Pixel to Wavelength mapping

  • Equation used:
 \begin{equation} \lambda(m,p)=\sum_{n=0}^{N} C_n((p-p_0)-\alpha(m-m_0))^n \end{equation}
  • $\alpha$ is an unknown variable - currently unable to identify its value. Therefore expanded the above equation to obtain:
 \begin{equation} \lambda(m,p)= C_0+C_1(p-p_0)-D_1(m-m_0)-E_1(p-p_0)(m-m_0)+C_2(p-p_0)^2+D_2(m-m_0)^2\end{equation}

  • $C_0,C_1,C_2,D_1,D_2,E_1$ are all coefficient, which were found using 2D curvefit function using python.
  • Made file with the micrometer setting, pixel position and wavelength to input into curve fit - the pixel position of the peaks were imporved by fitting a gaussian to the peaks.
Micrometer setting (mm) Pixel position Wavelength(nm)
2.00 40.8, 441.3 ,675.5 667.8, 686.7, 706.5
2.50 297.7,707.8 686.7, 706.5
5.50 147.9, 235.9 492.1, 501.5
6.00 5.9, 227.2, 424.5, 514.4 447.1, 471.3, 492.1, 501.5
6.50 269.1, 496.2, 695.6 447.1, 471.3, 492.1
7.00 0.4, 536.1 388.8, 447.1

  • Made a plot for pixel positions against wavlegnth to get and estimate for $C_0$.
  • Plot showing the relation between pixel and the wavelength:
    pixel_wavelength.png

  • Used curve_fit function to obtain the optimal values for the coefficient.
  • Guess for the parameter and outputted values were was (to first decimal place):
Parameter Initial guess values Output values
$C_0$ $446.6$ $581.2$
$C_1$ $0.1$ $9.7 \times 10^{-2}$
$C_2$ $3.8 \times 10^{-4}$ $52.6$
$D_1$ $0.2$ $2.9 \times 10^{-6}$
$D_2$ $2.0 \times 10^{-3}$ $-2.29$
$E_1$ $0.8$ $-9.1 \times 10^{-3}$
  • The above values are for micrometer setting of 06.00 mm.
  • Using the above output values, a plot of the spectrum at micrometer setting of 6.00mm was plotted.
  • Plot of the Helium spectrum at micrometer position 06.00mm:
    wavelength_plot.png
Observation

  • Took a spectrum of Venus and Aldebaran.
  • Attempted to look at Saiph
  • Plot of Spectrum of Aldabaran - micrometer position 4.00mm.
  • Considered a fluctuation a peak if values are above the cutoff value of 0.2 (from the second derivative).
  • The $x(i+\Delta x) - x(i-\Delta x)=5$
  • Minimum x range to be considered a peak is 3 pixels
  • Aldebaran peaks with median filter applied:
    Aldebaran_plot.png
  • Part of the spectrum we are looking at, for micrometer position of 4.00mm:
    aldebaran_online_spectrum.JPG
  • Source of the above image: https://hiveminer.com/Tags/aldebaran,spectrum/Timeline
-- JamesAngthopo - 19 Jan 2017
Topic attachments
I Attachment Action Size Date Who Comment
PNGpng Aldebaran.png manage 139.9 K 19 Jan 2017 - 14:22 JamesAngthopo Aldebaran peaks without medium filter applied cutoff is 0.02 instead of 0.2
PNGpng Aldebaran_plot.png manage 143.0 K 19 Jan 2017 - 14:21 JamesAngthopo Aldebaran peaks with medium filter applied
Texttxt Spectra.txt manage 17.7 K 19 Jan 2017 - 13:40 JamesAngthopo Python code for spectroscopy
Unknown file formatJPG aldebaran_online_spectrum.JPG manage 61.3 K 19 Jan 2017 - 14:16 JamesAngthopo Part of the spectrum we are looking at, for micrometer position of 4.00mm
PNGpng pixel_wavelength.png manage 87.9 K 19 Jan 2017 - 12:04 JamesAngthopo Plot showing the relation between pixel and the wavelength
PNGpng wavelength_6.5plot.png manage 83.0 K 19 Jan 2017 - 12:32 JamesAngthopo Plot of the Helium spectrum at micrometer position 6.50
PNGpng wavelength_plot.png manage 90.2 K 19 Jan 2017 - 12:22 JamesAngthopo Plot of the Helium spectrum at micrometer position 6.00

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Topic revision: r3 - 19 Jan 2017 - WillBurrows

 
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