Monte Carlo Study of Light Transmission Through a Cylindrical Tube

The transmission of light in vacuum through a cylindrical tube with specular walls has been evaluated using the Monte Carlo method. Uniform as well as cosine angular distributions have been assumed as the initial conditions at the entrance aperture; both cases were treated separately for a light cource of uniform density. From the results, which are given as a function of the tube's length-to-diameter ratio L / D and the reflectivity of the inner wall R (0 ≤ R ≤ 0.99), a simple expression has been derived that holds for long tubes L ≥ 4D/ln(1/R) and R ≤ 0.6. The relation T(L,D,R) also yields the molecular transmissivity if specular reflection applies with a sticking coefficient S = 1 − R.