The four-detector photopolarimeter (FDP) is analyzed for an arbitrary spatial configuration and any reflection characteristics (ri, /i, Ai) of the first three detectors. The instrument matrix A, which relates the output signal vector I to the input Stokes vector S by I = AS, and its determinant are derived explicitly. The essential condition that A be nonsingular (det A $ 0) is satisfied in general with uncoated absorbing detector surfaces, assuming that the plane of incidence (POI) is rotated between successive reflections by other than 90°. Therefore no special coatings on the detectors are required, and a thin dielectric (e.g., thermal oxide) layer would suffice. The differential reflection phase shift A is unrestricted for the first and third detectors and has optimum values of ±90' for the second. The optimum rotation angles of the POI are +45 0 and +135'. The optimum values of the surface parameter ip are 27.37°, 22.50 or 67.50, and 0 or 90° for the first, second, and third reflections, respectively. The following topics are also considered: (1) the partition of energy among detectors, (2) the effect of tilting the last detector, (3) operation of the FDP over a broadband spectral range, (4) choice of the light-beam path, and (5) calibration.

A computer-controlled four-detector photopolarimeter (FDP) has been constructed using four windowless planar-diffused Si photodiodes, operational amplifiers, an analog-to-digital (A/D) converter, and a personal computer with peripherals. A nonplanar light path is selected with incidence angles at the first three detectors of ∼65° and with rotations of ∼45° between the successive planes of incidence. The last detector, which is coated for minimum reflectance, intercepts the beam at a small angle and the residual light it reflects is dumped. A 1-mW He–Ne laser beam (λ=632.8 nm) passes through the polarizing optics of an ellipsometer to provide the polarization states needed for calibration and testing. With an optimum set of calibration states, the instrument matrix A is determined. The FDP is subsequently tested and found to correctly measure the normalized Stokes parameters of a large number of states with an average absolute error of ∼0.01, which is attributed to imperfections in the calibration optics. This first prototype instrument has a precision of ∼0.2%.

We have measured the scattered-light intensity as a function of the scattering angle for light scattered from soot particles in a premixed methane/oxygen flame. This yields the optical structure factor for the soot particles. We find that the structure factor shows the soot particles to have a morphology consistent with a fractal interpretation with a fractal dimension in the 1.6

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