To pre-select the beam, we will require that it pass through two holes A and B.
This will allow us to select both a diameter and a divergence angle.
To post-select the beam, we will require that it pass through two more holes C and E.
Finally to filter the beam, we will require it pass through a fifth hole F mounted midway between B and C.
All holes will be co-aligned along the optical axis, and perpendicular to it.. They will be circular cross sections in an opaque screen of negligible thickness. The light will be un-polarized, quasi-monochromatic, and plane parallel before it hits the first hole.
To make things precise, let’s assume A, B, C, and E are all 100 wavelengths L in diameter. Let’s also assume that A and B and C, and E are both one million wavelengths apart.
Given the light’s wavelength L, the distance D from B to F and also F to C, and the radius R of hole F, what is the formula for the percent of beam intensity transmitted from B to C?
I am interested in both the central hot spot and the infinite tails of this distribution. Please include all classical and quantum effects including misalignment, diffraction, the inverse square law, the uncertainty principle, and any others you are aware of.
Has any experiment similar or equivalent to this been done? (References?)
See my related question, “How fat is Feynman’s photon?