# Calculating Electron Multiplication GainImaging Topics

## Calculating Electron Multiplication Gain

This is a technical note on how to measure actual Electron Multiplication Gain in an EMCCD camera

Multiplication gain is defined as the ratio of (Charge with Gain) / (Charge without gain).

### Final Test Procedure

For Final test, a thirty five point curve of Multiplication Gain vs. Multiplication gain DAC is generated using the following procedure. For camera’s that are cooled a bias may be substituted for the dark.

1. Set the Multiplication DAC to 0.
2. Determine the exposure time so expected the image mean is shot noise limited. Typically 25 to 50% of single pixel full well capacity.
3. Acquire an image and Dark without any multiplication gain. Record the exposure time, dark mean, (image – dark) mean.
4. Set the Multiplication DAC to predetermined value. See curve for example.
5. Acquire an image and Dark with multiplication gain. Adjust exposure time as needed to get the image mean close to the same mean value obtained in step 2 or no less than 1ms.
6. Calculate the multiplication gain using the following formula:
$$G = {S(light,gain) – S(dark,gain) \over S(light,no\_gain)} \times {Exp(no\_gain) \over Exp(gain) }$$

Where

 G is the multiplication gain S(light,gain) is the mean number of counts with gain on and exposed to light S(dark,gain) is the mean number of counts with gain on in the dark S(light,no_gain) is the mean number of counts with gain off and exposed to light S(dark,no_gain) is the mean number of counts with gain off in the dark Exp(gain) is the exposure time in ms for the gain measurement Exp(no_gain) is the exposure time in ms for the initial, non gain measurement