Plotted Hyperbole to above plot of functional form:
Curve_fit parameters:
Parameter  Values 
A  0.0253 ± 1.56 x 10^5 
B  4.19 ± 4.60 x 10^3 
C  9.03 ± 3.23 x 10^3 
Gave value = 668.1
Best focus distance = 19.9mm
Plotted sine function to above plot of functional form:
Curve_fit parameters:
Parameter  Value 
Amplitude, A  0.0152 ± 1.74 x 10^4 
Frequency, f  0.911 ± 6.46 x 10^3 
Phase, p  2.25 ± 1.22 x 10^2 
Background, back  0.0366 ± 1.78 x 10^4 
Gives value = 73.4
Best camera angle = 3.95mm
Gaussian Fit
First Gaussian fit was fitted to the speactral line, this was done using the gaussian equation
and the parameters were
Parameter  value 
Amplitude, A  
mean,  
width, 

background, b 
The Gaussian was then convoluted with a Box plot which has the equation
.
The fit parameters were
Parameter  Value 
Gaussian Amplitude, amp  48.28 
Gaussian mean  34.11 
Gaussian  1.203 
Box Ampitude, A  1424 
Box start, a  29 
Box end, b  35 
Background, B  2908 
All of the covariance matrix elements were infinity?
As the fibres in the spectrometer are circular part of the instrumental line width could be due to this. Therefore the histogram of a uniformly illuminated disk was plotted,
and fit parameters of
Parameters  Value 
Radius, r  
Mean  
Amplitude, A  
Background, b 
This semicircular distribution was then convoluted with the Gaussian distribution and fitted to the spectral line.
The fit parameters were
Parameters  Value 
Gaussian Amplitude, amp  
Gaussian and Semicircle Mean,  
Gaussian  
Semicircle radius, r  
Semicircle Amplitude, A  
Background, b 
To find the positions of the hot pixels the plot was 'differentiated' by subracting the data rolled by one position. i.e
The plot of this can be seen below for the background summed onto the xaxis:
For the data summed onto the xaxis the hot pixels were found to be:
Frame 1  Frame 2  Frame 3 
90  90  90 
179  
180  180  180 
222  222  222 
4077  407  407 
490  
497  497  497 
617  617  617 
Therefore the hot pixels are the values which fall in all of the frames.
For data summed onto the yaxis the hot pixels were found to be:
Frame 1  Frame 2  Frame 3 
24  
52  52  
61  
84  84  84 
90  90  
98  98  
132  
197  197  197 
216  216  216 
223  223  
273  273  273 
286  
312  312  312 
348  348  
354  354  354 
381  381  
417  417  
440  440 
Again the pixel numbers in all three frames correspond to pixel values.
By then setting the pixel value of these hot pixels to the average of the pixels surrounding it, the hot pixels were emmited. The pixels were average over the 10 surrounding pixels. This is shown for the xaxis projection:
 AshleaKemp  08 Nov 2015
I  Attachment  Action  Size  Date  Who  Comment 

png  ANGLE.png  manage  37.0 K  10 Nov 2015  14:11  AshleaKemp  sigma vs angle 
png  FOCUS.png  manage  36.7 K  10 Nov 2015  14:09  AshleaKemp  sigma vs focus 