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Message ID: 2356     Entry time: Fri Jun 7 17:42:06 2019
Author: anchal 
Type: DailyProgress 
Category: BEAT 
Subject: Three Corner Hat Method 

A wise man told me to use three corner hat method to extract individual frequency noise information of Marconi, Moku and the Wenzel crystal. I updated my mokuReadFreqNoise.py to support frequency noise calculation for two channels and their difference.

I'm perplexed to see the result actually and I'm not sure if this is what was expected. 

Measurement details:

I did two identical runs (I wasn't sure if I was seeing the truth from my first run) with the following settings:

  • Both Marconi and Moku are directly connected to Rb 10 MHz clock with equal length cables.
  • Wenzel Crystal 500-13905 oscillating at 24.4835 MHz was connected to input 1 of Moku.
  • Marconi with set to same frequency was connected to input 2 of Moku. Note that modulation feature was not on in this experiment so the expected noise is lower than CTN:2286 experiment.
  • With two channels recording, the acquisition rate is 15.625 kSa/s only.


  • In the first plot, I just plotted the frequency noise of input 1 (Wenzel), input 2 (Marconi) and (input 2 - input 1) using mokuReadFreqNoise.py. Although I have checked this code multiple times, I really want a new set of eyes to go through it and confirm it is calculating this correctly.
  • I assumed that the difference between two channels will have negligible frequency noise of Moku itself and is a good approximation of frequency noise between Wenzel and Marconi.
  • In the second plot, I used the 3 corner hat method to calculate individual frequency noise ASDs of the three instruments. Some points are missing as the sum of two contributing PSDs was lower than non-contributing PSD at some points.
  • In the third plot, to disregard the assumption I have made above, I used data from CTN:2286 experiment. Remember though that in this experiment, modulation was on at 500 Hz/V actuation slope.
  • In the fourth plot, I used 3 corner hat method again but with CTN:2286 experiment data.


  • Well clearly the 4th plot is useless. It is comparing two different versions of Marconi data, so it is essentially blurring out all data.
  • From 2nd plot, if this experiment was meaningful, even though Moku seems an order of magnitude more noisy than Marcon (which is just freely running), Moku's frequency noise is less than 2 mHz/rtHz upto 400Hz and if we ignore the bump at 500 Hz as some experimental artifact, is less than 3 mHz/rtHz upto 1 kHz. Expected coating brownian noise is between 4-10 mHz/rtHz from 100Hz-400Hz region.
  • Ideally, we would like an order of magnitude lower instrument noise than what we are trying to measure. So maybe Moku is not a good choice.
  • But I still am not sure if I should take strong inferences from this experiment because when I do low acquisition and use Moku's inbuilt frequency noise ASD plotter, I get results as attachment 3 which is also a check of how good my code computes the ASD.
  • This graph shows that the difference spectra is growing above 100 Hz contrary to previous results. This would mean that the frequency noise of moku is least above 100 Hz.  But that is not the case when I do a fast acquisition.
  • So overall, after today's efforts, I'm back to square one. I'm not sure if Moku should be used for frequency noise measurement
Attachment 1: MokuFreqAnalysis3CorHat_Run1.pdf  107 kB  Uploaded Fri Jun 7 18:58:19 2019  | Hide | Hide all
MokuFreqAnalysis3CorHat_Run1.pdf MokuFreqAnalysis3CorHat_Run1.pdf MokuFreqAnalysis3CorHat_Run1.pdf MokuFreqAnalysis3CorHat_Run1.pdf
Attachment 2: MokuFreqAnalysis3CorHat_Run2.pdf  116 kB  Uploaded Fri Jun 7 18:58:45 2019  | Hide | Hide all
MokuFreqAnalysis3CorHat_Run2.pdf MokuFreqAnalysis3CorHat_Run2.pdf MokuFreqAnalysis3CorHat_Run2.pdf MokuFreqAnalysis3CorHat_Run2.pdf
Attachment 3: MokuReadFreqNoiseCheck.pdf  54 kB  Uploaded Fri Jun 7 19:54:16 2019  | Hide | Hide all
Attachment 4: MokuFreqAnalysis3CorHat.zip  1.031 MB  Uploaded Fri Jun 7 19:57:29 2019
Attachment 5: IMG_20190606_192741.jpg  1.671 MB  Uploaded Sun Jun 16 18:12:54 2019  | Hide | Hide all
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