Modeling of modulation functions of different configurations of optical chopper wheels

We present in this paper our results regarding the modeling of the modulation functions of the light flux of optical choppers working with top-hat (constant) light beam distributions. Two configurations of chopper wheels are considered: with windows with linear and with circular margins (the latter, to the best of our knowledge, we have introduced, works as an "eclipse" chopper). A rigorous analytical modeling has been performed for each type of device. For the first configuration, of windows with linear margins, all the four possible relationships between the diameter of the beam in the plane of the wheel and the dimensions of the window of the chopper have been considered and are discussed: (i) large wing and focused beam [in the plane of the wheel]; (ii) large wing and beam of finite diameter in the plane of the wheel, but with a wing large enough to cover the section of the beam; (iii) narrow wing, finite diameter beam and large windows, so there is only one wing at a time in front of the beam section; (iv) narrow wings and windows, so there are more wings at a time in front of the beam section. A recent study covered experimentally case (ii) presented above, obtaining a particular signal function (with an approximate trapezoidal profile). The second and more general wheel configuration that we have proposed in a previous study, with windows with circular margins (for which by example choppers with circular windows are a particular case) is also discussed. Both outwards and inwards circular margins are considered. The modulation functions of this second type of devices are also derived, studied and compared to those for the first, classical types of wheels (with windows with linear margins), which are but a particular case of this second type of chopper. From this study, the various profiles of the function of the transmitted flux are obtained: rectangular, approximate trapezoidal, approximate triangular, sinusoidal, and with nonnull values. The possible geometries of chopper wheels that may generate a required modulation function are thus concluded. An insight in the experimental part we are currently working on, with the stall we have developed to study the different configurations of chopper wheels, is also presented.