I?m counting photons and at high count rates I see a drop off in the numb er counted. It seems this may be due to the dead time of the detector. (H ow long it takes to recover after detecting one event till it can see the n ext.) So I found this in wiki,
My question is about the following equation,
(That probably won?t work.) So it says the real number of events N~= Nm /(1 - Nm*tau*T) where Nm is number measured, tau is the dead tim e, and T is the measurement time. I?m wondering about the approximate si gn. I figured it should be exactly equal to the above result. (But maybe I?m missing something.)
My reasoning is as follows, (OK first I wrote my equations for the rate of counts.) So I?ll call R_r the real rate of events, and R_m the measured rate. I?ll stick with tau for the dead time, and T for total time.) Then the real number of events I should count is, N_r = R_r*T, and the measured number is N_m = R_m *T. Now the total dead time is N_m*tau, and the number of events I missed durin g that total dead time is, N_missed = N_m*tau*R_r = R_m*R_r*tau*T. Then the real counts should be the number measured + the number missed. Or, R_r*T = R_m*T + R_m*R_r*tau*T
Dropping big T, I get R_r = R_m + R_m*R_r*tau or R_r = R_m / (1 ? Rm*tau) which is the equation from wiki, without the approimate sign.
Oh..frick.. I just realized that my detector is paralyzable (to use the wik i language.) (An event in the dead time resets the dead time.) That puts a monkey wrenc h in the works. Well, I'll post anyway, Thanks for reading.