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Spectral Reduction & Spectroscopy - Coggle Diagram
Spectral Reduction & Spectroscopy
Spectral Reduction
$$ SNR = \frac{S_{net}}{\sqrt{S_{total}+{\sigma_B}^2+N_d+n_s N_r^2}}$$
Bias and Dark(as usual)
Background substraction
sky substraction
Extraction of a 1-D Spectrum
Trace the oders
Remove the “background”
Reject cosmic rays
Collapse or Optimal extraction
Special Flats and Standards
Narrow flats
Telluric standards
Wavelength calibration frames
Wavelength Calibration
emission lamp (ThAr, Xe
absorption cell
real considerations
guiding,ADC,slit height, position of star,binning
stable between wavelength calibration and science and standards
Spectral Normalization
spectrograph
multiple slit diffraction
spectral order
Grating Equation
$$ m\lambda = \sigma(sin \alpha + sin \beta) $$
Dispersion: angular and linear and reciprocal
dispersing power $$ A = \frac{d\beta}{d\lambda}=\frac{m}{\sigma cos \beta}=\frac{sin \alpha + sin \beta}{\lambda cos \beta}$$
$$Af_2 = \frac{dl}{d\lambda}$$
$$(Af_2)^{-1} = \frac{d\lambda}{dl}$$
$$R= \frac{\lambda}{\delta \lambda}$$
$$ \delta \lambda=(\frac{d\lambda}{dl})w'$$
FSR $$ \Delta \lambda=\frac{\lambda '}{m}$$