Revisiting parallel catadioptric goniophotometers

A thorough knowledge of the angular distribution of light scattered by an illuminated surface under different angles is essential in numerous industrial and research applications. Traditionally, the angular distribution of a reflected or transmitted light flux as function of the illumination angle, described by the Bidirectional Scattering Distribution Function (BSDF), is measured with a point-by-point scanning goniophotometer yielding impractically long acquisition times. Significantly faster measurements can be achieved by a device capable of simultaneously imaging the far-field distribution of light scattered by a sample onto a two-dimensional sensor array. Such an angular-to-spatial mapping function can be realized with a parallel catadioptric mapping goniophotometer (CMG). In this contribution, we formally establish the design requirement for a reliable CMG. Based on heuristic considerations we show that, to avoid degrading the angular-to-spatial function, the acceptance angle of the lens system inherent to a CMG must be smaller than 60°. By means of a parametric study, we investigate the practical design limitations of a CMG caused by the constraints imposed by the properties of a real lens system. Our study reveals that the values of the key design parameters of a CMG fall within a relatively small range. This imposes the shape of the ellipsoidal reflector and drastically restricts the room for a design trade-off between the sample size and the angular resolution. We provide a quantitative analysis for the key parameters of a CMG for two relevant cases.