Tags:
create new tag
view all tags

20130412 Horizontal Fitting

Horizontal laser-wire scans were often non-Gaussian and although it was known that they were not strictly Gaussian, they were in the past close enough that a Gaussian approximation worked and was only a few percent wrong in the fitted sigma. The obvious solution is to use the overlap integral, but for this, the vertical size needs to be known - catch 22. However, there is some solice in the knowledge that the vertical size is likely to be between 0.5 and 1.5 microns.

Using the horizontal scans from the quad scans, the overlap integral was used to fit each scan for a range of different vertical sigmas to see the effect this would have on the fitted horizontal sigma. This is shown in the figure below.

20130301_quad_scan_horizontal_oi_fitting_sigma.pdf
(click here to display this PDF file by itself)

and zoomed in a little...

20130301_quad_scan_horizontal_oi_fitting_sigma_zoom.pdf
(click here to display this PDF file by itself)

This shows that the likely uncertainty on the horizontal size given the knowledge of the vertical beam size is likely to be up to 11% (at the focus of the quad scan - where ~$\sigma_{x}$/x = 15/130 = 11% )

For these fits it's also possible to look at the reduced chi squared to see how well the model fits for these different parameters. This is shown in the figure below.

20130301_quad_scan_horizontal_oi_fitting.pdf
(click here to display this PDF file by itself)

These show varying results, but generally a lower reduced chi squared between vertical sigma = 0.5 -> 1.5um for most cases than at other vertical sizes. Again, these show greatest sensitivity at the middle of the quad scan - the focus. Whilst you would normally expect the horizontal beam size to vary only slightly and generally in a linear way, with the specific optics that were in place during this scan, the (single) quad scan seem to focus in both the horizontal and the vertical! This is again shown in the figure below.

horizontal_sigma.pdf
(click here to display this PDF file by itself)

and zoomed into the focus...

horizontal_sigma_zoom.pdf
(click here to display this PDF file by itself)

Whatever the reason for this - perhaps strong coupling? - it is clear from the data.

Knock on Effect on Vertical

So this will have a clear effect on the measured vertical size. Below are the two graphs of the different horizontal fit models for the -92A case in the quad scan (approximately at the focus) on the last quad scan on 20130301. The horizontal data file is 20130301_1138_lws.dat and the nonlinear vertical scan is 20130301_1147_lws.dat

20130301_1138_lws_xy_fit_plot6_sey1_0um_OI_fit.pdf
(click here to display this PDF file by itself)
20130301_1138_lws_xy_fit_plot7_gauss_fit.pdf
(click here to display this PDF file by itself)

This shows a considerably better fit to the horizontal with the Overlap integral fit. For the first fit, a vertical sigma of 1.0um was assumed.

  • sigma_ey = 1.0um -> sigma_ex = 135.66 +- 4.80 (overlap integral fit); reduced chi2 = 3.12
  • sigma_ey = NA. -> sigma_ex = 215.75 +- 5.13 (Gaussian fit); reduced chi2 = 10.94
(graphs shown above for these fits)

Propagating this to the horizontal, the vertical fits are:

  • sigma_ex = 216um -> sigma_ey = 0.62 +- 0.07um; reduced chi2 = 17.91
  • sigma_ex = 136um -> sigma_ey = 1.30 +- 0.05um; reduced chi2 = 4.34
20130301_1147_lws_xy_fit_plot5.pdf
(click here to display this PDF file by itself)
20130301_1147_lws_xy_fit_plot4.pdf
(click here to display this PDF file by itself)

The fit with the smaller horizontal sigma is a better fit both by eye and by the reduced chi2. The vertical size is consequently larger and is therefore different from the assumed vertical size in the horizontal fit. Putting this back into the horizontal fit yeilds:

  • sigma_ey = 1.3um -> sigma_ex = 131.12 +- 4.91um; reduced chi2 = 3.13
  • sigma_ex = 131.13um -> sigma_ey = 1.35 +- 0.05um; reduced chi2 = 4.1
20130301_1138_lws_xy_fit_plot8.pdf
(click here to display this PDF file by itself)
20130301_1147_lws_xy_fit_plot6.pdf
(click here to display this PDF file by itself)

Iterating again...

  • sigma_ey = 1.35um -> sigma_ex = 130.34 +- 4.93um; reduced chi2 = 3.14
  • sigma_ex = 130.34um -> sigma_ey = 1.36 +- 0.05um; reduced chi2 = 4.07
20130301_1138_lws_xy_fit_plot9.pdf
(click here to display this PDF file by itself)
20130301_1147_lws_xy_fit_plot7.pdf
(click here to display this PDF file by itself)

and again...

  • sigma_ey = 1.36um -> sigma_ex = 130.19 +- 4.93um; reduced chi2 = 3.14
  • sigma_ex = 130.19um -> sigma_ey = 1.36 +- 0.05um; reduced chi2 = 4.07
20130301_1138_lws_xy_fit_plot10.pdf
(click here to display this PDF file by itself)
20130301_1147_lws_xy_fit_plot8.pdf
(click here to display this PDF file by itself)

So no further improvement in reduced chi2 nor reduction in uncertainties (chi2 contour)

<--

Settings just to customise this page

-->
Topic attachments
I Attachment History Action Size Date Who Comment
PDFpdf 20130301_1138_lws_xy_fit_plot10.pdf r1 manage 27.0 K 16 Apr 2013 - 17:07 LaurieNevay  
PDFpdf 20130301_1138_lws_xy_fit_plot6_sey1_0um_OI_fit.pdf r1 manage 27.1 K 16 Apr 2013 - 17:02 LaurieNevay  
PDFpdf 20130301_1138_lws_xy_fit_plot7_gauss_fit.pdf r1 manage 26.8 K 16 Apr 2013 - 17:02 LaurieNevay  
PDFpdf 20130301_1138_lws_xy_fit_plot8.pdf r1 manage 27.0 K 16 Apr 2013 - 17:07 LaurieNevay  
PDFpdf 20130301_1138_lws_xy_fit_plot9.pdf r1 manage 27.0 K 16 Apr 2013 - 17:07 LaurieNevay  
PDFpdf 20130301_1147_lws_xy_fit_plot4.pdf r1 manage 28.6 K 16 Apr 2013 - 17:08 LaurieNevay  
PDFpdf 20130301_1147_lws_xy_fit_plot5.pdf r1 manage 28.6 K 16 Apr 2013 - 17:08 LaurieNevay  
PDFpdf 20130301_1147_lws_xy_fit_plot6.pdf r1 manage 28.6 K 16 Apr 2013 - 17:08 LaurieNevay  
PDFpdf 20130301_1147_lws_xy_fit_plot7.pdf r1 manage 28.6 K 16 Apr 2013 - 17:09 LaurieNevay  
PDFpdf 20130301_1147_lws_xy_fit_plot8.pdf r1 manage 28.6 K 16 Apr 2013 - 17:09 LaurieNevay  
PDFpdf 20130301_quad_scan_horizontal_oi_fitting.pdf r1 manage 27.3 K 13 Apr 2013 - 20:49 LaurieNevay  
PDFpdf 20130301_quad_scan_horizontal_oi_fitting_sigma.pdf r1 manage 25.2 K 13 Apr 2013 - 20:28 LaurieNevay  
PDFpdf 20130301_quad_scan_horizontal_oi_fitting_sigma_zoom.pdf r1 manage 19.4 K 13 Apr 2013 - 20:42 LaurieNevay  
PDFpdf horizontal_sigma.pdf r1 manage 20.9 K 13 Apr 2013 - 20:54 LaurieNevay  
PDFpdf horizontal_sigma_zoom.pdf r1 manage 20.3 K 13 Apr 2013 - 20:55 LaurieNevay  
Edit | Attach | Watch | Print version | History: r2 < r1 | Backlinks | Raw View | Raw edit | More topic actions

Physics WebpagesRHUL WebpagesCampus Connect • Royal Holloway, University of London, Egham, Surrey TW20 0EX; Tel/Fax +44 (0)1784 434455/437520

Topic revision: r2 - 16 Apr 2013 - LaurieNevay

 
This site is powered by the TWiki collaboration platform Powered by PerlCopyright © 2008-2021 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding RHUL Physics Department TWiki? Send feedback