# Calculating SNR

##### THIS GUIDE IS FOR:

Biologists who want to see the math behind SNR

##### THIS GUIDE OFFERS:

Math, with explanations.

Easily compare microscope cameras and understand how camera specs affect performance using our SNR calculator.

SNR is a simple ratio of the total signal to the total noise. For microscope cameras, the equation looks like this: where

• QE = Quantum efficiency
• S = Photons/pixel
• Fn = Noise factor
• Ib = Background
• M = EM gain

From this equation we can see that the total signal is dependent on the QE (or effective QE (eQE) for EM-CCDs) of the camera. Learn more about QE and eQE in our Technical Guide, “Dissecting Camera Specifications: a field guide for biologists.”

The total noise is dependent on the noise factor, background, readout noise, and EM gain.

Signal and Background, S and Ib
Photons falling on the sensor have an average photon flux. The fluctuations in this rate are governed by Poisson statistics and therefore have a standard deviation that is the square root of the number of photons (i.e., photon shot noise). In imaging, there are two sources of photons (and photon shot noise): the signal of interest (S) and the signal from the background (Ib). Limiting the amount of Ib and increasing S is critical to getting images with high SNR.

Quantum Efficiency, QE
The QE of a camera is the wavelength-dependent probability that a photon is converted to a photoelectron. High QE is a fundamental attribute for obtaining high SNR, since QE is a predominant factor in the SNR equation.

EM-CCD Only, M and Fn
EM gain (M) occurs in a voltage-dependent, step-wise manner and the total amount is a combination of the voltage applied and the number of steps in the EM register. EM gain has a statistical distribution and an associated variance which is accounted for by Fn. At typical EM-CCD gains, Fn = √2 ≈ 1.4. All signal in an EM-CCD is subject to this additional noise. Since CCD and CMOS sensors do not have EM gain, Fn = 1 in these three cameras.

Camera Noise, Nr
Read noise (e-) is a statistical expression of the variability within the electronics that converts the charge of the photoelectrons in each pixel to a digital number expressing intensity.

Dark noise (Nd; not shown above) is camera noise that comes from thermally generated electrons and is time- and sensor-temperature dependent. Nd is not presented as a factor here because it is low and exposure times are short enough that it does not contribute significantly to total noise.