THIS CALCULATION IS WRONG FOR THE OVERCOUPLED CAV.

Summary:

Mode-matching efficiency of EX green light into the arm cavity is ~70*%, as measured using the visibility. 

Details:

I wanted to get an estimate for the mode-matching of the EX green beam into the arm cavity. I did the following:

1. Locked arm cavities to IR. Ran dither alignment servos to maximize the transmission of IR on both arms. The X arm dither alignment servo needs some touching up, I can achieve higher TRX by hand than by running the dither.
2. Aligned green PZT mirrors so as to maximize GTRX. Achieved level as 0.47.
3. Went to EX table and tweaked the two available mode-matching lens positions on their translational stages. Saw a quadratic maximum of GTRX about some equilibrium position (where the lenses are now).
4. Measured average value of the green PDH reflection DC level whiel green TEM00 mode was locked. .
5. Misaligned ITMX macroscopically. Measured the average value of the green PDH reflection DC level again. .
6. Closed EX Green shutter. Measured the average value of the green PDH reflection DC level. .
7. Modulation depth of the EX PDH was determined to be 90mrad. Based on this, power in sideband is negligible compared to power in the carrier, so I didn't bother correcting for sideband power in reflection.
8. Mode-matching efficiency calculated as .

Comments:

This amount of mode-matching is rather disappointing - using a la mode, the calculated mode-matching efficiency is nearly 100%, but 70% is a far cry from this. The fact that I can't improve this number by either tweaking the steering or by moving the MM lenses around suggests that the estimate of the target arm mode is probably incorrect (the non-gaussianity of the input beam itself is not quantified yet, but I don't believe this input beam can account for 30% mismatch). For the Y-arm, the green REFL DC level is actually higher when locked than when ITMY is misaligned. WTF?? Only explanation I can think of is that the PD is saturated when green is unlocked - but why does the ADC saturate at ~3000cts and not 32000?

This data is almost certainly bogus as the AA box at 1X9 is powered by +/-5VDC and not +/-15VDC. I didn't check but I believe the situation is the same at the Y-end.

3000 cts is ~1V into the ADC. I am going to change the supply voltage to this box (which also reads in ETMX OSEMS) to +/-15V so that we can use the full range of the ADC.

gautam Apr 26 630pm: I re-did the measurement by directly monitoring the REFLDC on a scope, and the situation is not much better. I calculate a MM of 70% into the arm. This is sensitive to the lens positions - while I was working on the EX fiber coupling, I had bumped the lens mounted on a translational stage on the EX table lightly, and I had to move that lens around today in order to recover the GTRX level of 0.5 that I am used to seeing (with arm aligned to maximize IR transmission). So there is definitely room for optimization here.