Done for the moment. 

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1. First plot shows how the mode matching is bad now

I thought I've improved it, but it turns out that it's not much.

Green is forward going beam (going to the chamber) picked off right after Faraday, red is the beam coming back rejected by Faraday. The overlap is 0.63.

This doesn't mean that the matching to the arm is 0.63, it  could be better by about a factor of 4 i.e. 1-(1-0.63)/4 = 0.91, and it could also be much worse than 0.63, but we already know that the matching to the arm is somewhat less than 1750/(1750+250)=0.88.

It was worse when I started (overlap 0.58). But this doesn't necessarily mean that the matching to the arm is better, either.

z=0 corresponds to the steering mirror downstream of the BS that separates WFS and PDH beam.

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2. Second and third plot show the beam propagation in the far firled WFS path when the first lens (L6) is placed 3in farther than the nominal position.

Jax's Gouy telescope design (which is a copy of Bram's) is that the near field telescope doesn't do much to the Gouy phase (except that it blows up the beam size). In the far field path, one lens makes a reasonable waist that is not too small so that the Gouy phase doesn't change rapidly, and place a second lens to blow up the beam at a pre-calculated position near the waist.

Since the actual beam parameter shown in 2. above is so much different from the design, placing things at a nominal location  we need a path length of like 4 or 5m, which is not practical. I moved the first lens 3" downstream, and obtained the 3rd and 4th plot. Note that the agreement of the upstream and downstream measurement is very good. Measurements downstream of the first lens (shown as crosses) come on top of the lines that are the fit of the upstream measurements (circles) fit to Gaussian and propagated through the lens.

The waist size is about right, but I decided that it's difficult to fit this on table without totally ruining the area reserved for Hartman sensor.

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3. Final (for now) FF WFS path = WFSB. Moved the lens again by 3" (4th and 5th plot)

So it's 6" downstream of the nominal design. I haven't measured the downstream points this time, as the downstream measurements agreed with upstream quite well in the previous step.  L7 is placed 65" downstream of L5. WFSB position is not important at all as far as the beam size is reasonable.

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4. NF path=WFSA (6th and 7th plot)

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5. z coordinate and distances:

• Steering mirror downstream of PDH-WFS splitter: z=0
• WFSA-WFSB splitter: z=12.5
• WFSA (NF)  path:
  • L5 (f=0.5):  4" downstream of the splitter
  • L5-pico=3.5"
  • pico-L5a=2"
  • L5a-WFSA=5"
• WFSB (FF) path:
  • z(L6) = 25.5"
  • L6-L7=65" (folded once)
  • L7-pico=18.5"
  • pico-WFS2=13.5"