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Message ID: 152     Entry time: Mon May 30 20:11:27 2011
Author: Aidan 
Type: Laser 
Category: Hartmann sensor 
Subject: Hartmann sensor lever arm calibration 

 I ran through the procedure to calibrate the lever arm of the Hartmann sensor. The beam from a 632.8nm HeNe laser was expanded to approximately 12mm diameter and injected into a Michelson interferometer. The Hartmann sensor was placed at the output port of the Michelson.

  1. I tilted one of the mirrors of the interferometer to induce a prism between the two beams at the output. This created about 135 vertical fringes on the CCD.
  2. With the Hartmann plate removed, I recorded the interference pattern and took its 2D FFT. There was a peak in the Fourier transform about 134 pixels from the DC level. 
  3. This next part is questionable ...  I centroided the frequencies around the peak in the FFT to try to determine the spatial frequency of the fringes to better than the bandwidth of 1/1024 pixels^-1 (yes, they're strange units). This is, probably acceptable at improving the accuracy of the frequency measurement if it is known that the signal is a generated by a pure sine wave in the spatial domain - this is not an unreasonable assumption for the output of an interferometer. Anyway, the peak fluctuated around 133.9 units from DC by around +/- 0.1 units.
  4. The prism between the two beams is the measured spatial frequency (measured as 133.9 oscillations across the CCD) multiplied by the wavelength and divided by the width of the CCD (= 1024 x 12um). In other words, the prism is the ratio of the wavefront change across the CCD divided by the diameter of the CCD (= 6.895 +/- 0.005 mrad)
  5. Next, I inserted the Hartmann plate, blocked one of the beams and recorded the spot pattern. I then blocked the other beam and unblocked the first and recorded another spot pattern. 
  6. The mean displacement between the spot patterns was calculated. Due to a fairly noisy intensity distribution (the 2" mirrors were AR coated for 700-1000nm and hence there were some stray beams), the mean displacement was relatively noisy - about 5.60 pixels with a standard deviation of around 0.3 pixels and a standard error of around 0.01 pixels ( = 67.2 um)
  7. The lever arm is equal to the mean displacement of the spots divided by the prism. In this case, 9.75 +/- 0.02 mm
  8. I removed the Hartmann plate and confirmed that the FFT of the fringes from the IFO still had a peak at 133.9 +/- 0.1 units. It did.


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