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1_SpectroscopicTraceTutorial.ipynb

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"\n",
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"(The first-order moment is the intensity-weighted mean position, \n",
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"\n",
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"$m_1 = \\frac{\\Sigma_i x_i f(x_i)}{\\Sigma_i f(x_i)}$, \n",
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"$$m_1 = \\frac{\\Sigma_i x_i f(x_i)}{\\Sigma_i f(x_i)}$$, \n",
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"\n",
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"where $x_i$ is the position and $f({x_i})$ is the intensity at that position. $f(x_i)$ must be zero in the signal-free region for $m_1$ to return an accurate estimate of the location of the peak.)"
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2_WavelengthCalibration.ipynb

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}
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"The moment-1 estimate of the peak location is, for a spectrum $f(x)$ and pixel location $x$ \n",
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"The moment-1 estimate of the peak location is, for a spectrum $f(x)$ and pixel location $x$,\n",
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"\n",
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"$$ m_1 = \\frac{\\Sigma x f(x)}{\\Sigma f(x)} $$\n",
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"which, through propagation of error, gives us variance of moment 1:\n",

3_Trace_Extract_Wavelength-CalibrateSpectrum.ipynb

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"metadata": {},
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"source": [
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"First, we do the calculation manually, following the optical definition\n",
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"$$v_{opt} = c \\frac{\\lambda-\\lambda_0}{\\lambda} $$"
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"$v_{opt} = c \\frac{\\lambda-\\lambda_0}{\\lambda} $"
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{

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