Measurement of the Mueller scattering matrix by use of optical beats from a Zeeman laser

A two-frequency beam from a Zeeman laser scatters elastically from an isotropic medium, such as randomly oriented viruses or other particles suspended in water. The Zeeman effect splits the laser line by 250 kHz, and beats can be seen electronically in the signal from a phototube that views the scattered light. There are independently rotatable half-wave and quarter-wave retardation plates in the incident beam and a similar pair in the observed scattered beam, plus a fixed linear polarizer directly in front of the detector. Each of the four retarders has two angular positions, providing a total of 16 possible polarization cases. For each of the 16 cases, there are three data to be collected: (1) the average total intensity of the scattered light, (2) the amplitude of the beats in the scattered light, and (3) the phase shift between the beats of the scattered light and those of a reference signal from the laser. When a singular value decomposition technique is used, these threefold redundant data are rapidly ransformed into a best-fit 4 × 4 Mueller scattering matrix. We discuss several different measurement strategies and their systematic and statistical errors. We present experimental results for two kinds of particle of wavelength size: polystyrene spheres and tobacco mosaic virus. In both cases the achiral retardation element M(34) of the Mueller matrix is easily measurable.