The following report summarizes the measurement and analysis of scans performed on 03-08-2026 in order to measure the arm Gouy phase. The aim is to verify that we recover the same Gouy phase as it was during the end of the last observation run. The Gouy phase is measured from the mode spacing measured from the frequency scans. The procedure to perform the slow FSR scan can be found on this page https://wiki.virgo-gw.eu/Commissioning/OptChar/Opt_Char_shift
Measurements:
At 14:54 UTC, ITF is locked using the state LOCKED_ARMS_BEATING
At 14:55 UTC, 1 iteration of scan is run as a test to verify that everything work
At 15:00 UTC, 15 iterations of scan, ended at 15:33 UTC
Results:
Tables 1 and 2 compare the mode spacing of the first four higher-order modes during the end O4 run and in the scan measured on 2026-08-03 in the west and north cavity, respectively.
Table 1 : North Cavity
| HOM 1 | HOM 2 | HOM 3 | HOM 4 | |
| 02 December 2025 | 0.1035±0.0003 | 0.2092±0.0003 | 0.3191±0.0002 | 0.4276±0.0002 |
| 03 August 2026 | 0.1057±0.0003 | 0.2113±0.0002 | 0.3215±0.0002 | 0.429±0.002 |
The measured mode spacing is very similar in each scan but slightly larger in the recent scans.
Table 2 : West Cavity
| HOM 1 | HOM 2 | HOM 3 | HOM 4 | |
| 02 December 2025 | 0.10246±0.0007 | 0.2076±0.0002 | 0.3201±0.0002 | 0.4304±0.0005 |
| 03 August 2026 | 0.103±0.001 | 0.2085±0.0008 | 0.3195±0.0003 | 0.4290±0.0003 |
The measured mode spacing is very similar in each scan, larger in the recent scan for the first two higher-order modes and smaller for HOM 3 and HOM 4. A supposition to explain the discrepancy between the different higher-order modes could be the change of the input test masses, resulting in a different transverse RoC asymmetry. The higher-order modes, presenting a larger area, experience a different portion of the mirror surface and as a result experience a different effective RoC. This hypothesis could explain why for HOM 1 and HOM 2 the mode spacing is larger during the scan performed on 03 August 2026 and smaller for HOM 3 and HOM 4.
To visualize what the observed difference represents in the scan, Figure 1 and Figure 2 show two scans plotted together. The blue curve represents the median scan performed on 03 August 2026 and the orange curve the old scan performed on 02 December 2025. The four plots below the full scan are a zoom on the first four higher order modes. These plots show that the difference is actually very small, suggesting that the Gouy phase is almost the same as in December.