MEASUREMENT OF ALL 10 2ND-ORDER MOMENTS OF AN ASTIGMATIC BEAM BY THE USE OF ROTATING SIMPLE ASTIGMATIC (ANAMORPHIC) OPTICS

The propagation of any general astigmatic laser beam through any parax ial optical system can be characterized to second order by a 4 X 4 mat rix of second moments in the transverse spatial and angular coordinate s, with this matrix having at most ten independent elements. We show h ow to interpret the two existing beam invariants that contain these el ements in terms of an overall beam quality factor M(eff)4 and an intri nsic antigmatism factor a. We describe a general procedure for determi ning all ten parameters for any arbitrary beam by measuring only secon d-order moments of the beam irradiance in a single transversal plane a fter the beam has passed through at most four simple astigmatic optica l systems. A number of such systems containing, in particular, only on e or two rotating cylindrical lenses and a CCD camera are proposed and analyzed in more detail.