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Entry  Tue May 5 23:44:14 2020, gautam, Update, ASC, IMC WFS WFSmatrixComparison.pdfWFSheadNoise.pdf
    Reply  Thu May 7 09:43:21 2020, rana, Update, ASC, IMC WFS 
       Reply  Thu May 7 10:58:06 2020, gautam, Update, ASC, IMC WFS 
Message ID: 15318     Entry time: Tue May 5 23:44:14 2020     Reply to this: 15320
Author: gautam 
Type: Update 
Category: ASC 
Subject: IMC WFS 


I've been thinking about the IMC WFS. I want to repeat the sort of analysis done at LLO where a Finesse model was built and some inferences could be made about, for example, the Gouy phase separation b/w the sensors by comparing the Finesse sensing matrix to a measured sensing matrix. Taking the currently implemented output matrix as a "measurement" (since the IMC WFS stabilize the IMC transmission), I don't get any agreement between it and my Finesse model. Could be that the model needs tweaking, but there are several known issues with the WFS themselves (e.g. imbalanced segment gains).

Building the finesse model:

  • I pulled the WFS telescopes from Andres elogs/SURF report, which I think was the last time the WFS telescopes were modified.
  • The in-vacuum propagation distances were estimated from CAD diagrams.
  • According to my model, the Gouy phase separation between the two WFS heads is ~70 degrees, whereas Andres' a la mode simulations suggest more like 90 degrees. Presumably, some lengths/lenses are different between what I assume and what he used, but I continue the analysis anyway...
  • The appropriate power attenuations were placed in each path - one thing I noticed is that the BS that splits light between WFS1 and WFS2 is a 30/70 BS and not a 50/50, I don't see any reason why this should be (presumably it was to do with component availability). see below for Rana's comments.


  • The way the WFS servos are set up currently, the input matrix is diagonal while the output matrix encodes the sensing information.
  • In finesse, I measured the input matrix (i.e. response sensed in each sensor when an optic is dithered in angle). The length is kept resonant for the carrier (but not using a locking signal), which should be valid for small angular disturbances, which is the regime in which the error signals will be linear anyways.
  • Then I inverted the simulated sensing matrix so as to be able to compare with the CDS output matrix. Note that there is a relative gain scaling of 100 between the WFS paths and the MC2T QPD paths which I added to the simulation. I also normalized the columns of the matrix by the largest element in the column, in an attempt to account for the various other gains that are between the optical sensing and the digitizaiton (e.g. WFS demod boards, QPD transimpedance etc etc).
  • Attachment #1 shows the comparison between simulation and measurement. The two aren't even qualitatively similar, needs more thought...

Some notes about the WFS heads:

  • The transimpedance resistor is 1.5 kohms. With the gain stages, the transimpedance gain is nominally 37.5 kohms, and 3.75 kohms when the attenuation setting is engaged (as it is for 2/4 quadrants on each head).
  • Assuming a modulation depth of 0.1, the Johnson noise of the transimpedance resistor dominates (with the MAX4106 current noise a close second), and these heads cannot be shot noise limited when operating at 1 W input power (though of course the situation will change if we have 25 W input).
  • The heads are mounted at a ~45 deg angle, mixing PIT/YAW, but I assume we can just use the input matrix to rotate back to the natural PIT/YAW basis.

Update 215 pm 5/6: adding in some comments from Rana raised during the meeting:

  1. The transimpedance is actually done by the RLC network (L6 and C38 for CH 3), and not 1.5 kohms. It just coincidentally happens that the reactance is ~1.5 kohms at 29.5 MHz. Note that my LTspice simulation using ideal inductors and capacitors still predicts ~4pA/rtHz noise at 29.5 MHz, so the conclusion about shot noise remains valid I think... One option is to change the attenuation in this path and send more light onto the WFS heads.
    The transimpedance gain and noise are now in Attachment #2. I just tweaked the L values to get a peak at 29.5 MHz and a notch at twice that frequency. For this I assumed a photodiode capacitance of 225pF and the shown transimpedance gain has the voltage gain of the MAX4106 stages divided out. The current noise is input referred.
  2. The imbalanced power on WFS heads may have some motivation - it may be that the W/rad TF for one of the two modes we are trying to sense (beam plane tilt vs beam plane translation) is not equal, so we want more light on the head with weaker response.
  3. The 45 degree mounting of the heads is actually meant to decouple PIT and YAW.
Attachment 1: WFSmatrixComparison.pdf  26 kB  Uploaded Wed May 6 01:05:32 2020  | Hide | Hide all
Attachment 2: WFSheadNoise.pdf  168 kB  Uploaded Wed May 6 23:37:55 2020  | Hide | Hide all
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