0.625 mm. If you want to have more area, we can pack a lot of calorimeters close together. This can be a bit tricky, because you need to find a way to get the signal connections out between the individual detectors and you need room for the connection to the heat sink. This is done on the XRS calorimeters by making the absorbers bigger than the thermometers to which they are attached. Thus, XRS has a 6 x 6 array of calorimeters (of which only 32 are actually read out) with a gap of only 0.015 mm between detectors. With X-ray optics with sufficiently good focusing capabilities, this would be an imaging array.

View of the XRS calorimeter
under construction.

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