[Saito, Tanaka, Fujimoto]
Abstract
We performed a PRX length measurement using the beat signal between the main laser and the auxiliary laser in OMC REFL.
As a cross-check of the data analysis, I analyzed the data independently from Saito-kun. In this entry, I show my results.
Please refer to Saito-kun’s klog entry (klog #37185) for the details of the measurement.
From my analysis, the measured PRX length is consistent with the design value within the measurement uncertainty of 1.3 cm, and this is consistent with Saito-kun's result:
- L_PRX_design = 68.2560 m
- L_PRX_measured = 68.267(13) m
- Difference between measurement and design: (1.1±1.3) cm
Details for analysis
Design values for PRX
The design values for PRX are as follows:
- L_PRX_design = 68.2560 m
- FSR_PRX_design = 2.19609 MHz
Measured beat frequency
We measured the beat frequencies between the main laser and the auxiliary laser when the auxiliary laser was resonant in PRX at four different frequency regions: around -160 MHz, -140 MHz, +140 MHz, and +160 MHz.
For the +140 MHz and +160 MHz cases, we measured the frequency range where the maximum could not be clearly distinguished, and estimated the center values and error bars from that range.
For the -140 MHz and -160 MHz cases, due to time constraints, we did not perform this range measurement. Instead, we used the frequencies that seemed to correspond to the maxima as the measured points. For their error bars, we used the uncertainty obtained from the +140 MHz measurement, which was 0.064 MHz.
The results are summarized in the table below:
| Beat frequency where aux. resonate | FSR index |
| +162.403(40) MHz | 147 |
| +140.430(64) MHz | 137 |
| -140.619(64) MHz | 9 |
| -160.371(64) MHz | 0 |
Fitting results
I plotted the beat frequency as a function of the FSR index and fitted the data with a linear function, a*x+b, where x is the FSR index.
Fig. 1 shows the measured data points and the fitted line.
The fitting model and the obtained parameters are as follows:
- Model: a*x+b
- Results:
- a = 2.19575(40) MHz
- b = -160.376(47) MHz
Results for the FSR and PRX length
The fitted parameter (a) directly gives the FSR of PRX.
The PRX length calculated from this FSR is as follows:
- FSR_PRX_measured = 2.19575(40) MHz
- L_PRX_measured = 68.267(13) m
- L_PRX_design = 68.2560 m
- Difference between measurement and design:
L_PRX_measured - L_PRX_design = (1.1±1.3) cm
Therefore, within the measurement uncertainty of 1.3 cm, the measured PRX cavity length is consistent with the design value.