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The Monte Carlo method has been applied to numerical modeling of an integrating sphere designed for hemispherical-directional reflectance factor measurements. It is shown that a conventional algorithm of backward ray tracing used for estimation of characteristics of the radiation field at a given point has slow convergence for small source-to-sphere-diameter ratios. A newly developed algorithm that substantially improves the convergence by calculation of direct source-induced irradiation for every point of diffuse reflection of rays traced is described. The method developed is applied to an integrating sphere reflectometer for the visible and infrared spectral ranges. Parametric studies of hemispherical radiance distributions for radiation incident onto the sample center were performed. The deviations of measured sample reflectance from the actual reflectance as a result of various factors were computed. The accuracy of the results, adequacy of the reflectance model, and other important aspects of the algorithm implementation are discussed. OCIS codes: 000.4430, 000.5490, 120.0120, 120.3150, 120.5700, 120.4570.

Conic mirror reflectometers are used to measure the diffuse reflectance and total integrated scatter of surfaces. In spite of the long history of using conic mirrors for these purposes, the maximum magnification of the three primary types of conic mirror (hemisphere, hemiellipsoid, and dual paraboloid) had not been compared quantitatively. To our knowledge, an exact magnification formula has not been published for any of the three primary conic mirrors. The maximum magnification is needed for proper sizing of detectors and radiation sources used with reflectometers. Exact analytical expressions for the maximum magnification of a Coblentz hemisphere, a hemiellipsoid, and a dual-paraboloid mirror system are derived and compared.

We have designed and constructed a linear polarizer for use with visible and infrared radiation. The broadband polarizer consists of four germanium plates arranged in a chevron geometry. Input radiation is incident near Brewster's angle for the first plate such that the reflected beam is preferentially s-wave polarized. This reflected beam is steered subsequently to the successive plates, always intersecting near Brewster's angle. The beam polarization at the output of the device is almost completely s-wave polarized. The ratio of the paraxial flux of the nearly extinguished p-wave polarized light to the s-wave polarized light transmitted through the device is found to be less than [10.sup.-5] for laser illumination at wavelengths of 0.633, 1.32, 3.39, and 10.6 [[micro]meter]. Calculations predict that extinction ratios less than [10.sup.-5] are achievable over the wavelength range from 0.4 [[micro]meter] to beyond 500 [[micro]meter]. Alternative design geometries involving fewer plates are also described along with their advantages and disadvantages.

A reflectometer design utilizing an integrating sphere with a lens and nonimaging concentrator is described. Compared with previous designs where a collimator was used to restrict the detector field of view, the concentrator-lens combination significantly increases the throughput of the reflectometer. A procedure for designing lens-concentrators is given along with the results of parametric studies. The measured angular response of a lens-concentrator system is compared with ray-trace predictions and with the response of an ideal system.