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.
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:
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