Calibration using emission lines

Identifying lines in one’s own data and associating them with published Angstrom values can be unexpectedly challenging.

I began by capturing spectra from a mercury gas discharge tube I purchased years ago. I installed it in the Calibrator and too spectra on my workbench. This is the setup I used:

Below is an example of one such spectrum of the glowing mercury tube.

I assumed I would be seeing emission lines for mercury only. For a long time, I struggled with trying to match between the lines I observed and the data published by the National Institute of Standards and Technology. Hard as I tried, I couldn’t get reliable results for the dispersion coefficients I needed to map wavelength to pixel number in my mercury (Hg) spectrum.

Then I came across Christian Buil’s Atlas of emission lines from gasses discharge tubes. The following annotated spectrum helped me identify lines up to the pair at 5769 and 5790 Angstroms, but I didn’t have any good resource for mercury lines for longer wavelengths to the right of that pair.

Finally it dawned on me: the lines above 5790 are not emission lines of mercury at all—they are lines of argon in the infrared region. Apparently it is common knowledge (among other people) that “Mercury vapor discharge tubes” contain argon as well. Sure enough, the infrared emission lines of argon perfectly matched lines I was seeing on the upper end of my spectrum.

But there was still one line I couldn’t identify: the bright line to the right of the pair in the middle of my gas tube spectrum. The following spectrum from the Atlas of Spectral Lamps was key to solving this mystery. The annotation “6562.852 (HI)”in the lower right corner indicates that this is the hydrogen alpha line! Not only does my mercury discharge tube have some argon in it, but it has hydrogen as well!

I can understand why there is argon in the tube (for the initial arc, to turn the liquid mercury into vapor), but I have no idea where the hydrogen comes from.

Here then is my final annotated spectrum that I can use for determining the dispersion coefficients of my spectrograph. Lines 1-10 are reasonably bright with well-separated lines. Line 11 can be used in spectra where it is bright enough to locate.

We now have a series of ten wavelength values; we need to determine a corresponding series of ten pixel positions. Then software can fit the points to an equation of order 3 and output polynomial coefficients. The equation will be of the form,

lambda = c0 + c1x + c2x2 +c3x3

where x is the pixel position from 0 to 2999 and lambda is the wavelength in Angstroms.

Coefficients c0, c1, c2 and c3, call “dispersion coefficients” can be determined using the configuration file CONF_COMPUTE_POLY (mode -4) described on p16 of Toolbox2.

First, we open our mercury/argon/hydrogen spectrum in the Image display tab of specINTI. then, while pressing the <alt> key, we click on each line for which we have a published wavelength value. The series appears in the box “X coord:” and can be copied and pasted into the fit_posx line in either one of the configuration files. We have, for example,

# Wavelengths of measured points
fit_wavelength: [4046.566, 4358.334, 5460.747, 5790.662, 6562.852, 
6965.431, 7067.218, 7383.980, 7723.761, 7948.180]

# Measured points' coordinates
fit_posx: [193, 411, 1164, 1386, 1895, 2157, 2224, 2427, 2645, 2787]

The configuration file, CONF_COMPUTE_POLY does a “Manual calculation of the dispersion law”. It takes a single spectral image file (I used a file of 13 stacked images). Pressing “Run” we get the following output in the console:

Polynomial fit
calib_coef: [-9.587175207753454e-10, 3.3610810724452596e-05, 1.4118365283007375, 3772.6974368777524]
O-C: [ 0.139 -0.239  0.645 -0.855  0.551  0.644 -1.103  0.482 -0.646  0.381]
Root Mean Square Error = 0.6286 A

The dispersion relation we are looking for is:

calib_coef: [-9.587175207753454e-10, 3.3610810724452596e-05, 1.4118365283007375, 3772.6974368777524]

with an RMS error is 0.6286 Angstrom.

With the dispersion relation in hand, we can now take the next step of calibrating the Alfirk profile by wavelength.

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