Discussion

The mean absolute error of INT_FRM(i,j) yields with ICONS = 1:

$$(\Delta I)^2 = \left({\partial I \over \partial S}\right)^2 (... ... + \left({\partial I \over \partial F}\right)^2 (\Delta F)^2$$ (18.7)

(Only the first letter is used for abbreviations.)

Computing the partial derivatives we get

$$(\Delta I)^2 = {(F - D)^2(\Delta S)^2 + (S - F)^2(\Delta D)^2 + (S - D)^2(\Delta F)^2 \over (F - D)^4}$$ (18.8)

A small error in $\Delta I$ is obtained if $\Delta S$, $\Delta D$ and $\Delta F$ are kept small. This is achieved by averaging Dark, Flat and Science frames. $\Delta I$ is further reduced if S=F, then Equation (B.8) simplifies to

$$(\Delta I)^2 = {(\Delta S)^2 + (\Delta F)^2 \over (F - D)^2}$$ (18.9)

This equation holds only at levels near the sky-background and is relevant for detection of low-brightness emission. In practice however it is difficult to get a similar exposure level for the FLAT_FRM and SCIE_FRM since the flats are usually measured inside the Dome. From this point of view it is desirable to measure the empty sky (adjacent to the object) just before or after the object observations.