The algorithm can also be written as:
This presentation of the optimal extraction is useful to see clearly the influence of the term 
. The idea is that when 
, the influence of this pixel is diminished in comparison of the pixel where 
.
To have a better understanding of the effect, we can go back to the weight presentation of the algorithm: 
, with 
.
Now, you can see that each pixel have a weight depending of the flux and the background. If the background is close to 0, 
(see previous paragraph). In the case of a pixel with a poor S/N ratio, some pixels are under-used ( 
), and the more important ones are over-used ( 
) . The role of the normalization factor ( 
) is thus to compensate so the flux is not changed.
Here is an example of the weights obtained for segment LIF 1a. For each wavelength, all the pixels are used, but the relative importance of each of them change:
