Error propagation

  • Equation to convert from wavelength to pixels:
 \begin{equation} p=\frac{-b\pm\sqrt{(b)^2-4ac}}{2a} \end{equation}
  • $a=C_2$
  • $b=C_1-E_1(m-m_0)-2C_2p_0$
  • $c=\lambda(p,m)-C_0-D_2(m-m0)^2+D(m-m0)+C_1p_0+E_1p_0(m-m_0)-C_2p_0^2$.
Hot pixels

  • 1s dark frame projection:
    DarkFrame_1s_spectrum.png

  • Hot pixels found at [90, 222, 407, 490, 497, 617]

  • 1s dark frame after reducing hot pixels via a mean and a median:

DarkFrame_1s_mean.png

DarkFrame_1s_median.png

Sigma_0

  • Modelled additional sigma term as:
 \begin{equation} \sigma_0(t; A, B, C) = C_1 + C_2t + C_3t^2 \end{equation}

  • Sigma_0 as a function of exposure time, with a quadratic fit:
    sigma0_plot.png
 \begin{equation} Q(x; A, B, C) = Ax^2 + Bx + C \end{equation}

  • Fitted parameters:
Parameter A B C
Fitted Value -2.67E-02 3.24E01 -1.35E-02
Uncertainty 2.68E-05 8.63E-03 9.99E-03

Fitting

  • Cadmium fits:

Gaussian fit Convolution fit

G_Cd_0600_edges.png

GC_Cd_0600_edges.png

G_Cd_0600_peak.png

GC_Cd_0600_peak.png

  • Vega fits:

Lorentzian + BG fits Convolution

LBG_Vega_0600_180_edges.png

conv_LC_Vega_0600_180_edges.png

LBG_Vega_0600_180_peak.png

conv_LC_Vega_0600_180_peak.png

  • $\chi^2$ per DOF for each peak in Vega
Micrometer position (mm) L + BG (HP) L + BG (no HP) Convolution C * L + BG (no HP)
0.80 121.00 34.43 34.58
1.60 84.58 8.32 8.35
2.30 86.71 22.96 22. 19
2.90 81.17 3.47 3.49
6.00 82.75 3.96 3.99
7.00 77.40 2.10 2.11

-- WillBurrows - 21 Feb 2017

Topic attachments
I Attachment Action Size Date Who Comment
PNGpng DarkFrame_1s_mean.png manage 60.4 K 22 Feb 2017 - 10:13 WillBurrows 1s dark frame after reducing hot pixels via a mean
PNGpng DarkFrame_1s_median.png manage 59.5 K 22 Feb 2017 - 10:14 WillBurrows 1s dark frame after reducing hot pixels via a median
PNGpng DarkFrame_1s_spectrum.png manage 40.4 K 22 Feb 2017 - 10:14 WillBurrows 1s dark frame projection
PNGpng GC_Cd_0600_edges.png manage 42.5 K 22 Feb 2017 - 10:38 WillBurrows Edges of the convolution fit to Cadmium peak at 6mm
PNGpng GC_Cd_0600_peak.png manage 32.6 K 22 Feb 2017 - 10:50 WillBurrows Peak of the convolution fit to Cadmium peak at 6mm
PNGpng G_Cd_0600_edges.png manage 38.5 K 22 Feb 2017 - 10:36 WillBurrows Edges of the Gaussian fit to Cadmium peak at 6mm
PNGpng G_Cd_0600_peak.png manage 34.5 K 22 Feb 2017 - 10:37 WillBurrows Peak of the Gaussian fit to Cadmium peak at 6mm
PNGpng LBG_Vega_0600_180_edges.png manage 61.3 K 22 Feb 2017 - 10:40 WillBurrows Edges of the Lorentzian + BG fit to the Vega peak centered at 6mm
PNGpng LBG_Vega_0600_180_peak.png manage 52.7 K 22 Feb 2017 - 10:40 WillBurrows Peak of the Lorentzian + BG fit to the Vega peak centered at 6mm
PDFpdf Part_spec.pdf manage 321.7 K 21 Feb 2017 - 22:40 JamesAngthopo A section of the report
PDFpdf conv_LC_Vega_0080_180.pdf manage 62.5 K 21 Feb 2017 - 21:18 WillBurrows Convolution fit to the peak in Vega, centered at 0.80mm
PDFpdf conv_LC_Vega_0160_180.pdf manage 55.8 K 22 Feb 2017 - 10:52 WillBurrows Convolution fit to the peak in Vega, centered at 1.60mm
PDFpdf conv_LC_Vega_0230_180.pdf manage 63.5 K 22 Feb 2017 - 10:53 WillBurrows Convolution fit to the peak in Vega, centered at 2.30mm
PDFpdf conv_LC_Vega_0290_180.pdf manage 61.9 K 22 Feb 2017 - 10:53 WillBurrows Convolution fit to the peak in Vega, centered at 2.90mm
PDFpdf conv_LC_Vega_0600_180.pdf manage 51.7 K 22 Feb 2017 - 10:54 WillBurrows Convolution fit to the peak in Vega, centered at 6.00mm
PNGpng conv_LC_Vega_0600_180_edges.png manage 51.0 K 22 Feb 2017 - 10:42 WillBurrows Edges of the convolution fit to the Vega peak centered at 6mm
PNGpng conv_LC_Vega_0600_180_peak.png manage 39.4 K 22 Feb 2017 - 10:42 WillBurrows Peak of the convolution fit to the Vega peak centered at 6mm
PDFpdf conv_LC_Vega_0700_180.pdf manage 52.6 K 22 Feb 2017 - 10:54 WillBurrows Convolution fit to the peak in Vega, centered at 7.00mm
PNGpng fitadata.png manage 265.9 K 22 Feb 2017 - 10:55 JamesAngthopo This shows all the data points and the fit for every micrometer setting
PNGpng sigma0_plot.png manage 29.5 K 22 Feb 2017 - 10:03 WillBurrows Sigma_0 as a function of exposure time, with a quadratic fit

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Topic revision: r6 - 22 Feb 2017 - JamesAngthopo

 
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