Two main steps are followed:

- pre-processing to convert raw images into one combined image with bias, dark and sky subtracted spectrum, using IRIS - no flat-field have been made during the observation sequences

- spectral calibration: wavelength and some flux normalization with a reference star, using Visual Spec

Another description of the spectral data reduction is available in a power-point presentation presented at the 8th astrophysical school of Oleron, CNRS: click here.

One the raw images of a 10 images sequence of HR Del, Cataclysmic variable. 120 sec individual exposure

One of the raw offset images

and the resulting offset once added

one of the raw dark image. The dark images are acquired at an exposure duration equal or close to the star images to optimize the thermal dark subtraction process.

and the resulting dark image once combined and offest substracted.

Combined sum of the sequence, after offset and dark removal and registered with the l_register command of IRIS. The registration requires the selection of an absorption (or emission in this case) line feature on one of image of the sequence. The computation shift the all set of images considering the intensity profile selected, searching the center of gravity of the line and computing the shift for every images. It then recompute each image of the sequence with the previoulsy computed shift. The next step is then to add all the images and normalized the sum to the max intensity to avoid saturation. 

An automatic IRIS panel can lead you through all the steps at once...

Another step is usually required to align the star spectrum with the x-axis of the image to then perform a correct binning when reducing to a spectral profile. Different geometric transformation are available in IRIS, depending of the geometric distorsion observed.

Tilt: to just rotate the spectrum of a predefined angle

Slant: to shift lines by lines the star spectrum to have straight lines

Smile: to eliminate the "smile" distorsion some times observed due to optical distorsion in the spectrograph.

In our case, only tilting correction was required.

The spectrum of the dark sky is superimposed on the star spectrum. To remove it, a zone is selected above and below the star spectrum and a column by column mean value of the sky zone is subtracted on all the image, including the star spectrum. Doing this removes the sky spectrum lines from the star spectrum. Several type of sky spectrum removal is available in IRIS, with different type of mean computing: single value, value per column, linear interpolation (l_sky3) to remove possible gradient as well.

Once all the previous processing have been applied, I usually crop the image to keep only the star spectrum surrounded by dark sky, with no other visible object spectra before saving it for later processing and binning into Visual Spec

To move from the image into a spectral profile, it is required to bin along the colum axis all the relevant intensity of the star spectrum.

Two options are possibles:

Automatic Binning

Visual spec applies a signal to noise criteria and pick only the lines which have an average intensity which maximize the signal to noise ratio of the mean profile.

Manual Binning

The user defines a zone around the spectrum, which includes all the star spectrum and almost no dark sky.

The choice beetween the two is quite tricky and it's more or less by trying the two that one can be decided. If the spectrum is not well focalized, showing some chromatism the manual method gives a better result.

The most used lines for linear calibration are the atmospheric line feature and one of Balmer line.
To improve the calibration process, after a first 2-lines calibration, other lines can be identified and then a non-linear calibration using all the identified lines and a polynomial interpolation.
Another more rapid way to achieve the calibration is to record the angstrom per pixel sampling value on one of the night object, and as this value does not change during the night, use this value and only one line to calibrate the other spectrum acquired during the night. Of course, this method provides a lower accuracy.

Final calibration in wavelength done, and spectrum cropped to show the relevant spectral zone.

The reference star is usually choosen not to close to the horizon (to minimize extinction effect) and of spectral type close to Vega like A0V. If the object spectrum is close to a solar type spectrum, as for comet of asteroids, it is better to pick a G-type star. Avoid I-III luminosity classes as emission lines can polluted the spectrum.

Reference star 26 Peg, of Spectral type A2V, with its theoretical spectral profile displayed.

Below, the resulting division of the raw profile of the reference star by its theoritical spectral profile. Artefacts are due to spectral lines which have to be removed in the next step.

A strong smoothing process is then applied to remove the star lines and only the overall continuum variation is kept as the response curve. This profile is saved as the night response curve to be used to correct all the spectra and restore the "theoritical" flux variation.

Smooting operation by setting points where no lines are and applying a spline smoothing function.

In orange, the resulting final overall continuum response curve from the 26 Peg reference star.

To perform an absolute flux calibration, the reference star shall have be picked from the Visual Spec response list (18 stars). Those 18 stars have their continuum calibrated in flux and by knowing the overall exposure time of the observations, the spectra can be corrected with this absolute response. In this case, the reference star shall be at the same elevation of the object studied or an extinction correction shall be also applied.

In green, the HR del spectrum, once the raw one in blue has been divided by the response of the above profile from the reference star 26 peg.