The regularity check method

The second method is used to find cosmics, wherever they fall, and the defective pixels. For every 4 consecutive pixels, a second order polynomial is fitted on their fluxes, by the least square method . It gives 4 residuals for each pixel. The 4 residuals are then quadratically summed to obtain a global rms deviation for each pixel. If a pixel belongs to the continuum, it will have a very small rms deviation because of the easiness to fit the continuum with a second order polynomial. If the pixel belongs to a portion of the spectrum containing stellar lines it will have, most of the time, a larger but still modest rms deviation, because the shape of the lines is an analytic function, correctly fitted by a second order polynomial over 4 consecutive points. If a pixel is defective, or has been hit by a cosmic, its value is very different from those of its neighbours. This change is so sharp, that it can't be well fitted by a second order polynomial, and then the pixel will have a high residual.

Then the mean absolute value of the residuals and their standard deviation $\sigma_r$over the order are calculated. Two cases are distinguished. If the pixel flux is above the estimated continuum determined by the flux method (Sect. 3.3.1), the pixel is suspected to have been hit by a cosmic and is removed if its residual exceeds the mean by more than $4.6 \sigma_r$.
If the pixel flux is below the continuum, the pixel is a defective pixel candidate and is removed if its residual exceeds the mean by more than $11 \sigma_r$.This lattest high value of the rejection coefficient, comes from the fact, that in a portion containing few narrow lines the rms deviation gets close to those of segments containing defective pixels.
The elimination procedure is iterated until no more pixels are removed. As in the first method, removed pixels are flagged at -100.0.