Cannot open file (/var/www/vhosts/aprendtech.com/httpdocs/wordpress/wp-content/backup/.htaccess)Cannot write to file (/var/www/vhosts/aprendtech.com/httpdocs/wordpress/wp-content/backup/.htaccess) AprendBlog » 2011 » October

Oct 29 2011

## Logarithm of PHA with deadtime

The logarithm of the data is often used in x-ray imaging systems because it is (very) approximately proportional to the line integral. The statistics of the log of the counts in photon counting detectors are are different than those of the counts as summarized in my last post and I derive them in this post. I then test the formulas using a Monte Carlo simulation.

Oct 29 2011

## Deadtime 4-Monte Carlo simulation of PHA data

I used a Monte Carlo simulation to test the formulas derived in my last post for the mean value, variance, and covariance of pulse height analysis (PHA) data as a function of deadtime. In this post, I discuss the simulation software and the results. The formulas were quite accurate except for the covariance where the relatively small value and the difficulty in getting good statistics for variance estimates in general caused a spread around the theoretical values.

Oct 17 2011

## Deadtime-3 Pulse Height Analysis Theory

In previous posts, I discussed the mean and variance and the energy spectrum of photon counting with deadtime. In this post, I will describe the statistics of pulse height analysis (PHA) data as a function of the deadtime of the detector. I will analyze the idealized case with perfect energy bins with zero transition width and no overlap and no added electronic noise. With these assumptions and no deadtime, the number of counts in each bin is Poisson distributed with a mean value equal to the number of incident photons and the data in different bins are independent. With deadtime, the PHA data mean and variance are smaller than those with no deadtime. In addition, the data in different bins become negatively correlated.

In my next post, I will describe a Monte Carlo simulation to validate the formulas derived here.

Oct 08 2011