Relative (or Differential) Photometry

Relative (or Differential) Photometry gives us a way to measure the relative magnitudes of stars. More importantly, if we take data of both stars using the same telescope with the same filter in place, we know that $A$, $\eta_{\nu}$, and $\Delta\nu$ in Equation 2 are the same for both stars. Thus, if we take the ratio of the fluxes from both stars, all of these constants with respect to our telescope cancel out and we get Equation 3.

$$m_{\nu}^{(1)} - m_{\nu}^{(2)} = -2.5 \log_{10} \left( \frac{... ...1}}\right) + 2.5 \log_{10} \left( \frac{N_{2}}{t_{2}} \right)$$ (3)

At this point, we can now measure the number of photons received by our camera for two different stars and, knowing the exposure time, we can find the relative apparent magnitudes of the different stars. If we know an accurate value for the apparent magnitude of one of these stars, then we can get the apparent magnitude of the other star. Thus, we can use this method with our telescope by taking an image of any one star and then taking a second image of a standard star (a star that has been meticulously studied to obtain an accurate measurement of its apparent magnitude in different wavelength bands of interest). We can then do relative photometry on these two stars and obtain an estimate for the apparent magnitude of the first star.