Improving the fit to the line

• Initially a gaussian convoluted with a circular distribution was fitted to the spectral line, with the equations of:
• Gaussian:

• Circle:
• This gave a plot of

• Then for the background term a quadratic was used of the form:

• This gave a plot of:

After this a skewed Gaussian was fitted to the spectral line:

• This has the equation:

• where
This gave a plot of:

• Finally the quadratic background was fitted with the skewed gaussian:

• The parameters for each of the its is listed below:

 Parameters Conv Conv+Quadratic back Skew Guass Skew Gauss + Quadratic back Gauss Amp 364.6 ±(1.8e7) 347.8 ±(4.8e6) (3.4±160569)e05 (6.23±1090)e4 Mean 59.41±0.0003 33.4±0.001 777±1729 -8.52±14871 Gauss 1.998±0.001 1.785±0.002 75.1±3489 1.354±2369 Circle radius 4.15±0.004 4.516±0.002 Circle Amplitude 369.8±(1.8e7) 388.2±(5.4e6) background 624.7±0.2 612±0.3 1295±931461 0.9306±679 -5.69±2644 -0.108±19.1 0.31±1407 -0.005±9.4 681±0.41 63.2±920 -0.366±0.009 0.126±480 0.096±0.001 -0.036±0.006 191158 138587 131805 127977 70 70 70 70 per DOF 2730 1979 1882 1828

• it was noticed that towards the edges of the frame the distributions were becoming skewed, this was symmetric on both sides of the chip as the plots below show:

• This shows a skew on the left side of the chip:

• This shows a skew to the right of the chip:

• This shows the same peak in the center

# Halogen Lamp

• To look at the response of the camera a halogen lamp was observed across its spectrum, this gave a plot of:

# Are Poisson?

• Wanted to check whether actually followed Poisson distribution, as the errors seemed too small
• Took 20 frames of the same spectral line. Then studied the same point for each of the 20 frames to see how it fluctuated in each frame.
• Plotted against the pixel position #350 for each of the 20 frames, and calculated the and for the 20 points

 Mean Standard Deviation 138928.0 623.85

• For a Poisson distribution, the standard deviation is equal to the square root of the mean, . For 138928 photoelectrons this corresponds to = 372.73
• This indicates that is NOT in fact Poisson distributed, as we had been assuming before?

# Mapping wavelength with pixel position and micrometer position

• First to visualise the fit to the 3d plot the residuals of the points were plotted, this is done by:

• The error bar for was calculated by propagating the errors in the pixel position and the micrometer position.
• This was done using the equation:
• where ,micrometer position and , the position on the camera.
• The first equation that was fitted was:

• This gave a residual plot of:

• This process was then repeated with a quadratic fit with the equation:
• This gave a residual histogram of:
• This was then repeated one more time with a cubic term within the fit:
• This have a histogram of residuals as:
• this gave parameters for each of the fits as:

 Parameters Linear Squared Cubed 275 ± 4 276±9 314.9±23.6 0.1069±0.0057 0.118±0.028 0.098±0.092 55.26±0.66 53.76±3.57 26.1±15.1 -(2±3)e-05 (-1.3±2)e-04 0.11±0.34 5.53±3.22 0.0014±0.003 0.003±0.002 (1.17±1.62)e-07 -0.321±0.219 (-3±20)e-05 (-2.75±1.67)e-03 7305 7220 6772 72 72 72 per DOF 101 100 94

* Ask about errors that go into the least squares fit, as currently set to one?

# ---+ Standard Deviation vs Exposure time

• Took frames of one spectral line of Helium at different exposure times starting at 0.1s, increasing in 0.3s increments up to 3.0s.
• This was to see how the of the line changed with exposure time
• Did fit an exponential distribution, however this is redundant without any error bars, so we need to sort out our errors before fitting it.

# Vega

• The plot below shows vega at 3.5mm grating setting,
• 120s frame

-- JosephBayley - 22 Nov 2015

Topic attachments
I Attachment History Action Size Date Who Comment
png PoissonTest.png r1 manage 39.6 K 23 Nov 2015 - 21:56 AshleaKemp
png SigmaError_Vs_Exposure.png r1 manage 31.0 K 25 Nov 2015 - 07:55 AshleaKemp
Edit | Watch | Print version | History: r10 < r9 < r8 < r7 < r6 | Backlinks | Raw View | More topic actions

Physics WebpagesRHUL WebpagesCampus Connect • Royal Holloway, University of London, Egham, Surrey TW20 0EX; Tel/Fax +44 (0)1784 434455/437520

Topic revision: r10 - 01 Dec 2015 - JosephBayley

 Home Public Web P P P P P View Edit Account
Copyright © 2008-2024 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding RHUL Physics Department TWiki? Send feedback