The derivation of the segment-specific readnoise variance (varsR) is shown here. This pertains to both the 'conventional' and 'weighted' readnoise variances - the only difference being the number of groups in the segment. This derivation follows the standard procedure for fitting data to a straight line, such as in chapter 15 of Numerical Recipes. The segment-specific variance from read noise corresponds to σb2 in section 15.2.
For read noise R, weight w = 1/R2, which is a constant.
n = number of groups (ngroups in the text)
t = group time (tgroup in the text)
x = starting time for each group, = (1, 2, 3, ...n + 1) ⋅ t
Sxx =
D = S1 ⋅ Sxx- Sx2
Summations needed:
The variance due to read noise = varsR = S1/D = S1/(S1 ⋅ Sxx − Sx2)
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This is the equation used in the step code and listed in the segment-specific computations section of the step Description.