Method for determining how many photons are in a pulse

At the right is a snapshot of the pulses produced by a hybrid photodiode (HPD, blue trace) illuminated by a blue light-emitting diode (LED, yellow trace). The average number of photons detected by the HPD per pulse is computed by taking the integral of the charge in a single pulse and dividing it by the average charge per photoelectron in the HPD. The manufacturer (DEP, Netherlands) specifies that the HPD collects 2700 e- of charge per photoelectron produced in the cathode. The signal from the HPD was not amplified. It was measured in Volts by the oscilloscope with a 50&Omega; terminating resistor. The blue trace in the figure displays 20 mV per division, which becomes 0.40 mA / division after dividing by R=50&Omega;. Visually integrating the red shaded area in the figure gives about 6.5 squares. Each square is 0.40 mA * 250 ns = 100 * 10-12C. The charge of each electron is 1.6 * 10-19 C, so this integral is 600 million collected electrons. Dividing by 2700 collected electrons per photoelectron gives 230,000 detected photons per pulse.


 * $$\int\ {f(x)}\, dx \approx 230000\ photons$$