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Hiroki Fujimoto - 2:53 Tuesday 07 July 2026 (37169) Print this report
Suggestion for a PRCL/SRCL length measurement method using the beat signal in OMC REFL

Here, I would like to propose a possible method for the PRCL/SRCL length measurement without sweeping the LO frequency.

The procedure is as follows:

0. Place an RFPD in OMC REFL.
1. Lock the main laser to SRY.
2. Lock the PLL of the auxiliary laser and the main laser.
3. Manually adjust the LO frequency and bring the auxiliary laser to resonance in SRY. In this step, the resonance can be checked using the beat signal observed with the RFPD in OMC REFL.
4. Measure the beat frequency in POS or OMC REFL and calculate the FSR by dividing it by an appropriate integer.

The SNR of this method can be roughly estimated as follows.
On the RFPD currently placed on the POS table, the powers and SNR are:

- Main laser: ~30/2 uW
- Auxiliary laser: ~1 mW
- SNR, defined as the ratio between the noise floor and the peak height: ~40 dB

On the other hand, the expected powers in OMC REFL are:

- Main laser: ~10 mW
- Auxiliary laser: ~20 uW

Therefore, if we reduce the main laser power incident on the RFPD placed in OMC REFL to 1 mW, the SNR will become worse than that on the POS table by a factor of about sqrt(10). However, the beat signal is still expected to be clearly visible.

In addition, in this measurement, we may be able to reduce the error in estimating the FSR by using a large LO frequency offset and bringing the auxiliary laser to a resonance far from the carrier resonance.

Comments to this report:
kentaro.komori - 23:19 Tuesday 07 July 2026 (37173) Print this report

[Fujimoto, Komori]

Abstract:

We discuss this estimation more concretely and quantitatively.
We should be able to measure the PRC and SRC lengths with a resolution of 0.1%, corresponding to an error of 6–7 cm.
Whether we can reach the 0.01% level, corresponding to 6–7 mm, will depend on how we determine the beat frequency.

Details:

The designed value of the SRY length, for instance, is 64.926 m, and the FSR of the SRY cavity is 2.3088 MHz.
On the other hand, using the method described in the original post, we should be able to measure the beat frequency with a resolution comparable to the cavity linewidth, which is approximately 0.2 MHz.
If we lock the beat frequency at 100 times the FSR, approximately 230 MHz, and measure it with a resolution of 0.2 MHz, the relative error of the measurement is 0.1%.
Therefore, the FSR can be estimated with the same relative error.

Let us simulate a realistic situation.
Suppose that we measure the beat frequency to be 221.3 ± 0.2 MHz.
The possible solutions are 95 × (2.330 ± 0.002) MHz and 96 × (2.305 ± 0.002) MHz, corresponding to absolute lengths of 65.03 ± 0.06 m and 64.33 ± 0.06 m, respectively.
Since the designed value is 64.926 m, and we can probably assume that the deviation from the designed value is less than 60 cm, we can select the solution of 65.03 ± 0.06 m.

However, an error of 6 cm is too large.
We have to measure the beat frequency with a relative error of 0.01% in order to estimate the absolute length with a resolution below 1 cm.

In addition to the method described in the original post, we propose another method to determine the beat frequency with the auxiliary laser frequency locked.
By dithering the auxiliary laser frequency at an audio frequency, for example 1 kHz and tuning the offset, we can minimize the peak height in the noise spectrum measured by the OMC REFL PD.
This method may be better than the original proposal because, generally speaking, minimizing a peak in a noise spectrum is easier than maximizing it.

The error of this method will be determined by RMS of the residual displacement of the SRC length.
If the RMS displacement with the SRC locked is less than 10% of the cavity linewidth, corresponding to 0.02 MHz, we should be able to achieve a relative error of 0.01% in the absolute length estimation.

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