# Reconciling gain (e/ADU), full well capacity and ADC bit depth

I have a CCD sensor datasheet which cites the following parameters in accordance with the EMVA 1288 standard:

``````ADC bits      14 bits
Well depth    17273 e-
``````

I'm unable to reconcile these numbers. Shouldn't the gain just be the ratio of the number of electrons in the well to the ADU pixel counts? In that case, shouldn't it be equal to 17273/2^14 = 1.054? Or am I missing some kind of nonlinear behavior close the full well depth which prevents one from calculating this ratio at full well capacity?

In case you are curious, this is the Grasshopper3 GS3-U3-14S5M-C camera from PTGrey. The datasheet is available on their website.

Interestingly enough, when I look at the specs for a different ST-8E camera: FWC=180000, ADC 16bit, the datasheet value of gain=2.8e-/ADU is quite close to the ratio FWC/2^16=2.74.

The well depth is a property of the sensor. In your example, the incident photons are converted into electrons with a ratio corresponding to the quantum efficiency and when the pixel has accumulated 17 273e-, the generated extra e- are not accepted anymore in the "fully booked" pixel.

ADC and gain are properties of the camera electronics design and are explaining how these damned electrons will be counted after transfer from the sensor.

ADC of 14 bits means that the electronics will be able to produce a digital signal in between 0 and 16 383 gray levels. And, finally, the gain of 0.17 is telling you that each 0.17e- is generating one digital level in 16bit. Then, the actual displayed gray level can be calculated by using the bit ratio between 16 and the actual converter.

Nothing is preventing a camera from being poorly designed or with an ADC converter not fitted to the selected sensor. Here, a saturated pixel with 17273e- will generate 101 606 digital levels (16 bits) which makes 25 401 gray levels in 14bits (divided by 4 for the 2 bits difference). Since 14 bits are limited to 16 383 levels, it means that your electronics will saturate the signal far before your sensor pixel will be saturated.

To put it simply, you would see no difference if your pixel was saturating at 11 140e-. Just try to redo the calculation with this new saturation value and you should see a good correlation with the gain.

• It's a good answer, but who am I kidding, you won me over with those damned electrons – OnBreak. Dec 4 '18 at 17:56

This is the answer I got from PTGrey technical support team:

Gain in the EMVA document is calculated using 16-bit data and it also accounts for noise. I cannot give you this formula but if you use 16 bits instead of 14, you will get a closer result.

If you compute 17273/2^16 it gives 0.26 which is indeed closer to 0.17 but doesn't exactly match. The EMVA1288 standard Eq(9) and Section 6.6 describe how this gain is estimated experimentally using the "photon transfer method."