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We have been developing a polarized light microscope with liquid crystal universal compensator and circular polarizer (the LC-PolScope) for recording images, which are independent of the orientation of birefringent objects. Separate images show the retardance and the slow axis azimuth distributions of the in-plane birefringence of the focused region in the specimen. However the measured (apparent) retardance still depends on the angle between the crystal optic axis and the axis of the illuminating beam of light. If the illuminating beam is close to parallel to the optic axis the measured retardance value decreases dramatically and becomes zero when the two axes are parallel. The description of birefringent objects oriented in 3-dimensional space requires the introduction of two additional parameters: the principal retardance and the inclination angle. Together with the azimuth angle they completely characterize the birefringence properties of a specimen, assuming the specimen has a uniaxial optical indicatrix. We devised a new technique for measuring the three birefringence parameters without moving the specimen. For exploring the out-of-plane birefringence the new instrument which is based on the LC-PolScope technique contains an additional spatial light modulator, implemented here as a liquid crystal mask. The mask is located in the aperture plane of the condenser lens. Partial occlusion of the condenser aperture changes the direction of the central ray of the cone of light converging on the specimen. So we can obtain the retardance and azimuth images using different sets of illumination rays. For experimental verification we used a biological object called an aster. An aster consists of nearly parallel arrays of microtubules, a stiff biopolymer, radiating from a common organizing center called a centrosome. The object is spherically symmetric, and its 3 dimensional distribution of birefringence orientation can be predicted. Experimental results have shown the developed polarizing microscope can successfully be used for imaging and measuring three-dimensional orientation of birefringent objects
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