Error propagation
• Assumed the photoelectrons distribution is a p.d.f therefore assumed error on the number of photoelectrons to be
• Plot showing the data and the gaussian fit for micrometer setting of 4.00mm and 6.00mm:
• Plot showing the error for Helium lamp at 6.0mm:

• The table shows the value, and the error on the location of the peak.
 micrometer setting (mm) width on guassian 1310296.532 764 2.44 847762.900 764 2.79
• Equation used for :
• is the observed value, is the expected values, is the error.
• Since the poisson distribution is assumed where is the gaussian mean.
• Therefore if it is a poisson distribution, the equation below is true.

• Compared and of Helium lamp for 3 micrometer setting:
 Micrometer setting (mm) 02.00 500.314 703.506 06.00 398.801 430.771 08.00 502.246 658.612

• Conclusion - not poisson distribution.
Calibration

• The equation for the propagation of the error is :

• Error on the lambda is given by

• On the left shows the fit and plots of data point with cadmium data, on the right it shows the same thing but the cadmium data has been excluded:
• The values of the parameters:
 Parameters Values(Without Cd data) Values (with Cd data) 0.102 9.98e-02 -4.95e-6 1.05e-05 52.8 53.3 -0.869 -8.69e-01 -2.80e-3 -2.65e-03 354 528 4.5 1e-4 4.13 1e-4 at 6.00mm 0.000411 0.3102 at 6.00mm 2 4 at 7.00mm 0.00321 0.0372 at 7.00mm 5 5

Fitting

• Lorentzian + background equation used:

• Lorentzian + (3rd order polynomial) background fits to the peaks in Vega, centered at 2.90mm and 6.00mm:

• Chi squared values for the Lorentzian + background fits to the centered Vega peaks, using both a second and third order polynomial:

 Micrometer Position (mm) Chi Squared 2nd Order Chi Squared 3rd Order (pixels) 0.80 1097009 1082766 37.0 1.60 1075022 1037859 125.1 2.30 2874083 2877388 32.1 2.90 1136163 926898 11.6 6.00 1152200 275787 10.0 7.00 1786081 1562246 11.3
• Needs errors to properly test how good of a fit
Convoluting

• Using a discrete convolution:

• Where the functions L and C are the Lorentzian + polynomial and circle functions respectively.
• Circle function used:

• Current convolution fit to the Vega peak centered at 6.00mm:
-- JamesAngthopo - 06 Feb 2017:
Topic attachments
I Attachment Action Size Date Who Comment
png Convolution_Vega0600_01.png manage 55.9 K 08 Feb 2017 - 10:15 WillBurrows Current convolution fit to the Vega peak centered at 6.00mm
png Vega_0290_LB.png manage 66.2 K 07 Feb 2017 - 21:55 WillBurrows Lorentzian + background fit to the peak in Vega, centered at 2.90mm
png Vega_0290_LB_zoomed.png manage 63.1 K 07 Feb 2017 - 21:56 WillBurrows Lorentzian + background fit to the peak in Vega, centered at 2.90mm
png Vega_0600_LB.png manage 67.4 K 07 Feb 2017 - 19:39 WillBurrows Lorentzian + background fit to the peak in Vega, centered at 6.00mm
png Vega_0600_LB_zoomed.png manage 62.7 K 07 Feb 2017 - 19:39 WillBurrows Lorentzian + background fit to the peak in Vega, centered at 6.00mm
png correctedplot.png manage 82.6 K 07 Feb 2017 - 23:44 JamesAngthopo This shows how the data point varies when cadmium data is excluded
png enchancedgaussplot.png manage 81.0 K 07 Feb 2017 - 23:02 JamesAngthopo Plot showing the error for Helium lamp at 6.0mm
png plotgaussfit.png manage 66.0 K 07 Feb 2017 - 22:39 JamesAngthopo Plot showing the data and the gaussian fit for micrometer setting of 4.00mm and 6.00mm
png quad0700.png manage 63.9 K 08 Feb 2017 - 10:53 JamesAngthopo plot for 7.00mm with cadmium data
png quadat0700.png manage 64.0 K 08 Feb 2017 - 00:24 JamesAngthopo Cadmium data included
png quaddata0600.png manage 80.9 K 08 Feb 2017 - 10:45 JamesAngthopo
png quaddata0700.png manage 80.2 K 08 Feb 2017 - 10:48 JamesAngthopo plot for 7.00mm without cadmium data
png quadonly.png manage 81.6 K 08 Feb 2017 - 10:35 JamesAngthopo
png quadonlydata.png manage 74.1 K 08 Feb 2017 - 00:15 JamesAngthopo This shows how the data point varies when cadmium data is excluded
png uncorrectedplot.png manage 99.2 K 07 Feb 2017 - 23:44 JamesAngthopo This shows how the data point varies when cadmium data is included

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Topic revision: r12 - 09 Feb 2017 - TomCrane

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