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4. Wavelength Calibration

Once one has extracted a 1-D spectrum of an emission-line exposure, one can use that to determine the wavelength calibration for spectra obtained with the same telescope pointing. To do so, one must identify the lines in the lamp spectrum. As an example of the process, I added two (2-D) lamp spectra that were obtained sequentially, with the telescope pointing at the zenith; an 8 second Hg lamp and a 2 minute Ne lamp. I then extracted a 1-D spectrum from a single row (row 125). I show the resulting spectrum in Figure 42. The vertical range has been clipped to show the weaker lines. Also, before generating the displayed spectrum, I flipped the data to produce a spectrum with positive dispersion (wavelength increasing with increasing pixel number).

  • Figure 42: Uncalibrated 1-D HgNe spectrum extracted from a single row of a combined 2-D spectral image, taken at low dispersion, through the narrow slit. The bright lines are clipped to show the fainter lines.

    One then compares the observed line list with a reference list of line wavelengths, and looks for matches that give self-consistent results. For this spectrum, there are a total of 31 line-matches with the HgNe line table. The line-matches are given in Table 8. These provide a set of measures to determine a relation between pixel number and wavelength for the spectrum. The simplest functional form for this is a linear fit. For such a fit, the slope is the dispersion (Angstroms per pixel). In general, there is enough flexure in the overall optical system that one can get substantially better results using higher-order fits. For this spectrum, I found that the residuals continued to improve up to a fifth-order fit. Figure 43 shows the wavelength-calibrated spectra using the linear and fifth order fits.

    Table 8 - HgNe Line Matching Example
    Pixel Wavelength Element
    182.50 5460.735 Hg
    253.95 5764.419 Ne
    258.85 5790.640 Hg
    273.55 5852.488 Ne
    280.40 5881.895 Ne
    294.95 5944.834 Ne
    314.70 6029.997 Ne
    325.00 6074.338 Ne
    330.00 6096.163 Ne
    340.90 6143.062 Ne
    345.45 6163.594 Ne
    358.05 6217.281 Ne
    369.50 6266.495 Ne
    378.40 6304.789 Ne
    385.25 6334.428 Ne
    396.65 6382.991 Ne
    400.90 6402.246 Ne
    425.10 6506.528 Ne
    431.20 6532.882 Ne
    446.55 6598.953 Ne
    473.95 6717.043 Ne
    523.20 6929.467 Ne
    547.05 7032.413 Ne
    579.80 7173.938 Ne
    596.50 7245.167 Ne
    609.15 7300.292 Hg
    641.40 7438.898 Ne
    759.10 7943.181 Ne
    793.35 8093.126 Hg
    859.25 8377.607 Ne
    937.80 8716.656 Hg

  • Figure 43: Calibrated 1-D HgNe spectra using a linear fit (top) and a fifth-order polynomial fit (bottom).

    Shown in the manner, the two fits look indistinguishable. That is very reassuring, as it tells us that flexure-induced nonlinearities in the wavelength calibration are small when the telescope is pointed at the zenith. Figure 44 two spectral regions, with both fits plotted for each region. The first is in the middle of the optical part of the spectrum (5700 to 6500 Angstroms). The match between the two fits is, again, very good. The second region is well into the near infrared (9000 to 11200 Angstroms). Here the linear and polynomial fits diverge. This is unsurprizing, as the longest wavelength line used for the fit is the 8717 Angstrom Ne line. It is also unlikely to be a problem, as the atmosphere will probably preclude any useful astronomical observations from our site at such long wavelengths.

  • Figure 44: Comparison of the linear fit (solid lines) with the fifth order polynomial fit (dashed lines) in the optical (top) and near infrared (bottom) parts of the spectrum.

    As an example of the details of finding a good polynomial fit, I show in Table 9 the results for the fits from first-order (linear) up to fifth-order. I note that the recovered dispersion of 4.3 Angstroms matches the specification from SBIG for the low-dispersion grating.

    Table 9 - HgNe Low-Dispersion Fit-Parameter Example
    Fit Std. Dev. Dispersion 2nd Order 3rd Order 4th Order 5th Order
    Angstroms Angs/pix
    0.437 4.31
    0.435 4.31 -2.23E-6
    0.438 4.31 -7.36E-6 -8.07E-9
    0.287 4.31 1.82E-5 1.25E-7 1.45E-10
    0.225 4.31 2.02E-5 1.08-8 6.10E-10 -9.07E-14

    I conducted similar tests on data taken with the high-dispersion grating on 22 July 2008. Here again, the quoted SBIG dispersion is recovered by our system. Table 10 shows the result of polynomial fits to an example high-dispersion HgNe lamp spectrum.

    Table 10 - HgNe High-Dispersion Fit-Parameter Example
    Fit Std. Dev. Dispersion 2nd Order 3rd Order 4th Order
    Angstroms Angs/pix
    2.693 1.04
    0.899 1.06 2.76-5
    0.218 1.06 2.31E-6 -4.67E-8
    0.080 1.06 -3.16E-5 2.40E-8 1.62E-10

    On 31 July 2008, I obtained a set of lamp spectra at both high and low dispersion, all with the telescope pointing to the zenith, using the wide slit. In Figure 45 I show an example of a summed HgNe spectrum from this set. It is a 1-D spectrum extracted with a 9-pixel aperture. The 2-D spectral image was rectified before extraction. The dispersion recovered for this spectrum is consistent with the nominal value (4.35 +/- 0.023 Angstroms). The fit deviation is much worse than for the narrow slit examples (~10 Angstroms). For high-dispersion spectra, the dispersion is also close to nominal, and the fit deviation is again much worse than for spectra obtained with the narrow slit (~2.5 Angstroms).

  • Figure 45: Calibrated 1-D HgNe spectrum extracted from a 9-pixel aperture of a combined 2-D spectral image, taken at low dispersion, through the wide slit.

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    Updated: 2010 July 19 [pbe]