You may be content just to view your spectrum images directly to spot differences qualitatively but if you want to make quantitative measurements on them then you need to do some processing using some or all of the stages described below.  The quality of the resulting spectra can be judged from the comparison of Epsilon Aurigae spectra using this technique with a professional high resolution spectrum of the same object filtered to give 15A resolution.

There is nothing particularly special in the processing of the spectra obtained this way.  The techniques outlined here are equally applicable to spectra taken using other equipment.

Converting the raw images into a fully calibrated spectrum consists of two main steps, Image Calibration and Data Reduction

Image Calibration

(See also this pdf document for more details)

If we are using a DSLR camera we first need to discard the colour information. I use the procedure in IRIS  "Digital Photo", "Decode raw files" , "CR2 >> B+W" to convert all my images, darks and flats to fits files in one batch.

The next stage is to correct the fits images using darks. (See here as to why I no longer recommend a flat correction) This is the same process as performed on conventional images so will not be described in detail here. I  currently happen to use ImageTOOLSca to do the dark correction and then inspect and correct any remaining hot/cold pixels/cosmic ray hits close to or embedded in the spectrum using Teleauto but that is a mainly historic personal preference. Many other programs, IRIS for example will do all these jobs.

Next the individual frames need to be aligned and stacked (I happen to use K3CCDTools but again many other programs can be used, including IRIS)

Note unlike "pretty picture" astro-imaging, this is as far as the image manipulation goes. We are after scientific accuracy not aesthetic appearance so no non linear stretching, noise reduction, blurring, sharpening etc!

Next we need to make some corrections which are unique to spectrum images.  IRIS has some specific tools for this.

1. Remove any tilt in the spectrum to make it horizontal. The procedure in IRIS is "Spectro" ,"Tilt of a 2D spectra"

(Note because these spectra are so narrow there is significant risk that this step can introduce artifacts so hopefully you will not need to do it if your orientation was spot on. Note also that a tilted spectrum alters the wavelength calibration by cos(angle) so the same grating orientation and tilt correction should be used for both calibration and target star. 

2. If you are using an undriven mount any slant in the spectral lines should be corrected to make the lines square to the dispersion direction. The IRIS procedure is "Spectro", "Slant of a 2D spectra"

3. Subtract the sky background. This is an important step if any quantitative measurements are going to be made on the spectrum. The procedure in IRIS is "Spectro" "Remove sky to a 2D spectra"  You have to select two zones, one either side of the spectrum which represent the local background. If you use the median option, it will discount faint stars in the zones but you need to avoid including any of the wanted spectrum, bright stars or any spectra from other stars. (Increase the brightness in the image to spot these)  I suggest using zones about 30-60 pixels wide.  Too narrow zones can introduce noise into the spectrum.  Too wide zones and the accuracy of subtraction deteriorates.

Because of the short focal length of  the lens compared with a telescope, the star size is very small and therefore the individual spectra are too narrow to average out coverage of the different filter colour  pixels.  This can give artifacts which appear as sawtooth variations from pixel to pixel. These can be reduced by stacking a large number of spectrum images, moving the camera slightly between each exposure. Even so, some residual variation may be seen.  This can be reduced by slight filtering (in this case a spline filter was applied using Visual Spec) without significantly affecting the resolution.