The purpose of this web page is to understand optimal extraction algorithm. I hope that after reading it, you will agree that it is worth using it for the data extraction. Hence, this web page will focus on the algorithm, and not on the reasons which lead us to it.
Here is the algorithm:
x and y are the coordinates of each pixel. x is corresponding to the wavelength.
In fact, behind this equation lay a simple idea: putting a weight on each pixels so the ones which are the most important prevail in case of low S/N ratio. Thus, we can rewrite the algorithm:
is the weight for each pixel, and 
is a normalization factor, allowing 
to be conservative when the weights are changing.
is the dataset coming from one aperture.
Example of dataset for segment LIF 1a:
correspond to the background.
is the probability for a photon with a given wavelength to come on that pixel. This knowledge is coming from a calibrated file named wgts*.fit. Note that 
.
Example of the calibrated file for segment LIF 1a:
and 
are the flux on a column x. is an estimation of the flux and is the flux obtained by optimal extraction. It means that before doing optimal extraction, you need to have an estimation of the flux, obtained here by using box extraction. Then, to increase the effectiveness, the algorithm is repeated several times, using the last flux results as an estimation for the new flux calculation. By default, optimal extraction is executed 3 times.