Fitting the dispersion curve

Now you have in total three possibilities to perform your wavelength calibration:

mode IDENTIFY

You identify at least 2 arc lines in one slitlet with the command IDENTIFY/MOS. The command CALIBRATE/MOS then performs a first fit for the CCD row with the identified lines.

mode LINEAR

You know the central wavelength and the mean linear dispersion of your grism. These values are used as first fit of the first selected CCD row. As the program assumes that an offset of 0.0 means that the slitlet is in the center of the CCD you have to correct the central wavelength if you used the command OFFSET/MOS - because here the offset 0.0 only means that this is the `reference' slitlet.

mode FORS

This mode takes the identification of the grism you used from the header of the wavelength calibration frame and reads the central wavelength and the mean linar dispersion from the associated keyword. For example if you used grism01 the values are stored in . These linear values are again used for a first fit of the first selected CCD row.

The first fit is used to identify as many lines as possible in the corresponding CCD row. For the identified lines a polynomial fit of chosen order is performed (using Legendre or Chebyshev polynomials - the type being selected with the keyword ). The automatic line identification is repeated with this fit in order to identify additional lines to further improve the dispersion curve. This iteration is repeated until a stable solution is obtained or the maximum number of cycles () is reached.

According to the fit mode you choose if lines with residual greater than the tolerance () are thrown out or not. The fit modes available are:

CONSTANT

linelist: no bad lines are thrown out and the dispersion relation found for one row is used as estimate for the next. Thereby you get a dispersion curve that smoothly varies along the slit and takes into account small distortions.

VARIABLE

linelist: bad lines are thrown out, but the dispersion relation of the first fitted row is used as estimate for all following rows. Thereby you avoid the proliferation of errors that may occur with FIT.

FIT

all: bad lines are thrown out AND the dispersion relation found for one row is used as estimate for the next. This method is the most exact one for good natured data, but for low resolutions it will produce unstable solutions by throwing out more and more 'bad' lines as it proceeds through the slitlet.

The calibration itself is performed in the same way as in the LONG context: noch einfügen

The resulting dispersion coefficients are stored in table .tbl, together with the r.m.s. error of the fit, the slitlet and the y-coordinates (world and pixel coordinates). Also a plot option for the resulting residuals and various degrees of display are available.

After fitting all rows of the respective slitlet with fits of the chosen order the program performs at last a linear fit to get the central wavelength and the mean linear dispersion necessary to derive a starting wavelength for the next slitlet from its known offset. Rows where no fit could be achieved are stored in the table .tbl with the slit number -1.

Any selection of slitlets made in the table .tbl will be taken into account, but all selections of the table .tbl will be ignored. If you want those to be respected, too, redo the search for the wavelength calibration lines with the chosen selection in .tbl.

After the wavelength calibration you may rebin your frame two-dimensionally to constant wavelength steps with REBIN/MOS. If you prefer to avoid the resampling noise until you have finished the sky-subtraction and extraction of your objects you may rebin the extracted frames with REBIN1D/MOS. This command splits the quasi-2-dimensional frame that is produced by EXTRACT/MOS up into single, 1-dimensional frames. It then takes - separately for each extracted spectrum - a dispersion relation that has been averaged over the CCD rows from which the spectrum was extractedi, and rebins the spectrum to constant wavelength steps with this relation.

If you prefer to avoid the resampling noise at all you can appoint to each pixel of an extracted frame its correct wavelength (table option) without rebinning to constant wavelength steps with the command APPLY/MOS.