FYI:

PRM actuation efficiency in L at DC measured by Oplev L is about 2e-9 m/cnt.
If what Nakano-kun mentioned is at DC, it is consistent.

PRM calibration procedure

- Lock PRY
- Measure the transfer functions from BS(PRM)_ISCINF to PRCL_IN1 (shown in first attached figure.)
- Take ratio of them (top left of second attached figure)

The ratio of PRM actuator efficiency to BS one is ~47.5, and the BS actuator efficiency is 6.28e-11/f^2 m/ct (klog14557). So the actuator efficiency of PRM is 2.983e-11/f^2.

This number is inconsistent with the number got in Febrary(13020). Did we change anything...?

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

1. Lock PRX(Y) with PRM
2. Excite the MCL and measure the transfer function from the MCE excitation signal to the PRM control signal.
3. 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.