Transformation of a Gaussian beam by elements of a laser anemometer

The transfer matrix mathod is used in a theoretical analysis of the transformation of a Gaussian beam passing through various optical elements of a laser anemometer such as lenses, inclined plane-parallel plates, and media with different refractive indices. The transfer matrices are found for an inclined plate and for the investigated medium bounded by two plates. Analytic expressions are derived for the beam parameters in the medium under study, including the position, dimensions, and radii of curvature of the beams in the meridional and sagittal planes. The misalignment of the laser anemometer optical system is calculated by scanning the element under study along the bisectrix of the intersection of two beams allowing for astigmatism. The main theoretical conclusions are compared with the experimental results.