# Photon Counting SNR Simulator

Signal-to-Noise Ratio (SNR) is a figure of merit that is used to describe how discernable the signal is from the noise. In principle SNR must be at least greater than 1 in order to be measure an input.

How to use the simulator:
1. Choose your detector type, up to five detectors can be compared simultaneously (Detector A to E)
2. Input your detector specifications, or simply choose a preset detector from the dropdown menu.
3. Adjust the global parameters such as light input conditions flux $$ph \over second$$ or flux density $$ph \over sec*sq. millimeter$$, and integration time.
4. If you are using a preset detector, the sensitivity will change automatically when you change the wavelength. Please note that adjusting any of the specifications will override the preset and disable the sensitivity vs. wavelength estimating function.

This simulation should be regarded as a reference only, no guarantee of detector performance is implied by the results of this simulation.

Please contact our Applications Engineers by submitting a web inquiry or by calling the Hamamatsu technical support line for a more thorough and in-depth simulation and detector selection.

Measurement Conditions:

Global Settings:
Detector A
Detector B
Detector C
Detector D
Detector E

How to calculate SNR:
SNR can be calculated for photon counting using the following equation. $$SNR = { \Phi_q \eta t \over \sqrt{ 2n_dt + \Phi_q \eta t } }$$ Where $$\Phi_q$$ is the rate of photons per second, $$\eta$$ is the quantum efficiency, $$n_d$$ is the dark count rate, and $$t$$ the integration time.
It's interesting to note the absence of excess noise, and readout noise in this equation. These noise terms can be effectively ignored because photon counting is achieved by counting pulses generated from photon and dark events. Thus small fluctuations in pulse height (excess noise), and amplitude (readout noise) do not significantly affect the measurement. This is the primary advantage that enables photon counting to achieve lower limits of detection than analog measurement.

Noise Sources:
Upon inspection, we find that the dark noise contribution is the standard deviation of two times the dark count. This is due to the need to take a reference measurement in dark conditions to establish the baseline. Consider that the resulting counts for a single counting measurement is the sum of the photon counts and dark counts. $$n_{total} = (\Phi_q \eta + n_d)t$$ To get the true signal count rate we must also subtract a reference measurement from the initial measurement to arrive at the true photon counts. $$n_{photon} = (\Phi_q \eta + n_d)t - n_d t$$ The measurement with light and the reference measurement in the dark are taken independently therefore their noise sources, which we've aptly named $$\sigma_{light}$$ and $$\sigma_{dark}$$, are also independent. $$\sigma_{light} = \sqrt{n_dt + \Phi_q \eta t}$$ $$\sigma_{dark} = \sqrt{n_dt}$$ Independent sources of noise are summed in quadrature resulting in the following equation for the total noise. $$\sigma_{total} = \sigma_{light}^2 + \sigma_{dark}^2$$ $$\sigma_{total} = \sqrt{n_dt + \Phi_q \eta t}^2 + \sqrt{n_dt}^2$$ $$\sigma_{total} = 2n_dt + \Phi_q \eta t$$ We arrive at the final form of the SNR equation including the added noise from subtracted dark measurement. $$SNR = { (\Phi_q \eta + n_d)t - n_dt \over \sqrt{ 2n_dt + \Phi_q \eta t } }$$ $$SNR = { \Phi_q \eta t \over \sqrt{ 2n_dt + \Phi_q \eta t } }$$

Count Rate Linearity:
At high photon rates of photon incidence the SNR will decrease due to saturation. Photon counting circuits have an inherent dead time which limits the minimum arrival time between successive photon detections. Thus at high count rates the detector experiences pulse pile-up effects which results in missed counts. Change the vertical axis to 'Accumulated Counts' or 'Counts per Second' to see how the measured counts are affected, which in turn affects the SNR.