Signal-to-Noise Ratio (Exposure Time)

Using our star data, we can find the SNR for our telescope as a function of exposure time for stars of different magnitudes. The SNR equation is given in Equation 5. By inputting a calibration magnitude and varying the time, we can find a value for the flux at different exposure times using Equation 3. We can also vary the magnitudes and obtain the flux at different magnitudes. Inputting this flux into Equation 5 as $F_{N}$ with all other variables held at constant values gives us the SNR at each of these new points.⁷ We graphed these points in Figure 6.

$$SNR = \frac{F_{N}}{[F_{N}+N_{1}(B_{i}+I_{i}+\sigma_{RO}^{2}) + N_{1}(B_{i}+I_{i}+\sigma_{RO}^{2})/N_{23}]^{\frac{1}{2}}}$$ (5)

Figure 6: Here is a plot of the SNR as a function of exposure time for stars of different magnitudes. Notice that as we increase the exposure time the SNR increases. Also, the SNR increases as the brightness of the star increases (decreasing magnitudes). The top line is for a magnitude 4 star. Each of the lower lines represent increasing magnitudes at a step size of 1 magnitude.