D4 Full Well Capacity and Gain Estimates
Prepared 2012-01-16 by Bill Claff (Revised 2012-01-19, annotated 2012-03-20)

Full Well Capacity (FWC) and gain are interrelated and important sensor characteristics.

Generally what we call FWC is stated at the limit of the Analog to Digital Converter (ADC).
In this article ADC units are call Analog to Digital Units (ADU), also often called Digital Number (DN) elsewhere.
There are 16,384 14-bit ADU values.
FWC and gain are interrelated in that FWC in electrons * gain in ADUs/electron = the ADC range in ADUs.

Gain is important so that we can convert to common units and understand the relative effect of noise sources such as read noise and photon noise.

With a proper test target and a reasonable number of pairs of images it’s straightforward to get an accurate determination of gain.
The pairs of images play a key role in effectively eliminating all but photon noise and making the measurement easy.
However, at this time with the D4 announced but not released we cannot obtain data in that fashion.

Without pairs of images we must be satisfied with data that will have and accept that other forms of noise will adversely affect our measurement.

I performed three procedures that cross-check reasonably.

The techniques rely on examining NEF files and measuring the signal and noise in small regions of the images.

The first technique locates the region with the highest variance normalized for the full ADC range, not including data beyond the white point.

Marianne Oelund posted a single figure of 62,807 on dpreview using this technique.

My technique is slightly different in that I use the full ADC range of 16,384 whereas she used 16,000; I also analyzed more data.

Marianne and I have both chosen one of the green channels for our analysis.

Noise values are converted to variance, adjusted to the ADC range, and adjusted to an assumed base ISO of 200.
[ISO 100 was originally rejected because of lack of data and that it would produce such a high value.
But as it turns out, ISO 100 is the correct base ISO.]

Skipping the details my results using the technique are:

ISO	Signal	Noise	FWC
	ADUs	ADUs	electrons
200	4735.79	38.14	53,300
400	3681.74	43.82	62,800
800	3879.79	63.48	63,100
1600	3864.01	86.33	68,000
3200	4804.48	137.71	66,400
6400	5796.86	212.02	67,600
12800	3528.48	237.7	65,500
12800	5339.65	294.07	64,700

[The FWC values would be double for ISO 100.]

I list two ISO 12800 results because I have far more ISO 12800 data available to me and because both are reasonable data points.

Excluding the ISO 200 number, which is much lower than the others, the average of all other these results is a FWC of 65,400 electrons or a gain of 3.99 electrons/ADU.
[ISO 100 would be FWC of 130,800 and gain of 7.98.]
Note that because more than photon noise was present the FWC and gain are probably understated.

The second technique uses the signal and noise data as if performing a gain analysis in the normal fashion.
However images are not paired and subtracted so rather than performing a linear fit a quadratic fit is performed.

The linear term in the quadratic fit should be a good approximation of gain (actually inverse gain ADU/electron).

Again, since ISO 12800 is by far the largest data set:

Adjusting to ISO 200 we have (12800/200)/14.16 = 4.52.

Since this technique accommodates for other forms of noise this cross-check is reasonable.

The higher values of 4.52 electrons per ADU gain and a FWC of 74,100 electrons might be reasonable.
[At ISO 100 this would have been FWC of 148,200 and gain of 9.04!]

Fortunately, two of the ISO 12800 images available are quite close and are candidates for pairing.

So for the third techniques we attempt the usual gain analysis.

Discarding poor data at higher signal levels the chart and fit look like this:

This is a remarkably good fit considering that the pair of images was not “properly” taken.

The fit produces a gain of 4.05 electrons per ADU and a FWC of 66,400 electrons.
[At ISO 100 this would be 8.10 and 132,800 respectively.]
Of the figures obtained these are the ones in which I currently have the most confidence.

In closing I must emphasize that these are only estimates until proper measurements can be made.

[Current data indicates an FWC of 144,400 with a gain of 7.22.
Had the original analysis been for ISO 100 rather than ISO 200 the values would have been as much as 11% too high.]