This situation is relevant to many common reflector telescope designs that incorporate a secondary mirror, including Newtonian telescopes and Schmidt-Cassegrain telescopes.
I(\theta) = \frac{I_0}{ (1 - \epsilon ^2)^2} \left ( \frac{2 J_1(x)}{x} - \frac{2 \epsilon J_1(\epsilon x)}{x}\right )^2 .