Optimization of a dual-rotating-retarder polarimeter as applied to a tunable infrared Mueller-matrix scatterometer

The value of Mueller-matrix (Mm) scatterometers lies in their ability to simultaneously characterize the polarimetric and directional scatter properties of a sample. To extend their utility to characterizing modern optical materials in the infrared (IR), which often have very narrow resonances yet interesting polarization and directional properties, the addition of tunable IR lasers and an achromatic dual-rotating-retarder (DRR) polarimeter is necessary. An optimization method has been developed for use with the tunable IR Mm scatterometer. This method is rooted in the application of random error analysis to three different DRR retardances, lambda/5, lambda/4 and lambda/3, for three different analyzer (A)-to-generator (G) retarder rotation ratios, theta(A):theta(G) = 34:26, 25:5 and 37.5:7.5, and a variable number of intensity measurements. The product of the error analysis is in terms of the level of error that could be expected from a free-space Mm extraction for the various retardances, retarder rotation ratios and number of intensity measurements of the DRR. The optimal DRR specifications identified are a lambda/3 retardance and a Fourier rotation ratio, with the number of required collected measurements dependent on the level of error acceptable to the user. Experimental results corroborate this error analysis using an achromatic 110-degree retardance-configured DRR polarimeter at 5 mu m wavelength, which resulted in consistent 1% error in its free-space Mm extractions.