The 1-σ statistical errors in the mask-weight count rates, which depend on the number of background counts, are derived.
The mask-weight counts are defined as:
From error propogation,
This is pretty simple to calculate for real data, but if one doesn't know Ni (which includes a background component as well as the number of counts resulting from direct photons), it's a little trickier.
Suppose we assume that:
Furthermore, let's define the mask-weighting factor as:
and is a constant that depends only on the
distance between the source and the array. For a source at infinity,
K=0.27.With wi normalized in this way,
Then,
In order to go farther, we have to make some assumptions. For one thing,
we need to know the position of the source. If the source is on axis and
at infinity, then
= 0.000112674 and
= 0.000226089. Note that
≅ 2⋅.
I believe this is true for all source positions. Just for the sake of
simpler notation, let's define a constant k to be equal to
.
Let's also define x to be B / No. Then,
If x=0 (no background), then
If x=1 (B = No),
then
If x=10 (B = 10No),
then
If x=100 (B = 100No),
then
