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.
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.
Aligning a Michelson interferometer can be tedious. Be patient and you will succeed!