Realistic ports in integrating spheres: reflectance, transmittance, and angular redirection

We use Monte-Carlo ray tracing modeling to follow the stochastic trajectories of rays entering a cylindrical port from inside an integrating sphere. This allows us to study and quantify properties of realistic ports of non-negligible length, as opposed to the common thin-port assumption used in most theoretical treatments, where the port is simply considered as a hole in the spherical wall. We show that most practical ports encountered in integrating spheres applications cannot be modeled as thin ports. Indeed, a substantial proportion of rays entering the port can be reflected back into the sphere, with port reflectances as high as 80% demonstrated on realistic examples. This can have significant consequences on estimates of the sphere multiplier and therefore pathlength inside the sphere, a critical parameter in many applications. Moreover, a non-zero port reflectance is inevitably associated with reduced transmittance through the port, with implications in terms of overall throughput. We also discuss angular redistribution effects in a realistic port and the consequences in terms of detected throughput within a fixed numerical aperture. Those results highlight the importance of real port effects for any quantitative predictions of optical systems using integrating spheres. We believe that those effects can be exploited to engineer ports for specific applications and improve the overall sphere performance in terms of pathlength or throughput. This work carries important implications on our theoretical understanding of integrating spheres and on the practical design of optical systems using them.