Wavelength Calibration and Distortion Correction

Wavelength calibration is divided into two steps. The first step is to identify comparison lines which have known wavelengths. From this step one obtains a relation between the pixel number along the dispersion direction and wavelength. This is called the dispersion solution. The second step is to convert the non-equal wavelength interval per pixel into `equal wavelength interval' per pixel and to redistribute the pixel value (flux) along the wavelength by appropriate interpolation. This is called the linearize.

Geometrical distortion correction along the spatial direction must also be accomplished. The slit images or monochromatic line images have curvature and inclination as shown in § 2.4. The distortions of images vary with wavelength or pixel number along the dispersion axis (Eq. 17). The relation between the pixel number and distortion can be obtained from the comparison lines. We will call it as the distortion solution. The slit images are then corrected to be a straight line perpendicular to the dispersion axis at each wavelength.

Both wavelength calibration and distortion correction can be accomplished simultaneously with the noao.twodspec.longslit package (Massey, Valdes, & Barnes, 1992; Valdes, 1986). The overall process is as follows:

1. To identify comparison lines along the dispersion direction at the center of the aperture.
2. To measure the distortions along spatial direction for the comparison lines.
3. To determine a two dimensional transformation function between the image coordinates and user coordinates obtained from the dispersion and distortion solutions.
4. To transform the original image into an image with uniform and orthogonal grid in the user coordinates.

Figure 40: A conceptional diagram of transformation from the image coordinates to the user coordinates during wavelength calibration and distortion correction. This diagram shows before and after the application of transformation of coordintes. Two images of a comparison line at the upper part show difference between before and after the distortion correction. Two aperture images at lower part show difference between before and after the wavelength calibration.