The most straight forward way of measuring the rotation angle caused by the change in magnetic field is to measure directly. We can see from Eq. \ref{eq:Diode_Response}, the voltage signal from the photodiode is a cosine wave with respect to angle. To create these waves, we found an angle at which light intensity is close to greatest when \(\vec{B_{1}}=0\textrm{T}\), and incrementing in \(10^{\circ}\) steps for a whole cycle of \(360^{\circ}\), the voltage output from the photodiode was read. This is then repeated with a magnetic field \(\vec{B_{2}}=33.3\textrm{T}\). Both of these waves are plotted on a single graph, shown in Fig. \ref{fig:MethodOneGraph} for easy comparison. Measurements can be taken at several other \(B\) values as well for more accurate \(v_{c}\).
By fitting the two waves on the graph, the shift in angle can be read directly. This corresponds to the difference in \(dB=\vec{B_{2}}-\vec{B_{1}}\). \(d\phi/dB\) and \(v_{c}\) can be then be calculated.
Using a modified Eq. \ref{eq:Light_Intensity}, we have \(V_{pd}\)as a function of \(\theta\), adapted for real experimental data:
\begin{equation} V_{\mathrm{pd}}(\phi)=V_{0}cos^{2}(\phi+\varphi)+C\\ \\ \end{equation}\(dV_{\mathrm{pd}}/d\phi\) was calculated to find the angle at which the \(dV_{\mathrm{pd}}\) is most sensitive to phase shift due to \(dB\). This will give us the same result as evaluating Eq. \ref{eq:sensitivity}, \(\phi=\pi/4\). This angle \(\phi\) is carried into our second method, where data is only collected at one fixed angle for a varying magnetic field.