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Entry  Sat Jun 6 14:07:30 2020, Jon, Update, BHD, Stock-Part Mode-Matching Telescope Option ASpathStock.pdfLOpathStock.pdf
    Reply  Mon Jun 8 11:50:02 2020, Hang, Update, BHD, Astigmatism and scattering plots 6x
       Reply  Mon Jun 8 12:49:07 2020, Koji, Update, BHD, Astigmatism and scattering plots 
          Reply  Mon Jun 8 17:40:22 2020, Jon, Update, BHD, Astigmatism and scattering plots LOpathStock2.pdf
             Reply  Mon Jun 8 21:45:47 2020, Jon, Update, BHD, Astigmatism and scattering plots 
                Reply  Thu Jun 11 09:37:38 2020, Jon, Update, BHD, Conclusions on Mode-Matching Telescopes 
Message ID: 15380     Entry time: Mon Jun 8 11:50:02 2020     In reply to: 15379     Reply to this: 15381
Author: Hang 
Type: Update 
Category: BHD 
Subject: Astigmatism and scattering plots 

We consider the astigmatism effects of the stock options. The conclusions are:

1. For the AS path, the stock should work fine for the phase-one of BHD, if we could tolerate a few percent MM loss. The window for length adjustment to achieve >99% MM for both s and t is only 1 mm for 1% RoC error (compared to ~ 1 cm in the customized case). 

2. The LO path seemed tricky. As LO3 & LO4 are both significantly curved (RoC<=0.5 m), the non-zero angle of incidence makes the astigmatism quite sever. For the t-plane the nominal MM can be 0.98, yet for the s-plane, the nominal MM is only 0.72. We could move things around to achieve a MM ~ 0.85, which is probably fine for the phase-one implementation but not long term. 


Attachments 1-3 are for the AS path; 4-6 are for the LO path. 

1 & 4. Marginalized MM distribution for the AS/LO paths. Here we assumed 5 mm positional error and 1% fractional RoC error. Due to the astigmatism, the nominal s-plane MM is only 0.72 for the LO path. 

2 & 5. Scattering plots for the AS/LO paths. We color coded the points as the following: pink: MM>0.99; olive: 0.98<MM<=0.99; grey: MM<=0.98. For the AS path, MM is mostly sensitive to the AS1 RoC and can be adjusted by changing AS1-AS3 distance. For the LO path, the LO3 RoC and LO3-LO4 distance are most critical for the MM. 

3 & 6. Assuming +- 1% AS1 (LO3) fractional RoC error, how much can we compensate for it using AS1-AS3 (LO3-LO4) distance. For the AS path, there exists a ~ 1 mm window where the MM for s and t can simultaneously > 99%. For the LO path, the best we can do is to make s and t both ~ 85%. 



For the initial phase of BHD testing, we recently discussed whether the mode-matching telescopes could be built with 100% stock optics. This would allow the optical system to be assembled more quickly and cheaply at a stage when having ultra-low loss and scattering is less important. I've looked into this possibility and conclude that, yes, we do have a good stock optics option. It in fact achieves comprable performance to our optimized custom-curvature design [ELOG 15357]. I think it is certainly sufficient for the initial phase of BHD testing.


It turns out our usual suppliers (e.g., CVI, Edmunds) do not have enough stock options to meet our requirements. This is for two reasons:

  • For sufficient LO1-LO2 (AS1-AS4) Gouy phase separation, we require a very particular ROC range for LO1 (AS1) of 5-6 m (2-3 m).
  • We also require a 2" diameter for the suspended optics, which is a larger size than most vendors stock for curved reflectors (for example, CVI has no stock 2" options).

However I found that Lambda Research Optics carries 1" and 2" super-polished mirror blanks in an impressive variety of stock curvatures. Even more, they're polished to comprable tolerances as I had specificied for the custom low-scatter optics [DCC E2000296]: irregularity < λ/10 PV, 10-5 scratch-dig, ROC tolerance ±0.5%. They can be coated in-house for 1064 nm to our specifications.

From modeling Lambda's stock curvature options, I find it still possible to achieve mode-matching of 99.9% for the AS beam and 98.6% for the LO beam, if the optics are allowed to move ±1" from their current positions. The sensitivity to the optic positions is slightly increased compared to the custom-curvature design (but by < 1.5x). I have not run the stock designs through Hang's full MC corner-plot analysis which also perturbs the ROCs [ELOG 15339]. However for the early BHD testing, the sensitivity is secondary to the goal of having a quick, cheap implementation.

Stock-Part Telescope Designs

The following tables show the best telescope designs using stock curvature options. It assumes the optics are free to move ±1" from their current positions. For comparison, the values from the custom-curvature design are also given in parentheses.

AS Path

The AS relay path is shown in Attachment 1:

  • AS1-AS4 Gouy phase separation: 71°
  • Mode-matching to OMC: 99.9%
Optic ROC (m) Distance from SRM AR (m)
AS1 2.00  (2.80) 0.727  (0.719)
AS2 Flat   (Flat) 1.260  (1.260)
AS3 0.20  (-2.00) 1.864  (1.866)
AS4 0.75  (0.60) 2.578  (2.582)

LO Path

The LO relay path is shown in Attachment 2:

  • LO1-LO2 Gouy phase separation: 67°
  • Mode-matching to OMC: 98.6%
Optic ROC (m) Distance from PR2 AR (m)
LO1 5.00  (6.00) 0.423  (0.403)
LO2 1000 (1000) 2.984  (2.984)
LO3 0.50  (0.75) 4.546  (4.596)
LO4 0.15  (-0.45) 4.912  (4.888)

Ordering Information

I've created a new tab in the BHD procurement spreadsheet ("Stock MM Optics Option") listing the part numbers for the above telescope designs, as well as their fabrication tolerances. The total cost is $2.8k + the cost of the coatings (I'm awaiting a quote from Lambda for the coatings). The good news is that all the curved substrates will receive the same HR/AR coatings, so I believe they can all be done in a single coating run.


Attachment 1: AS_MM_hist_stock.pdf  68 kB  Uploaded Mon Jun 8 13:06:56 2020  | Hide | Hide all
Attachment 2: AS_MM_t_scat_stock.pdf  721 kB  Uploaded Mon Jun 8 13:07:16 2020  | Hide | Hide all
Attachment 3: AS_MM_adj_stock.pdf  100 kB  Uploaded Mon Jun 8 13:08:08 2020  | Hide | Hide all
Attachment 4: LO_MM_hist_stock.pdf  68 kB  Uploaded Mon Jun 8 13:09:14 2020  | Hide | Hide all
Attachment 5: LO_MM_s_scat_stock.pdf  755 kB  Uploaded Mon Jun 8 13:09:58 2020  | Hide | Hide all
Attachment 6: LO_MM_adj_stock.pdf  100 kB  Uploaded Mon Jun 8 13:10:54 2020  | Hide | Hide all
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