William P. Gammel edited Our_beam_had_a_power__.tex  over 8 years ago

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To monitor the frequency of our light, we used a Bristol Wavemeter. The wavemeter is a scanning Michelson interferometer. For information on how this wavemeter works, see \cite{BWM}. Our attempt to use the wavemeter as a frequency calibration ultimately failed. The intent was to calibrate the time axis of our transmission graph with a frequency. As mentioned above, the frequency should follow the same sawtooth function as the cavity length. Unfortunately the wavemeter was not stable enough across a single scan to do this, as can be seen in Figure~\ref{fig:FrequencyScan}. The Ti:Sapphire laser cavity also drifts in time making exactly repeatable scans not possible. This instability contributes an additional systematic error that was too time intensive to study for this experiment.   We scanned the laser over a frequency range for each of the electronic transitions, tuning the central frequency of our scan to make sure that the absorption was happening in the middle of each scan. The absorption curve for Doppler spectroscopy is a convolution between a Gaussian and a Lorentzian, but we fit to a Gaussian for the reasons described in our Introduction. An example of our data fitted to a Gaussian is shown in Figure~\ref{fig:NegativeGaussian}. We plot this transmission peak as a function of wavelength. \textbf{Initially transmission data is () directly from the oscilloscope and is plotted as voltage versus time. We can correlate the time from the oscilloscope scan to a () of the frequency scan at that point in time.}  It should be noted that this conversion comes from the linear fit extracted from the wavemeter data, see Figure~\ref{fig:badFreqScan}. While not exact, it is more intuitive to plot the transmission as a function of wavelength, keeping in mind that the independent variable has a small uncertainty.