Zeeman effect in helium using a home-made Fabry-Perot etalon

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thesmiths
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Zeeman effect in helium using a home-made Fabry-Perot etalon

Post by thesmiths »

We have finished a fairly extensive study of the Zeeman effect in helium using the same Fabry-Perot interferometer and magnet used in our earlier study of Zeeman splitting in neon. The following series of photos shows the thought process behind the current experiment. First we looked at the spectral lines of a helium discharge tube in the normal way with a transmission grating. The tube was driven by a neon transformer, which provides a fairly high current (total power was around 10W). Helium is a very good light source for these experiments as it is quite bright and the tube does not age (unlike hydrogen and mercury).
helium spectrum
helium spectrum
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The principle lines of helium are (in Angstroms): violet 4471, blue 4713, green 5016, yellow 5876, red 6678. We examined the effect of putting a dark-red (#29 Lumicon 2-inch) and violet (#47 Meade 1.25 inch) in the path of the helium emission. Both the red and violet lines are nicely separated. We revisit this fact later.
red filter
red filter
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violet filter
violet filter
4647.jpg (61.16 KiB) Viewed 403 times
The spectrometer used above employed a 600 line/mm grism from Paton Hawksley, a 10 micron slit from Thorlabs and an 80mm enlarging lens as a collimator. To use with the home-made etalon, we fabricated a very wide slit by cutting a 2.4mm slit into a piece of thin black cardboard. In front of the cardboard slit we put a 100mm f4 bellows lens to act as a collimator. A 600 line/mm transmission grating from Paton Hawksley (50mm square) was attached to the front of a 100mm camera lens (with another bellows that could be angled). The result when using helium light:
wide slit
wide slit
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Careful observation reveals the two green lines and the blue line overlap. We then put the Fabry-Perot etalon in between the collimating lens and the transmission diffraction grating. The setup then looks like the following, as viewed from the camera (the helium discharge tube is behind the black screens):
experimental setup
experimental setup
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The etalon creates interference fringes in the wide vertical spectral lines:
etalon wide slit
etalon wide slit
4813.jpg (707.99 KiB) Viewed 403 times
The bright yellow line of helium (first discovered in the solar spectrum) is composed of several very closely spaced lines of similar brightness; hence the interference pattern in the yellow line is not very sharp. Next the helium tube was put in the magnetic field created by the pair of neodymium magnets:
Zeeman no polariser
Zeeman no polariser
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The interference fringes split due to the Zeeman effect. This is most notable in the redline. Next a linear polariser was attached to the front of the camera lens parallel to the magnetic field:
parallel to field
parallel to field
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Finally, the polariser was rotated to be perpendicular to the magnetic field:
perpendicular to field
perpendicular to field
4851.jpg (937.42 KiB) Viewed 403 times
We then decided to examine the red line in more detail. We removed the diffraction grating from the optical path and added the #29 dark-red filter. We also increased the focal length of the camera lens from 100mm to 150mm. The visibility of the Zeeman splitting was enhanced. First with no polariser, all three lines are visible:
red filter no polariser
red filter no polariser
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With the polariser parallel to the magnetic field, only the central line is visible:
red filter parallel polariser
red filter parallel polariser
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With the polariser rotated perpendicular to the magnetic field, only the two magnetically split lines are visible:
red filter perpendicular polariser
red filter perpendicular polariser
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To conclude the experiment, we replaced the #29 dark-red filter with the #47 violet filter. First with the polariser parallel:
violet filter parallel polariser
violet filter parallel polariser
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Then with the polariser perpendicular:
violet filter perpendicular polariser
violet filter perpendicular polariser
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Although the fringes are not as sharp as with the red line, the "classical" Zeeman splitting seems to be the same. The green line also seems to be "classical" rather than "anomalous". The lack of sharpness of the violet line could be from the camera or etalon optics.
sodium doublet calibration
sodium doublet calibration
4960b.jpg (828.21 KiB) Viewed 403 times
Following the suggestion of Peter Zetner, I took a calibration image with our low-pressure sodium lamp (above), using the same conditions as the final images (150mm camera lens with the filters vs the earlier 100mm with the diffraction grating). Other parameters: original image size is 5184 x 3456 pixels (Canon 100D); all images were reduced in size by 50% in post-processing (i.e. 2592 x 1728).

Notes on collimation: the finesse of the etalon remains a little disappointing. While the collimating lens in this experiment provides a sharp image of the slit, the light from the helium tube is collimated the old fashioned way: the 7mm diameter discharge tube is visible through a similarly sized hole and placed approximately 200mm away from the slit (i.e. f29). Using a lens in between did not seem to help (in fact seemed to make it worse). So perhaps the relatively low finesse is due the etalon itself; more work needed here.

Homework problem: assuming the magnetic field strength is 9450 gauss (my best first principles guess), what is the electron charge to mass ratio derived from the splitting of the red and violet helium spectral lines?


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

Post by thesmiths »

Here is a video of the helium red line through the #29 filter. It is a slightly different setup that maximises brightness in order to make a video so the lines are not quite as sharp as the setup above. You can see the interference fringes change from single to double as the polarising filter is rotated.


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

Post by marktownley »

The results you are achieving are very impressive!


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

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One improvement we wanted to make in our spectroscopy was to try using a monochrome camera. So we attached a 135mm f5.6 enlarger lens to a ASI 174MM monochrome camera (normally used for solar and planetary imaging) using some tube extensions adapters and a Pentax M42 helical focuser. The ASI Studio deep sky imaging software turned out to be fairly good for image capture for this experiment. The GIF below shows the red and infrared lines: from the left in Angstroms: 6678 (normal Zeeman effect), 7065 (Paschen-Back Zeeman effect), 7281 (normal Zeeman effect). The GIF is composed of first an image with no polariser; then with the polariser parallel to the magnetic field; then finally with the polariser perpendicular to the field.
helium red Zeeman spectrum
helium red Zeeman spectrum
20210306-helium-red-3.gif (3 MiB) Viewed 326 times
With the Canon 100D, it was not possible to see the wavelengths longer than 668nm line due to the built-in IR cut-off filter. I would have to say, though, that having no colour makes it much easier to get "lost" in the spectrum of lines. The ASI 174MM is also not really the best choice of camera for this since there is considerable "amp glow" with longer exposures. There are many better monochrome cameras to use but this was what was at hand. Also, the high frame rate functionality of this camera turned out to be very useful because it allowed for easier tuning of the etalon and positioning of the transmission grating.


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

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To conclude our study of the Zeeman effect in helium, we fine tuned the etalon a bit by bringing the mirrors slightly closer together. This reduced the free spectral range, or in other words gives the split lines a bit more room before they repeat. We also increased the magnetic field slightly by reducing the gap between the pair of magnets. The following GIF shows the Zeeman splitting with the polarisation filter at 45 degrees (equivalent to no filter), zero degrees and 90 degrees with respect to the magnetic field. Colour has some advantages vs monochrome in terms of immediately recognising the lines, although the resolution is not as good.
helium Zeeman
helium Zeeman
5447-48-49.gif (3.68 MiB) Viewed 263 times


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

Post by marktownley »

Way cool! I think spectroscopy could well be a retirement hobby for me. Not enough time for solar at the moment let alone anything else! :D


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

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marktownley wrote: Sat Mar 20, 2021 10:33 am Way cool! I think spectroscopy could well be a retirement hobby for me. Not enough time for solar at the moment let alone anything else! :D
To Mark: the great thing about spectroscopy is that it uses a lot of the same hardware and skill set but not so dependent on the weather!


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

Post by p_zetner »

This is an interesting set of experiments and I thought I would have a go at some analysis, especially of the He 7065 angstrom red line which I thought would be challenging but relatively straightforward. I was right and wrong! The theoretical problem turned out to be quite challenging and not so straightforward but reminded me of happy days doing similar things as a graduate student, four decades ago (Yikes!) so I had fun tackling it.

The He red line comprises a triplet (in zero field) of closely spaced spectral lines (wavelengths shown in angstroms) from the upper n=3, triplet S level to the lower n=2, triplet P, J=0,1,2 levels as shown in the diagram.

fig1 triplet levels
He triplet levels.png
He triplet levels.png (210.66 KiB) Viewed 197 times

In the presence of a magnetic field, the energy degeneracy of the magnetic sublevels is lifted and up to 19 transitions with differing wavelengths can appear. These are numbered in the diagram above with the numbering corresponding to that of Ovsiannikov and Tchaplyguine in the reference "The Paschen–Back effect in helium spectra revisited" V.D. Ovsiannikov and E.V. Tchaplyguine, Can. J. Phys.80: 1383–1389 (2002). I used this reference as a guide to solve the Zeeman splitting problem for the 7065 angstrom line.

Both the wavelengths and intensities of these 19 lines vary with magnetic field strength. These are the quantities I calculated to generate synthetic spectra with which to compare to the interferograms. The varying wavelengths arise because of the magnetic sublevel energy level shifts induced by the magnetic field. Here is a plot of my calculation of the n=1, triplet P, J=0,1,2 sublevel energies as a function of field.

fig2 zeeman triplet p levels
triplet P eigenergies.png
triplet P eigenergies.png (114.2 KiB) Viewed 197 times
The upper triplet S sublevel energies shift as well but in a simple (linear) way: E = E0 + 2MB where M is the magnetic sublevel number (-1,0,+1) E0 is the zero field energy and B is the magnetic field. Consequently, since the wavelength of any of the given 19 transitions is determined by the energy difference between the upper and lower level, the transition wavelengths vary in a somewhat complicated way with magnetic field strength. Here is a calculated spectrum for a small field (25 milliTesla) resolved into pi and sigma components. The pi spectral lines correspond to energy level transitions in which the upper and lower magnetic number are the same while, in sigma lines, the upper and lower magnetic numbers differ by one. In experiments where the light is observed in a direction perpendicular to the field such as those described in this thread, the pi spectrum is observed for polarizer parallel to the magnetic field while the sigma spectrum is observed with polarizer perpendicular to the field. In the figure, the pi components (red) are shown to be negative going but this done for graphical purposes in order to easily distinguish them from the sigma components (blue).

fig3 25mT spectrum
B0025mT plot2.png
B0025mT plot2.png (92.49 KiB) Viewed 197 times
If the magnetic field were shrunk to zero, we would see the lines present in the figure “collapse” to three lines centred at frequencies of zero, 29.617 and 31.908 GHz respectively. These transition frequencies are measured with respect to the zero field, triplet S to triplet P (J=0) transition which therefore defines the zero on the frequency scale. In the first figure (above) the absolute wavelengths of these lines are given as 7065.7086, 7065.2153 and 7065.1771 angstroms.

Here are calculated spectra which include many of the 19 lines for four different values of the magnetic field strength. These spectra are centred around the triplet P, J=1,2 levels in order to zoom in on a smaller frequency span.

fig4 four fields
four fields spectra.png
four fields spectra.png (156.29 KiB) Viewed 197 times
The synthetic spectra were generated using Lorentzian lineshapes of 0.05 GHz. This linewidth is much narrower than that achieved in the experiments described in this thread but the complexity of the spectra is obvious to see at this resolution. You can also see that there is quite the variation of line intensities with field strength. The calculation of these is more complex than the transition frequencies and is quite physics intensive so I won’t describe it here.

For an idea of what to expect from the experimental data, I used Lorentzian lineshapes of 8 GHz (0.13 angstroms) and a field strength of 850 milliTesla to be somewhat close to the experimental parameters. Here is the result:

fig5 850 mT
B850mT_plot0.png
B850mT_plot0.png (113.99 KiB) Viewed 197 times
The frequency span of 60 GHz corresponds to a wavelength span of 1.0 angstroms.

The comparison of this result with experiment proved to be a little difficult. Here are the interferograms I analyzed.

fig6 interferograms
DSmith - 03Mar2021 - interferograms.png
DSmith - 03Mar2021 - interferograms.png (1.19 MiB) Viewed 197 times
The first problem I encountered was that the mercury calibration spectrum had different image dimensions than the helium interferograms. Consequently, the calibration procedure I described earlier didn’t work.
viewtopic.php?f=8&t=30741
Secondly, the analysis of these helium interferograms gave a rather peculiar result. Here are intensity plots of the unpolarised, pi and sigma interference patterns.

fig7 interferogram plots
He7065 interferograms mosaic.png
He7065 interferograms mosaic.png (69.23 KiB) Viewed 197 times
It seems quite unusual that the pi feature doesn’t fall between the two sigma features. I haven’t come across any theoretical indication that this should occur. So, at the moment, a sensible comparison between experiment and theory can’t be made for this He red transition.

All in all, a fun exercise though. Thanks, Douglas, for the motivation to look at this problem.

Cheers.
Peter


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Re: Zeeman effect in helium using a home-made Fabry-Perot etalon

Post by thesmiths »

To Peter: Thank you for the thorough analysis. The problem you mention at the end is, I suspect, due to the thermal instability of my Fabry-Perot. There can be, depending on circumstances, quite a bit of drift of the mirror spacing. Although the parallel and perpendicular measurements are taken only 10 seconds or so apart (the time required to manually rotate the filter), this is enough time to cause a positional shift. In this regard, the unpolarised image is a better one to analyse.


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