# 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

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

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,

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

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.

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:

And also summed on to the y-axis:

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:

and for the y-axis projection:

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

Topic attachments
I Attachment History Action Size Date Who Comment
png ANGLE.png r1 manage 37.0 K 10 Nov 2015 - 14:11 AshleaKemp sigma vs angle
png FOCUS.png r1 manage 36.7 K 10 Nov 2015 - 14:09 AshleaKemp sigma vs focus

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Topic revision: r8 - 02 Feb 2016 - AshleaKemp

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