- 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 |

- 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:

- CadmiumScan1.png:

- 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 |

- 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

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

Topic revision: r5 - 18 Nov 2015 - JosephBayley

Copyright © 2008-2023 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

Ideas, requests, problems regarding RHUL Physics Department TWiki? Send feedback