Free-Motion Beam Propagation Factor Measurement by Means of a Liquid Crystal Spatial Light Modulator

In contrast to the mechanical scanning procedure described in the standard ISO/DIS 11146, the use of electronically tunable focal length lenses has proved its capability for the measurement of the laser beam propagation factor (M²) without moving components. Here, we demonstrate a novel experimental implementation where we use a low-cost programmable liquid crystal spatial light modulator (SLM) for sequentially codifying a set of lenses with different focal lengths. The use of this kind of modulators introduces some benefits such as the possibility for high numerical aperture or local beam control of the phase of the lenses which allows for minimizing systematic errors originated by lens aberrations. The beamwidth, according to the second-order moment of the irradiance, is determined for each focal length by using a digital sensor at a fixed position with respect to the spatial light modulator. After fitting the measured data to the theoretical focusing behavior of a real laser beam, the beam propagation factor is obtained. We successfully validated the results in the laboratory where a full digital control of the measurement procedure without mechanical scanning was demonstrated.