PRX and PRY length measurements
Principle
The frequency fluctuation df and the cavity length fluctuation has the relationship written as
df/FSR = dL/(lambda/2),
where FSR is the free spectral range of the cavity and lambda is the wavelength of the laser. From this equation, we can derive the cavity length L as
L = dL/df * f_laser,
where flaser is the laser frequency.
Measurement
- Lock PRX(Y) with PRM
- Excite the MCL and measure the transfer function from the MCE excitation signal to the PRM control signal.
- MCE (klog14562) and PRM (klog14564) are calibrated. The UGF is around 100 Hz, and the measurement range is around 10 Hz. So, dL can be approximated as dL ~ C_PRM * V_fb, where C_PRM is the calibration factor and V_fb is the feedback signal. df = C_MCE * Vexc. Therefore, we can obtain L/flaser = dL/df = (C_PRM * V_fb)/(C_MCE * Vexc)
Result
The attached figure shows L/flaser. From the figure, we can read L/flaser as 2.62(PRX) and 2.49(PRY). From those numbers, the calculated PRC length is 74.4 m (PRX) and 70.2 m (PRY). They are longer than the designed value by roughly 6m.
I also measured L/flaser by locking PRC with MCE and exciting PRM. The result is shown in the second attached figure. The result is a similar value.
Discussion
Low frequency and high frequency are not flat, although they should be flat. The reason for low frequency is because I assumed the suspension response as C/f^2. They have a resonance at around 1 Hz, so the calibration is not good for low frequency. For high frequency, this is because the OLG is not high enough. The UGF is around 80 Hz, and that effects appear above 10 Hz.
Anyway, the result is not consistent with the designed value. This means we are using the wrong calibration factor of MCE or PRM. MCE calibration is based on the laser PZT calibration, and PRM calibration is based on the BS calibration. They are the most likely to be the source of these problems.
