J. Kissel

I attach updated figures from the SPI Conceptual Design Document (G2301177) slides on the the expected performance of the SPI w.r.t. the HAM2-HAM3 ISI system for the purposes of the Final Design Document (T2400145). These "final answer" figures are attached as .pngs, attached in L, P, Y order. For posterity I attach a .pdf which shows the entire plot series from the code (${SeiSVN}/seismic/Common/SPI/Scripts/plot_spi_motivation_20250314.m).

"The code" is an updated version of that from LHO:70306. Really, the only updates are to use the modern version of each of the SPI's DOF's noise budget, most recently documented in LHO:12273. Please revisit LHO:70306 if you'd like to understand the estimate of the ISI platforms; that has not changed at all, as we have not made substantial performance improvements to the HAM2 - HAM3 ISIs since (remember, O4 started in June 2023 and is on-going today.)

DISCUSSION
A brief bit of discussion about the changes in SPI noise budget:

SPI LONG: (See first .png, or page 20 of the .pdf plot series)
The modern modeled SPI longitudinal IFO performance is worse below 0.5 Hz, where the model now includes a real estimate of the frequency noise of its laser source -- which is now the PSL (with frequency noise from LHO:73976) rather than what was proposed in the conceptual design phase; an independent laser source with (0.01 * free-running NPRO frequency noise) = 1 [Hz/rtHz] * (100 [Hz] / f). For that same reason, it's better above 0.5 Hz, and the limit is instead the next noisiest source in the modern design -- ADC noise.

SPI PIT/YAW: (See second .png and third .png or pages 9 and 15 of the .pdf plot series)
The modern modeled SPI Pitch / Yaw optical lever performance is split into two curves:
    - one for spot size of 5 mm at the "reflector" ISI (i.e. the spot size at "ISIJ," which is HAM2 in this pathfinder instantiation, after having diverged over the ~16 [m] traverse and measured by "QPDA"), and
    - one for spot size of 1 mm at the "transceiver" ISI (i.e. the spot size at "ISIK," which is HAM3 in this pathfinder instantiation, after having been refocused to the original transmitted size by the ~16 [m] ROC reflector on HAM2 and measured by "QPDB" on the HAM3 transceiver.)

The CDD's model did not account for the spot size increase, so it was essentially the 1 mm spot size model. The changes in 1 mm spot size model from CDD to FDD are (1) an updated [whitened] ADC noise curve, showing an improvement below 0.3 Hz, and (2) the addition of an estimate for the shot noise on the QPD, which makes the >30 Hz performance slightly worse.

Both the 1 mm and 5 mm modern estimates are limited by ADC noise across the entire frequency band.

CONCLUSION
My interpretation of the plots -- regardless of these changes to each DOF of the expected SPI performance, comparing these against the estimate of the June 2023 performance of the HAM2-HAM3 ISI system, the conclusions from the conceptual design remain: we still expect the pathfinder to provide a range of "interesting" (YAW) to "delightful" (PIT, LONG) amount of improvement to the system; more-so in some regions and less in others. We look forward to making these plots with a real measured system rather than a model!!