Extinction

This is how we quantify how a star's magnitude changes with the airmass between the observer and the observed star.

Unfortunately, extinction varies with wavelength, since the sky absorbs some wavelengths more intensely than others ... so we'll see different values of $k$ for each filter used.

To correct for this, let $k=k^{\prime }+k^{\prime \prime }C$, where $C$ is a color (i.e. $B-V$) - then, $$m_0=m-k^{\prime }X-k^{\prime \prime }CX$$ 2nd-order $k^{\prime \prime }$ extinction is normally quite small (~0.04 magnitudes), but still important to include for high-precision photometry & blue stars. It can be determined with a close pair of different-color stars by fitting the slope of $\Delta m$ vs $X\Delta C$ (since $\Delta C$ is a constant change-in-color for the two) - we end up with $$V=v_0+{\mu }_v(b_0-v_0)+C_V$$ $$B=b_0+{\mu }_b(b_0-v_0)+C_B$$

Image Reduction Pipeline

Use several Jupyter notebooks, rather than a single "The Master Notebook" - it can get long and big and slow.

1. Take calibration frames (biases, flats (dome and/or sky) and darks, if necessary)
2. Observe targets (science, standard stars and airmass-constraint stars (extinction stars))
3. Remove instrumental signature from observations using calibration frames.
4. Measure stellar fluxes (i.e. with aperture photometry or PSF photometry)
5. Solve for extinction coefficients / the space magnitude