Sep 10

## NQ detector SNR

In this post, I continue to discuss the results in my paper “Near optimal energy selective x-ray imaging system performance with simple detectors[Alvarez2010].” The paper discusses fundamental limits on the signal to noise ratio of x-ray detectors with energy spectrum information. It also describes how we can design practical systems with low energy resolution detectors whose performance gets close to the optimal limit. The paper uses statistical detection theory to show that the performance depends on the signal to noise ratio (SNR) and derives a formula (see this post) to compute the SNR as a function of the detector spectral response and noise properties. In this post, I use the formulas for the NQ (simultaneous photon counts and integrated energy) detector data statistics from my last post to compute the SNR. We can use the formulas to show that the NQ signal (almost) always has a larger SNR than the N and Q individual signals. The SNRs are equal if the spectrum has zero-width.

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