Given the current status of the low round-trip arm losses at LHO even since the ITMY replacement in 2021, 
one might wonder what PRM transmission best impedance-matches our arm losses (in other words, what PRM transmission minimizes carrier reflection).

Background
Right now, the interferometer is overcoupled with a PRM trans of 3.1%, an ITM trans of 1.5%, and an ETM trans of ~5 ppm.
From alog 68401, we see that with 60W input, our current carrier reflection is 6.0% for a total of 6.4 mW incident on each LSC RFPD.
Of this, 90% of the light (5.8 mW) is carrier.
At the same time, the PRG measured was 49.4.
These numbers yield a round-trip loss estimate of around 66 or 67 ppm, respectively. 
These loss numbers assume a place-wave coupled-cavity model with no loss in the PRC (i.e. all losses are grouped into the round-trip loss).

We can lower the amount of light in reflection by changing the PRM transmission.
This will help us by reducing our REFL shot-noise limits, and allow us to increase the PRM to REFL PD path efficiency which right now is very low (0.0017, see alog 63510).
This could help us reduce the frequency noise level at Hanford, which is shot-noise limited between 10 and 4 kHz (refl spectra from alog 66718). 

We would also achieve more PRG (and more arm power) for the same amount of losses.  Of course, we can always substitute more input power to get more arm power, so this isn't a real priority.
What is important is when we increase the resonating arm power, the losses also tend to increase, so if we plan on further increasing the arm power we have to be more conservative with the PRM transmission choice than indicated here.

Measurements
One priority of choosing the PRM transmission is to ensure the IFO remains overcoupled throughout the locking sequence.
Our 2W locks are always a higher PRG (and lower loss) than at high power, so I've only considered high power locks that thermalized for at least a few hours.

I've looked through every long lock we've had from April 2023 to August 2022, and chose four example locks.
I looked at the REFL and PRG at the very beginning of high power, 
and after thermalization when both REFL and PRG had stabilized.
From these four numbers (initial REFL, thermalized REFL, initial PRG, thermalized PRG) I estimated the round-trip loss for the the interferometer.
These are represented by the markers in the below plots.

At present (brown), we start with a reflection ratio of around 4.5% which increases to 6%.
It's worth mentioning that before our recent ETM RH change (pink) we had much lower losses compared to now,
and therefore we ended up with quite a bit more reflected power after thermalization (up to almost 9%!)

I also plotted a 50 W lock from August 2022 (yellow), whose PRG and REFL seem to be telling us slightly different stories but says our highest loss is somewhere between 73 to 69 ppm.

All measurements tell us our loss gets lower with thermalization.

Models
The model is a simple plane-wave coupled cavity.
All I've done is change the transmission of the PRM from 3.1% to 2.3%, 2.2%, 2.1%, and 2.0% in PDF 2.

These models seem to suggest that, at current arm powers and losses, a 2.1% transmission PRM would be sufficient to maintain an overcoupled IFO, but 2.0% would not.

Since we want to be more conservative with higher arm powers on the horizon, 2.3% PRM transmission would be more than sufficient to maintain an overcoupled IFO while lowering the REFL ratio to around 2% from 9% in the lowest loss case,
while maintaining a 10 ppm buffer in case of higher losses at higher powers.

EDIT:
I fixed a small error in the August 4, 2022 REFL results (due to it having 50 W of input power, not 60 W, and therefore less RF power refl)
I also added the 80 W input power lock from April 5, 2023, whose REFL values may be untrustworthy but the PRG seems to indicate initial losses on the order of 80 ppm.