Evaluation of a geometrical optics solid angle transfer function for a defocused, forward-scattered light collecting optical system

Because of the ambiguity in the trajectory of a particle embedded in a flow across the probe volume of a Laser Doppler Velocimeter, scattered light intensity measurements as a function of the particle size become difficult to interpret. By choosing the proper combination of photo-detector aperture setting, aperture magnification, and collecting lens focal number, a reduction in the field of view of the collection optics can be obtained such that only centrally localized scattered light from the probe volume gets detected. Hence, by applying appropriate optical design techniques, partial elimination of the trajectory ambiguity can be achieved, resulting in a higher level of confidence in the interpretation of the recorded data.

This study is the quantitative analysis of the scattered light collecting performance of a lens-aperture optical system, as used in a general applications Laser Doppler Velocimeter. Different ray trace analysis techniques are employed to support a common model for a defocused, forward-scattered light collecting optical system. A solid angle ratio function is developed on the basis of geometrical optics and allows for all calculations to be performed in the image of the aperture space. The solid angle ratio makes the computations easier by eliminating the need to perform lens transformations. The results are used to plot normalized solid collection angle contours as a function of the point-source scattering position in the image of the aperture space. These contours are the graphical representations of a general functional expression which has been defined as the geometrical optics solid angle transfer function.