Laser beam shape invariance parameters

Quantitative characterization of laser beam intensity distribution shape is of great importance for beams comparison, to analyze their transformation along the propagation path or as criteria for DOE synthesis. One important application is distinguishing between the near field, Fresnel and Fraunhofer diffraction zones. For laser beams, such parameters have to be based on measured intensity distribution due to phase front measurements being too difficult in practice. The most general approach to the definition of Shape Invariance Error (SIE) has to be used. The well known Gelder norms of vectors or matrices for SIE calculation are proposed here. As examples, SIE for 3D-propagation of typical beams are considered. These parameters can be used as criteria in beam shape and technology process monitoring, resonator optimization to form beams with specified shape, optical systems development and optimization, etc. The fixed SIE level Shape Invariance Range (SIR) is an effective tool for comparison of laser beams or optical elements.