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Entry  Wed Mar 30 19:43:33 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching 
    Reply  Wed Mar 30 19:54:19 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching laser_output_non_circular.png
       Reply  Wed Mar 30 20:08:34 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching Beam_Matching_02c_Vertical.pngBeam_Matching_02c_Horizontal.png
          Reply  Wed Mar 30 20:14:17 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching 
             Reply  Wed Mar 30 20:31:30 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching 
                Reply  Wed Mar 30 20:50:43 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching After_Faraday.pngAfter_Faraday_and_Rotated_Lens.png
                   Reply  Wed Mar 30 21:21:15 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching Oven_Lens_Solution_66mm.pngMatching_Into_Green_Oven_zoomed_out.pngMatching_Into_Green_Oven_zoomed_in.png
                      Reply  Thu Mar 31 02:59:49 2011, Koji, Configuration, Green Locking, The wonderful world of mode-matching 
                         Reply  Thu Mar 31 14:10:00 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching P3310028.JPGP3310029.JPG
                         Reply  Thu Mar 31 15:23:14 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching Zoomed_out_fitting01.pngZoomed_in_fitting01.png
                            Reply  Mon Apr 4 14:20:32 2011, Bryan, Configuration, Green Locking, The wonderful world of mode-matching Waist_Fits_from_laser.pngWaist_Fits_Bench_Position.png
Message ID: 4477     Entry time: Thu Mar 31 15:23:14 2011     In reply to: 4473     Reply to this: 4485
Author: Bryan 
Type: Configuration 
Category: Green Locking 
Subject: The wonderful world of mode-matching 

Quote:

3. Zoomed-in plot for the SHG crystal show no astigmatism. However, the zoomed out plot shows some astigmatism.

How consistent are they? ==> Interested in seeing the fit including the zoomed out measurements.

Right. Fitting to the data. Zoomed out plots first. I used the general equation f(x) = w_o.*sqrt(1 + (((x-z_o)*1064e-9)./(pi*w_o.^2)).^2)+c for each fit which is basically just the Gaussian beam width parameter calculation but with an extra offset parameter 'c'

Vertical fit for zoomed out data:

Coefficients (with 95% confidence bounds):

       c =   7.542e-06  (5.161e-06, 9.923e-06)

       w_o =   3.831e-05  (3.797e-05, 3.866e-05)

       z_o =       1.045  (1.045, 1.046)

 

Goodness of fit:

  SSE: 1.236e-09

  R-square: 0.9994

 
Horizontal fit for zoomed out data:
 

Coefficients (with 95% confidence bounds):

       c =   1.083e-05  (9.701e-06, 1.195e-05)

       w_o =   4.523e-05  (4.5e-05, 4.546e-05)

       z_o =       1.046  (1.046, 1.046)

 

Goodness of fit:

  SSE: 2.884e-10

  R-square: 0.9998

  Adjusted R-square: 0.9998

  RMSE: 2.956e-06

 

Zoomed_out_fitting01.png

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

 

OK. Looking at the plots and residuals for this, the deviation of the fit around the waist position, and in fact all over, looks to be of the order 10um. A bit large but is it real? Both w_o values are a bit lower than the 50um we'd like, but… let's check using only the zoomed in data -  hopefully more consistent since it was all taken with the same power setting.

 

 

Vertical data fit using only the zoomed in data:

 

Coefficients (with 95% confidence bounds):

       c =   1.023e-05  (9.487e-06, 1.098e-05)

       w_o =   4.313e-05  (4.252e-05, 4.374e-05)

       z_o =       1.046  (1.046, 1.046)

 

Goodness of fit:

  SSE: 9.583e-11

  R-square: 0.997

 

Horizontal data fit using only the zoomed in data:

 

Coefficients (with 95% confidence bounds):

       c =   1.031e-05  (9.418e-06, 1.121e-05)

       w_o =    4.41e-05  (4.332e-05, 4.489e-05)

       z_o =       1.046  (1.046, 1.046)

 

Goodness of fit:

  SSE: 1.434e-10

  R-square: 0.9951

 

-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-

Zoomed_in_fitting01.png

 

The waists are both fairly similar this time 43.13um and 44.1um and the offsets are similar too  - residuals are only spread by about 4um this time.

 

I'm inclined to trust the zoomed in measurement more due to the fact that all the data was obtained under the same conditions, but either way, the fitted waist is a bit smaller than the 50um we'd like to see. Think it's worthwhile moving the 62.9mm lens back along the bench by about 3/4 -> 1cm to increase the waist size.

 

 

 

 

 

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