Standard Deviation vs Focus/Angle plots

• Normalised into per pixel number per exposure time and replotted graphs of vs focus distance/camera angle.
• Converted from units of pixel number into mm using dimensions of CCD: 765 x 510, 6.9mm x 4.6mm
• Standard Deviation vs Focus Distance:

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

• Standard Deviation vs Camera Angle:

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

Fitting the spectral line

Gaussian Fit

First Gaussian fit was fitted to the speactral line, this was done using the gaussian equation

• GaussianFit.png:
  

This shows a value of

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

• GaussianBox.png:
  

This gave a value of as

.

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,

• CircleHist.png:
  

This has 30 bins with 100000 entries. This gave a distribution of a uniform circle, which look roughly semicircular therefore a semicircular distribution was fitted, where

• CircleHistFit.png:
  

This gave a of

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.

• GaussianSemicircle.png:
  

This gave a of

The fit parameters were

Parameters	Value
Gaussian Amplitude, amp
Gaussian and Semicircle Mean,
Gaussian
Semicircle radius, r
Semicircle Amplitude, A
Background, b

Ommiting Hot Pixels

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 x-axis:

• VerticalBackDiff.png:
  

And also summed on to the y-axis:

• HorizontalBackDiff.png:
  

By choosing the hot pixels as values greater than one above the mean and that occurred in more than one frame, the hot pixels positions could be determined.

For the data summed onto the x-axis 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 y-axis 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 x-axis projection:

• VerticalBack.png:
  

and for the y-axis projection:

• HorizontalBack.png:
  

In both of these plots the intensity of the background can be seen to rise towards one side, this is due to the electronics in that corner of the CCD, by taking a bias frame of 0s exposure this can be accounted for.

-- AshleaKemp - 08 Nov 2015