telescope aperture, $D$ is the telescope diameter, $\Upsilon$ is the fraction of the diffraction limited PSF contained within the aperture defined by the angular radius $\theta = X \lambda/D$, $\lambda = \lambda_V$ is the central wavelength of the $V$ bandpass, $T$ is total facility throughput, and $\Delta \lambda$ is the bandwidth. We assume simple aperture photometry with $X=0.7$ such that $\Upsilon=0.69$, which roughly maximizes the planet to background flux ratio. In reality, coronagraphs will broaden the PSF of the telescope, such that the optimal $\Upsilon \ne 0.69$. We leave a detailed analysis of how coronagraph PSF broadening will affect $\Upsilon$ to future work. Expanding all dependencies on $\lambda$ and $D$, we find $$\label{CRp_equation_expanded}
    {\rm CR_p} = F_0\, 10^{-0.4\left({\rm m}_V + \Delta {\rm mag_{obs}}\right)}\, \frac{\pi D^2}{4}\, \Upsilon\, T\, \Delta \lambda,$$ such that the planet’s count rate is proportional to the collecting area of the telescope.

We assume negligible read noise for broadband detections using future detector technologies. Thus, three sources of background flux dominate ${\rm CR_b}$: the leaked stellar light (${\rm CR_{b,\star}}$), the local zodiacal light (${\rm CR_{b,zodi}}$), and the exozodiacal light (${\rm CR_{b,exozodi}}$). The count rate for leaked stellar light is expressed as $$\label{CRbstar_equation}
    {\rm CR_{b,\star}} = F_0\, 10^{-0.4{\rm m}_V}\, 