flux from star F_{∗} = \frac{L_{∗}}{4π r_{orb}^{2}} Lum of planet L_{p} = F_{∗} α πR_{P}^{2}

\frac{L_{p}}{L_{∗}} = \frac{α}{4}(\frac{R_{P}}{r_{orb}} )^{2}

S/N ∼ \frac{photons from star}{\sqrt{(photons from star) + (photons from sky)}} I_{∗}(θ) = number of photons from star at angular distance θ

σ_{∗}(θ) = noise of photons from star at angular distance θ

= \sqrt{I_{∗}(θ)}

P = number of photons from planet
P > \sqrt{I_{∗}(θ)}

I(θ) = I_{0} e^{−θ^{2}/(2s^{2})} ≃ I_{0} e^{−θ^{2}/(0.36 FWHM^{2})}

s ≃ FWHM/2.35 I(θ) = I_{0} e^{−2.76 (θ/FWHM)^{2}}

star noise at θ, in mag = −2.5 log_{10} (\frac{\sqrt{I(θ)}}{I(θ)})

\frac{L_{p}}{L_{∗}} = (\frac{R_{P}}{R_{∗}} )^{2}(\frac{B_{λ}(T_{P})}{B_{λ}(T_{∗})})^{4}