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

Attachments Attachments
Topic attachments
I Attachment History Action Size Date Who Comment
PNGpng DarkFrame_1s_mean.png r1 manage 60.4 K 22 Feb 2017 - 10:13 WilliamBurrows 1s dark frame after reducing hot pixels via a mean
PNGpng DarkFrame_1s_median.png r1 manage 59.5 K 22 Feb 2017 - 10:14 WilliamBurrows 1s dark frame after reducing hot pixels via a median
PNGpng DarkFrame_1s_spectrum.png r1 manage 40.4 K 22 Feb 2017 - 10:14 WilliamBurrows 1s dark frame projection
PNGpng GC_Cd_0600_edges.png r1 manage 42.5 K 22 Feb 2017 - 10:38 WilliamBurrows Edges of the convolution fit to Cadmium peak at 6mm
PNGpng GC_Cd_0600_peak.png r1 manage 32.6 K 22 Feb 2017 - 10:50 WilliamBurrows Peak of the convolution fit to Cadmium peak at 6mm
PNGpng G_Cd_0600_edges.png r1 manage 38.5 K 22 Feb 2017 - 10:36 WilliamBurrows Edges of the Gaussian fit to Cadmium peak at 6mm
PNGpng G_Cd_0600_peak.png r1 manage 34.5 K 22 Feb 2017 - 10:37 WilliamBurrows Peak of the Gaussian fit to Cadmium peak at 6mm
PNGpng LBG_Vega_0600_180_edges.png r1 manage 61.3 K 22 Feb 2017 - 10:40 WilliamBurrows Edges of the Lorentzian + BG fit to the Vega peak centered at 6mm
PNGpng LBG_Vega_0600_180_peak.png r1 manage 52.7 K 22 Feb 2017 - 10:40 WilliamBurrows Peak of the Lorentzian + BG fit to the Vega peak centered at 6mm
PDFpdf Part_spec.pdf r1 manage 321.7 K 21 Feb 2017 - 22:40 JamesAngthopo A section of the report
PDFpdf conv_LC_Vega_0080_180.pdf r1 manage 62.5 K 21 Feb 2017 - 21:18 WilliamBurrows Convolution fit to the peak in Vega, centered at 0.80mm
PDFpdf conv_LC_Vega_0160_180.pdf r1 manage 55.8 K 22 Feb 2017 - 10:52 WilliamBurrows Convolution fit to the peak in Vega, centered at 1.60mm
PDFpdf conv_LC_Vega_0230_180.pdf r1 manage 63.5 K 22 Feb 2017 - 10:53 WilliamBurrows Convolution fit to the peak in Vega, centered at 2.30mm
PDFpdf conv_LC_Vega_0290_180.pdf r1 manage 61.9 K 22 Feb 2017 - 10:53 WilliamBurrows Convolution fit to the peak in Vega, centered at 2.90mm
PDFpdf conv_LC_Vega_0600_180.pdf r1 manage 51.7 K 22 Feb 2017 - 10:54 WilliamBurrows Convolution fit to the peak in Vega, centered at 6.00mm
PNGpng conv_LC_Vega_0600_180_edges.png r1 manage 51.0 K 22 Feb 2017 - 10:42 WilliamBurrows Edges of the convolution fit to the Vega peak centered at 6mm
PNGpng conv_LC_Vega_0600_180_peak.png r1 manage 39.4 K 22 Feb 2017 - 10:42 WilliamBurrows Peak of the convolution fit to the Vega peak centered at 6mm
PDFpdf conv_LC_Vega_0700_180.pdf r1 manage 52.6 K 22 Feb 2017 - 10:54 WilliamBurrows Convolution fit to the peak in Vega, centered at 7.00mm
PNGpng fitadata.png r1 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 r1 manage 29.5 K 22 Feb 2017 - 10:03 WilliamBurrows 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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