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Modifying the wavelength solution with 2dfdr

The 2dfdr data reduction system used for processing AAOmega data is designed to automatically process and wavelength calibrate spectroscopic data. This process is driven by keywords in the image header. This page discusses some of problems that can occur and the strategies available for improving the wavelength solution. Details of how to reduce data with 2dfdr can be found in the cookbook.


Problems with the automatic wavelength solution

It is critically important that the wavelength solution is derived accurately. With AAOmega data reduced by 2dfdr RMS solutions of ~0.1 of a pixel are the norm. However, thermal variations within the spectrograph can occasionally result in the initial guess solution, being too far from the true value. This can lead to a failure of the wavelength calibration. This page describes the simplest solutions to the problem.

This error most commonly occurs in the blue arm of the AAOmega system. The practical result of this error is twofold:
This process occurs on a month-to-month basis, rather than nightly since the thermal inertia of the AAOmega spectrograph room is high.

Example symptoms

The two most common wavelength solution problems are outlined below:
Poor arc line solution

If the initial estimate wavelength solution is not close enough to the true solution, the arc line-fitting routine can fail to find the correct stable solution, resulting in fuzzy regions of the reduced arc line frame as seen in Figure 2 below. This is usually best fixed by adjusting the GRATLPMM (grating lines-per-mm) FITS header keyword for the data, see Modifying the initial estimate solution below.

Note: Some fibres are marked as Type=U, and are deemed Unusable by 2dfdr. These are usually broken fibres. No new wavelength solution is fitted for these fibres and hence they will often show a sharp discontinuity in the arc solution. Since they contain no science data (even though they will sometimes contain arc line light) no information is lost here - this is illustrated in Figure 3.

Figure 1: A correct AAOmega arc solution is shown, with the arc lines perfectly vertical. Note that bad columns on the CCD have constant x(pixel) and so now exhibit an opposite spectral curvature in this reduced arc frame.

A correct AAOmega arc solution
Figure 2: For data with the incorrect value of the GRATLPMM header keyword parameter, the initial guess solution fails to find the correct solution for some fibres. Here we see a fuzzy region of the arc solution from the bottom right of the arc solution (redder wavelengths).

poor arc solution

Figure 3: An example Unusable (Type=U) fibre for which no wavelength solution has been derived. This fibre is not available to AAOmega, but has transmitted some arc light to the spectrograph and so shows a sharp discontinuity in the arc solution. This spectrum does not contain any information and so can be safely ignored.
Unused fibre example
Poor central wavelength and missing pixels.

Figure 4 below shows data which has been correctly reduced and wavelength calibrated, but which has been rebinned to a sub-optimal output solution. This rebinning has corrected for spectral curvature, and placed all spectra on a common wavelength solution, but in doing so it has rebinned the data to a wavelength solution which required a large number of filler or padding pixels to be added to all spectra at one end of the data. At the same time real spectral data have been clipped from the other end of the spectra. In this unfortunate example the valuable 3727 [OII] doublet has been clipped from these planetry nebula spectra.

The solution to the Final output wavelength problem is discussed below.

Figure 4: In this example, a poor choice of central wavelength by the data reduction software has resulted in a large number of blank padding pixels at the red end of the spectrum, and the important 3727 [OII] doublet has been clipped from the reduced spectra even though it is clearly visible at the blue end of the raw data frame for these Planetry Nebulae.

An example of poorly centred data

Final output wavelength solution

The 2dfdr software places all reduced data onto a common output wavelength solution, after correctly fitting and rebinning the observed solution for each fibre. While maximum signal-to-noise with minimum correlation of noise between adjacent pixels would be achieved by preserving the as observed wavelength solution for each fibre at all times, the utility of placing the data onto a common output solution, with a single rebinning step, is usually the better solution. That this solution is defined in advance, rather than on a frame-by-frame basis, means that repeated observations of the same target over multiple nights (or even multiple months) can be easily combined (although we note that 2dfdr correctly rebins data on different solutions if required). This definition of the wavelength solution in advance does have the side effect that if the true wavelength solution for an observation differs markedly from the predicted solution then valuable information may fall outside the output solution wavelength range and hence be lost. For example, with AAOmega in low resolution mode, this can result in the valuable 3727 [OII] doublet being clipped from the final output data even though it was successfully observed.

Fits Header Keywords

The AAOmega wavelength solution is controlled by the header keyword parameters outlined in the table below. If the wavelength calibration does not succeed, the user may need to manually intervene. The most common solution is to modify the initial guess parameters in the image headers to provide an improved initial solution. This modification can be achieved easily in a number of ways, e.g. in IRAF with the hedit task:

IRAF> hedit *.fits[0] KEYWORD VALUE add- update+ ver- show+

Header Keyword Meaning Typical blue data
low resolution value
GRATLPMM VPH grating lines per millimeter. The ruling separation of the virtual facets in the VPH grating. Small thermal expansions and contractions with seasonal variations in the temperature within the spectrograph cause small physical shifts in this value with time. 582
GRATANGL The grating angle. This is usually half of the camera angle, although not if the grating is to be used at a blaze different from the central wavelength. 8.0
CAMANGL The camera angle. This is typically twice the grating angle. 16.0
ORDER The VPH gratings for AAOmega are always used in first order 1

Modifying the initial estimate solution

In the absence of any other information from the user in the start up .idx file (see below) the 2dfdr system uses the initial wavelength solution estimate to determine the final output solution onto which each spectrum is re-binned. This solution is derived as follows:

CENWAVE = 1E7 * (sin(ALPHA) + sin(BETA))/(ORDER * LPMM)

ALPHA = Grating angle in radians
BETA = (Camera angle - Grating angle ) in radians

Grating angle is obtained from the header keyword GRATANGL or GRATANGR
Camera angle is obtained from the header keyword CAMANGL
ORDER is obtained from the header keyword ORDER, but is always 1 for AAOmega
LPMM is obtained from the header keyword GRATLPMM

If an alternate central wavelength is deemed more appropriate for the data, the user can calculate the modified values, usually small adjustments to the Angles and the Grating lines-per-mm, and update the header values accordingly. Small errors in the wavelength solution are typically fixed by small adjustments the the GRATLPMM parameter (over the range +/-3 to the value stored in the image header). This corresponds to small seasonal variations in the true ruling spacing of the grating due to thermal expansion.
Modifying the output solution within an .idx file

It is possible to modify the final output wavelength range via the 2dfdr .idx input file:

.idx file parameter Meaning Typical 580V blue values
DISTORTION Distortion coefficient 4.125E-9
DISTX X centre of distortion 1000
DISTY Y centre of distortion 2048.5
SKYSCRUNCH Wavelength calibrate from sky lines TRUE
SKYFITORDER Polynomial order for sky line fitting 1 (i.e. a small linear offset)

Sarah Brough sb@aao.gov.au