- 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

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Topic revision: r5 - 18 Nov 2015 - JosephBayley

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