Error bars
• A gaussian function fitted over the test lamp's data.
• Using the amended equation, error on the lamp's data found. This is due to Poisson error being an underestimate.
• Some examples of the values, and their corresponding error on the peak location.

 Lamp Micrometer setting (mm) Error in peak location value Error on Wavelength Cadmium 02.50 2.62E5 0.0961 55.17 55 0.1054 Cadmium 05.00 5.48E5 0.0840 55.12 55 0.0984 Cadmium 06.50 4.30E5 0.0765 55.10 55 0.0944 Helium 02.00 6.22E5 0.0878 55.31 55 0.1068 Helium 04.00 5.04E5 0.0791 55.08 55 0.1014
• To find the , its value was changed for every spectral line for different micormeter setting. This didn't make a lot of physical sense as did not depend on exposure time but it only depended on the intensity of individual peaks.
• plot of a spectral line for Helium lamp.:

• Another method used to find .
• Fitted Gaussian for different spectral lines and found which spectral line had the least value with just the poisson error. Lets call this spectral line .
• Then value was added to equation and changed until for .
• Then this value was used to determine the error on every peak location for that exposure time.
• This process was repeated for different exposure times.
• This shows the spectral line which had the best fit with a Gaussian curve for 0.1 s exposure time.:

• some examples of values and their corresponding error on peak location and value.
 lamp micrometer setting (mm) Exposure time (s) xrange Error on peak location Error on wavelength Cadmium 03.00 0.1 61 55.95 0.0175 6.40E04 0.1043 Cadmium 02.50 0.1 61 384.301 0.0203 6.40E4 0.10568 Cadmium 05.00 0.1 61 1061.95 0.0965 6.40E4 0.09866 Cadmium 06.50 0.1 61 274.833 0.0119 6.40E4 0.09446 Helium 02.00 1.0 61 1329.78 0.01011 7.28E4 0.107122 Helium 05.50 1.0 61 2.29957 0.12450 7.28E4 0.097027 High Mercury 04.00 1.0 81 76.62 0.0656 7.28E4 0.09995 High Mercury 07.00 10.0 91 2.94541 0.42922 3.22E5 0.09749

• Last method to find different .
• Know the background of vega to be third order polynomial.
• Used this to find , when , for different intensity.
• Made plot of against intensity.
• plot of intensity against :
• Used the fit to find different values for all the spectral lines which had different intensity.
• Plot of cadmium at 03.00mm showing the error bar derived from intens vs plot:
• some examples of values and their corresponding error on peak location and value.
 lamp micrometer setting (mm) Exposure time (s) xrange Error on peak location Intensity Error on wavelength Cadmium 03.00 0.1 61 21.7893 0.0281 1.02E5 7.203E6 0.104312632822 Cadmium 02.50 0.1 61 381.8706 0.0231 6.42E4 5.76E6 0.1057 Cadmium 05.00 0.1 61 32.5048 0.0695 4.57E5 1.47E7 0.0985 Cadmium 06.50 0.1 61 27.2785 0.0355 2.03E5 9.97E6 0.0944 Helium 02.00 1.0 61 37.6274 0.0601 4.33E5 1.43E7 0.1069 Helium 05.50 1.0 61 474.5811 0.0086 5.01E3 1.06E6 0.0973 High Mercury 04.00 1.0 81 7016.7390 0.0110 7.00E3 1.682E6 0.1015 High Mercury 07.00 10.0 91 4149.4471 0.0133 9.90E3 2.18E6 0.0930

G*C convolution

• G*C fit to middle Cd peak, 6mm
• Fixed: amp = 1E12, mu = 300, = 1

 Parameter r = 5 10 20 47 50 1000 3.68 3.01 2.98 2.11 2.81 2.98 r 1.50 1.5 1.49 3.95 2.5 1.5 amp 3.60E11 2.68e+11 2.62e+11 1.46e+11 2.2e+11 2.64e+11 mu 2.92E2 292 292 292 292 292 bg 2.77E5 345000 350000 357000 351000 350000 1.45E7 2.22e+06 2.08e+06 1.43e+06 2.02e+06 2.07e+06 ndf 195 195 195 195 195 195 / ndf 7.43E4 11400 10600 7320 10300 10600

• Fixed: amp = 1E12, mu = 300, r = 1
• Varying starting :

 Parameter = 2 5 10 40 100 2.98 2.11 2.98 2.82 2.98 r 1.44 3.95 1.09 2.5 1.4 amp 2.56E11 1.46e+11 2.04e+11 2.2e+11 2.5e+11 mu 2.92E2 292 292 292 292 bg 3.50E5 357000 350000 351000 350000 2.07E6 1.43e+06 2.07e+06 2.02e+06 2.07e+06 ndf 195 195 195 195 195 / ndf 1.06E4 7320 10600 10300 10600

• Fixed: amp = 1E12, mu = 300, = 5, r = 5
• Varying starting fit range:

 Parameter 50 100 150 200 2.98 2.82 -2.1 2.82 r 1.48 2.5 3.95 2.5 amp 6.55e+11 1.1e+11 1.09e+11 2.21e+11 mu 292 292 292 292 bg 349000 358000 361000 350000 2.01e+06 1.92e+06 1.37e+06 2.05e+06 ndf 45 95 145 195 / ndf 44800 20200 9470 10500

Normalised line shape

 Layered normalised profiles for all lines in all lamps Gaussian fit to the mean values of the normalised layered lines from all .fit files Layered normalised profiles for 'best' lines in all lamps Gaussian fit to the mean values of the normalised layered lines from 'best' .fit files

• Gaussian fit used:

• Gaussian fit values:
 Parameter All lamps Best lamps amp 6.01 6.58E-2 7.93 3.83E-2 6.85E-1 4.01E-2 6.30E-1 1.61E-2 3.54 4.16E-2 3.16 1.67E-2 b 3.09E1 1.52E-3 2.47E-2 9.34E-4 Normalised 5.61E-2 6.60E-2 96 96 Normalised per N 5.85E-4 6.87E-4

• used:
• No used
-- WillBurrows - 22 Feb 2017
Topic attachments
I Attachment Action Size Date Who Comment
png Bestfitcadmium.png manage 115.1 K 25 Feb 2017 - 12:45 JamesAngthopo This shows the spectral line which had the best fit with a Gaussian curve for 0.1 s exposure time.
png Caderror.png manage 108.5 K 28 Feb 2017 - 22:44 JamesAngthopo Plot of cadmium at 03.00mm showing the error bar derived from intens vs simga0 plot
png Heliumdata.png manage 78.0 K 23 Feb 2017 - 15:54 JamesAngthopo plot of a spectral line for Helium lamp.
png LS_all.png manage 77.2 K 28 Feb 2017 - 21:17 WillBurrows Layered normalised profiles for all lines in all lamps
png LS_all_mean_gauss.png manage 38.3 K 28 Feb 2017 - 21:20 WillBurrows Gaussian fit to the mean values of the normalised layered lines from all .fit files
png LS_best.png manage 36.7 K 28 Feb 2017 - 21:19 WillBurrows Layered normalised profiles for 'best' lines in all lamps
png LS_best_mean_gauss.png manage 35.5 K 28 Feb 2017 - 21:21 WillBurrows Gaussian fit to the mean values of the normalised layered lines from 'best' .fit files
png bgfitsigplot.png manage 221.5 K 01 Mar 2017 - 00:34 JamesAngthopo This plot shows the error obtained for when sigma0 was found by using vega background
png expsigplot.png manage 216.6 K 01 Mar 2017 - 00:33 JamesAngthopo This plot shows the error obtained for when sigma0 was found for different exposure time
png indsigplot.png manage 177.6 K 01 Mar 2017 - 00:33 JamesAngthopo This plot shows the error obtained for when sigma0 was found for individual spectral lines
png intvsig.png manage 71.0 K 01 Mar 2017 - 10:43 JamesAngthopo plot of intensity against sigma_0

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Topic revision: r9 - 01 Mar 2017 - JamesAngthopo

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