# Errors

• The root mean square was found for each pixel column across 10 frames, for each exposure.

• where
• By then plotting the rms against the average, we could see how the error varies with intensity.
• This shows a plot of rms against the average for exposure times from 0.05-1s, for all 10 frames.
• This was not what we expected so we then plotted the same plot at one exposure time of 1s, however changes which images we used.
• This plot shows all 10 images:
• This plot shows the first 5 images:
• This plot shows the second 10 images
• This may be due to the fact that we took the first five frames at a different time to the second five frames.
• Therefore we then plotted for all exposure times the second five frames:

# Mapping

• Initially this equation gave the best fit to the data:
• however there may be additional terms to the equaiton.
• Looking at the manual for the spectrometer it give the equation for the grating as:
• and also:
• and
• From which the dispersion can be derived as:
• where
• therefore

• so would vary with as ?
• If so then from the grating equation an extra term could be added similar to:
• However adding this term did not change the fit that much

# Vega Lines

• All of the lines that could be found in vega were fitted with the voigtian:

• Of which our best fit was at 3.5mm:

• The parameters for the Voigtian fit are shown below:

 Parameters 1.5mm 2.0mm 2.5mm1 2.5mm2 3.0mm 3.5mm 5.0mm 5.5mm Amplitude -1.96±0.44 -1.94±0.78 -1.82±40 -2.85±0.94 -2.12±29 -96.7±1102 -1.14±6000? -2.72±2410? Mean 102±3 101±1 105±5 105.4±0.6 100±4 96.5±0/64 81±1 85.7±0.56 Gaussian 5.19±2 0.36±1.5 0.31±3 1.57±2.1 0.22±98 0.098±1 0.195±2887? 0.16±32 Skew -(0.0092±0.0002) (-9.33±0.05)e-03 (-9.5±18)e-03 (-8.9±58)e-03 (-9.78±290)e-03 (10.3±0.8)e-03 -0.012±50 (1.16±0.09)e-02 Lorentzian width 16.5±1.4 19.1±0.8 19.6±1 22.1±0.4 20.2±0.6 21.1±0.2 8.17±0.74 22.2±0.7 Circle radius 4.00±5.27 5.16±1.55 2.86±37.3 2.61±0.6 3.81±2.16 2.47±5.6 3.97±3.01 4.00±1.6 2.21±0.01 2.202±0.001 2.11±0.01 3.00±0.001 2.37±0.003 3.698±0.003 3.55±0.002 2.95±323? (1.62±0.008)e-03 (1.37±0.01)e-03 (1.36±0.01)e-03 (7.05±0.09)e-04 (5.99±0.17)e-04 (8.7±0.2)e-04 (-1.29±0.03)e-03 (-7.41±0.2)e-04 (-2.58±2)e-07 (3.71±0.25)e-07 (1.85±0.18)e-06 (-4.6±0.2)e-06 (-2.13±0.22)e-06 (-9.08±0.43)e-06 (1.17±0.04)e-05 (1.56±0.7)e-06 Slice [390:600] [340:550] [60:270] [550:764] [280:480] [10:200] [600:764] [600:764] 809 835 896 750 773 621 626 599 201 201 201 205 191 181 155 155 Reduced 4.02 4.15 4.46 3.65 4.04 3.4 4.04 3.86