deletions | additions       diff --git a/Our_beam_had_a_power__.tex b/Our_beam_had_a_power__.tex  index 07eceb9..970a1d6 100644  --- a/Our_beam_had_a_power__.tex  +++ b/Our_beam_had_a_power__.tex 
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Our beam had a power of 1 mW. It passed through the rubidium cell, which contained both rubidium 85 and rubidium 87, and hit a photodiode. The photodiode was connected to an amplifier to convert the current output to a voltage with a gain of 1250. The output of the amplifier was monitored by an oscilloscope from which we could collect data. The Ti:Sapphire laser frequency was scanned by applying a linear ramp to the internal cavity of the laser. By changing the length of the cavity, the frequency of the laser is also changed. The cavity length, and thus the frequency of the laser, was changed using a triangle function with period T=10 s. The cavity length is controlled by a piezo electric (PZT). After analysis, the PZT appeared to have noticeable nonlinear effects, which results in a not perfectly linear frequency scan, as will be discussed below.   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 \textbf{reference}. ~.  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. 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.