QPD calibration
In a previous entry I described the setup used to build the QPD calibration curve and the method used to take measurements.
Here I show the results of our measurements and calculate the Volts/displacement ratio and the laser's beam radius.
X axis calibration
 In the following plot the X axis QPD calibration curve is shown and a fit in the linear region is made:
The errorbars on the plot where estimated by looking at the fluctuations of the voltage output.
The fit in the linear region with the function
returns:
where gives us the Volts/displacement ratio.
 The following plot shows the fit of the QPD calibration curve with the error function
The fit with the function:
returns:
The QPD's X output is a voltage given by:
where is a constant, while is the difference between the power on the right and left side of the QPD. Thus:
where is the total power transmitted by the beam, is the distance from the beam's center to the QPD center, is an offset and is the beam radius.
From the expression above and the fit's results we obtain:
Y axis calibration
The fit with the function:
returns
where gives us the Volts/displacement ratio.
The fit with the function:
returns:
The expression for the QPD's Y output is analogous to the one for the X axis:
From the fit results we obtain:
 Observation: Both and are compatible with the beam spot size we observed in laboratory.
The Volts/displacement ratios obtained here will be used to measure the resonant frequencies of the rhomboid motion.
