Using an interferometer to calibrate the frequency of the laser
Your absorption spectra will consist of photodiode voltage as a function of time as recorded by the digital scope. The vertical axis measures the intensity of the light passing through the vapor cell. As the piezo voltage varies linearly with time, and as the laser frequency varies with piezo voltage, we may convert the sweep times to changes in the frequency of the laser output. Ultimately what we want to measure are the energy differences between hyperfine levels, so all we need are frequency differences between features in the spectra. We can accomplish this by using a Michelson interferometer to measure the change in frequency of the laser as a function of time.
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| Figure 10: Layout of the Michelson interferometer. |
The geometry of the Michelson interferometer is shown in Fig. 10. The beams from the two arms of the interferometer will combine at the photodetector with varying degrees of constructive interference depending on their phase difference $\Delta\phi$. It can be shown that the phase difference depends on the difference in lengths of the two arms of the interferometer and the frequency of the light as
| $\phi_1 - \phi_2 = \Delta \phi = \dfrac{4\pi f}{c}(L_1 - L_2)$ | (7) |
where $f$ is the frequency of the light, $L_1$ and $L_2$ are the path lengths of the two arms of the interferometer, and $c$ is the speed of light. From this relation, it can be shown that the frequency spacing of the interference maxima at the output of the interferometer is
| $\Delta f = \dfrac{c}{2(L_1 - L_2)}$ | (8) |
Using Fig. 10 as a guide, set up the optical path for the interferometer. A good value for $L_1 - L_2$ is ~20 cm.
- Turn around the mirror mount which serves as a beam stop for the spectroscopy setup. Retro-reflect the beam back onto the beam splitter. You should now have a beam from each arm of the interferometer striking the face of the detector. Use the CCD camera to check the overlap of the beams on the face of the detector.
- Once you have the beams aligned on the photodetector watch the output on the scope while making very slight adjustments to one of the mirrors. When the alignment is correct, a sinusoidal waveform will appear on the scope.
- It is possible to see other sources of sinusoidal signals induced in the detector or from pickup in the cables. To check that the signal you see on the scope is truly the interference signal, use your hand to block one of the beams. If the signal does not vanish, you have not reached proper alignment.
Aligning a Michelson interferometer can be tedious. Be patient and you will succeed!