# Mapping wavelength with the grating position

• In each of the frames the peaks mean position was noted along with its micrometer setting for the grating.
• These peaks were then matched to their actual wavelengths found from NIST.
• A plot of the three parameters was the made and a function for a plane was fitted with the equation. where is the setting of the micrometer for the grating, is the mean position of the spectral line and are constants.

• A plot of the wavelength against the grating position and the position on the CCD can be seen below:

• HeliumMap.png: • This process was repeated for the Cadmium, Low and High pressure Mercury lamps
• The values of the constants were found to be
 Parameter/Lamp Cadmium Helium Low Mercury High Mercury I 242±4 269±4 271±3 272±2 0.11±0.01 0.118±0.014 0.133±0.01 0.11±0.03 60.4±1.5 61.01±1.63 57.2±1.8 58.7±0.9 (-1.61±3.28)e-06 (-1.24±1.77)e-05 (-3.26±1.25)e-05 (-7.51±40.7)e-07 -0.51±0.16 -0.639±0.183 -0.015±0.28 -0.24±0.16 133 62643? 329 232

# Scan of peak across camera

• A peak was places at one side of the frame and then the grating position was changed so that the peak was scanned across the whole frame.
• The width of the spectral line was measured at each of these points and then plotted against the position on the camera.
• The plots below shows that the width of the line increases towards the edge of the frame.
• These plots show a scan of a peak in the helium and cadmium spectrum.

• HeliumScan1.png:  # Convolution with Fourier Transform

• To try to speed up the fitting of the convolution Fourier transfrms were used to convolute the functions instead. • By numerically calculating the Fourier transforms, multiplying them and then calculating the inverse Fourier transform, this function was then fitted to the data?
• For this the guess and fit parameters are
 Parameters Guess Fit Gauss Amplitude 23195 253 ±(4.0e05) mean 40 39.64 ±0.001 Gauss Sigma 3 1.28 ±0.001 Semicirc Radius 4 3.96 ±0.001 Semicirc Amplitude 23195 601 ±(9.5e05) background 400 455 ±0.14
• Where the method of convoling with and without Fourier transforms gave the same fit parameters.
• The fit gave • The times for each of the methods were
 Method Time/s Convolute 0.1675 Fourier 0.1585 difference 0.009

# Errors

• Our errors are still coming out very small which is increasing our value massively.
• Started by scaling the to per pixel per second so that: • the error is then: where .

• For example we had , , and • so • and • This seems a very small error?
• when plotted they are not visible  • The , which is very large however even the best fit points don't go through the error bars, as shown below:   -- JosephBayley - 17 Nov 2015

This topic: Public > UserList > StewartBoogert > StewartBoogertAstronomy > StewartBoogertMSciProjects > StewartBoogertSpectroscopy2015 > 20151117_MSciSpectrocopyLab
Topic revision: r6 - 03 Nov 2016 - JamesAngthopo

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