Correct relationship between Read Noise and RMS error?

[SCO]

Could you please clear something up for me.  I am trying to determine the relationship between the camera read noise and the RMS error of a typical measurement on a scatter plot (assuming all other factors are equal).  I am not sure if the relationship is linear or square root (or perhaps something else).

As an example, assume camera1 has a RN of 9e- and Camera2 has a RN of 1.6e-

Using a square root relationship:

Camera 1 RMS Error = (RN)^1/2 = (9)^1/2 = 3.0
Camera 2 RMS Error = (RN)^1/2 = (1.6)^1/2 = 1.265

Percent Reduction in RMS Error = (3.0 - 1.265)/3.0 x 100% = 57.84%

Assuming a linear relationship:

RMS Error Ratio = 1.6/9.0 = 0.178

Percent Reduction in RMS Error = (1 - RMS Error Ratio x 100%) = (1-0.178) x 100% = 82.22%

Since we are dealing with a Gaussian distribution, I would assume that the square root model would be more accurate.  Could you please give me your thoughts on this?

[karenacollins]

The noise equation is given by equation B1 in the AIJ paper. Read noise is a squared term that is under a square root, but many other factors are also under the square root.

[SCO]

Thanks Karen.  A bit more complicated than I expected, but I am sure much more precise as well.  

Ed