This paper gives a simple, conservative way to turn a detector’s sensitivity goal into limits on stray light near the central optics of a ground‑based gravitational wave (GW) interferometer. The authors derive compact analytical formulas that estimate how much scattered light can return to the main beam and how that light turns movements of nearby surfaces into noise. They show how these estimates can be used early in design work and illustrate the approach with parameters for the planned Cosmic Explorer observatory.

The work focuses on the core optics region. That region includes the power recycling cavity, the beam splitter, internal telescope optics, the input test masses, and the signal extraction cavity. It does not attempt to re‑solve stray light in the long arm cavities, which are studied separately. The paper develops formulas for several scattering regimes. It also treats collections of flat baffles and gives a similar requirement for deterministic “ghost” beams that should be intercepted by beam dumps.

At a high level the calculation has two parts. First, the authors estimate the fraction of laser power that can leave the main beam, reach a secondary surface, and then return so it overlaps with the interferometer mode. That overlap depends on the scattering behavior of the emitting optic and of the back‑scattering surface, and on how well the returning light matches the main beam after diffraction over the distance involved. The paper models surface scattering using a simple bidirectional reflectance distribution function (BRDF). BRDF stands for bidirectional reflectance distribution function and describes how likely light is to scatter into different angles. The authors use a power‑law form BRDF(θ) = α θ^n (with parameters α and n left explicit) so the results can be adapted to different surface qualities.