The quotients between the 3 normalized flat images were investigated. The quotient between set 1 and set 3 showed a gradient of 1%, and other variations of % or less. The quotient between set 2 and set 3 showed no gradient, and other variations of %.
The slit profile (cf. below) was taken out of nff2 and nff3, and the mean of the resulting images was used as the final flat field image.
Besides dome flats, also 6 sky flat images were obtained. These were reduced as outlined above, and then divided by the above slit profile image. First it was noted, that the position of the slit with respect to the CCD was not the same as for the dome flats - the slit profile image had to be shifted 1.5 pixels to match the 5 steep minima in it (probably caused by 5 grains of dust stuck on the slit)6.2. Second it was noted, that the slit profile extracted from the combined sky flat was not flat, despite that the images had been divided by the slit profile derived from the dome flats. This is caused by a difference in the way the slit is illuminated when the telescope is pointed at the illuminated dome, and when the telescope is pointed at the sky. The effect was modeled by fitting a linear function to the profile. After being normalized, the variation was from 0.985 to 1.01.
The final slit profile image was constructed as the product of the slit profile image derived from the dome flats, and the correction derived from the sky flats. The slit correction of the science images was performed by division with the slit profile image, shifted with an offset determined from the thorium lamp exposure taken just after the given science frame.
During the observations at night, after each science spectrum (of a galaxy or a star), a spectrum of the thorium (Th) calibration lamp was obtained, with the telescope and instrument at the same position. Using a table with wavelengths for the different Th lines (see below), the Th spectra were used to establish the mapping of wavelength in Å as function of position on the CCD, i.e. - this could be done, since the spectral lines are at constant , whereas they extend over the entire spatial direction. The galaxy spectra themselves were used to establish the mapping of spatial coordinate as function of position on the CCD (the S-distortion), i.e. s(x,y) - this could be done, since the center of the galaxy is at one spatial point, whereas the wavelength varies. The above two mappings were established using the tasks identify, reidentify, and fitcoords. Note, that there is one set of mappings for each science spectrum.
The spectra were then geometrically rectified, wavelength calibrated, and linearized in using the task transform. The output images were specified to have the wavelength range 4954.2-5612.5 Å, which was the common range for the night time Th exposures, and to have 1024 pixels in the wavelength direction. With these 3 figures specified, the output pixel interval is fixed as . Note, that the output spectra are still 2-dimensional.
The Th lamp had the advantage of having a high signal, therefore requirering only a short exposure time. It had the disadvantage of having blended lines, so that a line list based on atomic data could not be used. For the helium (He) and neon (Ne) lamps, the opposite was the case. To link Th with He+Ne, high signal-to-noise spectra of all 3 lamps were obtained during the daytime on two occasions. From the He+Ne spectrum the mapping was established using a line list based on atomic data. The rms scatter of this dispersion solution was 0.16 Å. This mapping was used to rectify and wavelength calibrate the two day time high S/N Th spectra. Wavelengths for all the blended Th lines were then determined (rms scatter 0.1-0.15 Å), and the resulting line list was used when identifying lines in the Th spectra obtained at night. The rms scatter of the dispersion solutions for the latter ranged from 0.07 Å to 0.44 Å, with a mean of 0.14 Å = 8.1 km/s 6.3.
The resolution was determined as from a Gaussian fit to the 5577 Å night sky line, in averages of 10 columns. The mean value (N=75) was = 1.358 Å = 79 km/s, with an rms scatter of 0.014 Å = 0.8 km/s. The position of the 5577 Å night sky line had an rms scatter of 0.11 Å = 6.6 km/s, which is a good measure of the accuracy of the wavelength calibration.
Properties of E and S0 Galaxies in the Clusters HydraI and Coma
Master's Thesis, University of Copenhagen, July 1997
Bo Milvang-Jensen (firstname.lastname@example.org)