Wavelength Calibration

Wavelength calibration requires the identification of known lines in a spectrum of an arc to determine the transformation between pixel space and wavelength.

HRSModel

HRSModel is a class for producing synthetic HRS spectra. HRSModel is based on the PySpectrograph.Spectrograph class. It includes a simple model for both arms that is based on the instrument confirguration and the spectrograph equation. After adjusting for offsets in the fiber position relative to the CCD, the model can return an approximation for the transformation that is accurate to within a few pixels.

The residuals between the model and the actual solution though are well described by a quadratic equation. This quadratic does slowly vary accross the orders and is different between the two arms. Due to the change in the fiber position between the different resolutions, this quadratic can change between the different configurations as well.

For these reasons, the initial guess for the wavelength solution is based on HRSModel plus a quadratic correction. The correction can either be calculated manual or by automatically fitting a single row of an order.

Calibrating a single order

To calibrate a single order, the following steps are carried out:

1. Curvature due to the optical distortion is removed from the spectra and a square representation of the 2D spectra is created. Only integer shifts are applied to the data
2. A model of the spectrograph is created based on the order, camera, and xpos offset that are supplied. A small correction described by a quadratic equation is added to the transformation calculated from the model.
3. In each row of the data, peaks are extracted and matched with a line in the atlas of wavelengths that is provided. Due to the accuracy of the initial guess, lines are matched to within an angstrom and any line that might be blended is rejected.
4. Once the first set of peaks and lines are matched up, a new solution is calculated for the given row. Then the processes of matching lines and determining a wavelength solution is repeated using this new solution. The best result from each line is saved.
5. Using all of the matched lines from all lines, a ‘best’ solution is determined. Everything but the zeroth order parameter of the fit is fixed to a slowly varying value based on the overall solution to all lines. See fit_solution for more details.
6. Based on the best solution found, the process is repeated for each row but only determing the zeropoint.
7. Based on the solution found, a wavelength is assigned to each pixel

All of these steps are carried out by wavelength_calibrate_order. In the end, this task returns an HRSOrder object with wavelengths correspond to every pixel where a good solution was found. In addition, it also returns the x-position, wavelength, and solution for the initial row.

Calibrating an arc

For full automated calibration of an arc, wavelength_calibrate_arc can be used. In this task, it applies wavelength_calibrate_order to each of the orders in the frame. It uses pyhrs.HRSModel for the first guess but takes the quadratic correction from the solution of the nearest order. It starts with the initial order and the first row is also set by the user.