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'
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
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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
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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.