PFA the results of beam profile analysis of transmitted laser from south cavity.

Description:

We are profiling the transmitted laser beam from the south cavity. All measurements of z-direction are from a reference line marked on the table. A razor blade mounted with a micrometer stand is used to profile the beam. The razor moves in the vertical direction and the whole mount is fixed using holes on the optical table so it moves in steps of 25.4 mm.

The beam is first split using a beam splitter and the other port is used as witness detector. The mean value of voltage from the photodetector over 4s time is normalized by the witness detector mean value to cancel out effects of laser intensity fluctuations. The peak to peak voltage from PD over 4 s is used to estimate the standard deviation of the signal. I assumed the error to be sinusoidal and estimated standard deviation as 1/sqrt(8) times the peak to peak voltage.

The profiles at each z point is then fitted with A*(0.5 - erf(norm_x)) + C where norm_x = (x - mu)*np.sqrt(2)/w . This gives estimates of beam radius w at each z position. This data is then fitted to w0*np.sqrt(1 + ((z-zc)*1064e-6/(np.pi*w0**2))**2) to estimate the beam wasit position and wasit size. I have also added the reduced chi-square values of the fits but I'm not sure how much it matters that our standard deviation is calculated in the manner as explained above.