Orientation-dependent visibility of long thin objects in polarization-based microscopy.

Under conditions of directional illumination, the visibility of long, thin objects depends very strongly on the direction and polarization of the incident light. Solutions to Maxwell's equations for the case of an infinite cylinder in an electromagnetic field are well known, and have been used by others in the past for theoretical analysis of light scattering by long, thin objects. The existence of those solutions allows us to calculate the expected angular distribution and polarization of the light scattered from long, thin objects illuminated by a plane wave at any angle. In this paper we show for the first time how one can incorporate these solutions of Maxwell's equations into a quantitative description of the expected appearance of filamentous biological structures in polarization-based microscopy. Our calculations for unidirectional polarized illumination show that thin, dielectric linear objects such as microtubules (or shallow interfaces) observed with finite aperture optics 1) are totally invisible when the angle (phi) between the object's long axis and incident illumination is outside the range magnitude of 90 - phi < or = sin-1 [1.33/N.A.obj]degrees; and 2) are seen with maximum intensity when phi = 90 degrees for incident illumination and scattered light polarized, either both parallel or both perpendicular to the long axis of the object; whereas 3) two maxima appear at phi approximately equal to 90 +/- 25 degrees for polarization of the incident illumination parallel to, but the scattered light perpendicular to the long axis, or vice versa; and 4) in either of these latter conditions, the objects are invisible when the illumination is near normal incidence. These counterintuitive predictions were exactly borne out by our experimental measurements of light-scattering intensity from flagellar axonemes as a function of orientation in a polarizing microscope. These calculations and measurements provide a foundation for furthering our understanding of textural or form birefringence. Calculations based on a solid cylinder model accurately predict the shapes of the measured intensity versus orientation curves. However, the relative intensities of axonemes viewed with different polarizer-analyzer settings differ from those calculated for a homogeneous solid cylinder. Thus we find that these relative intensities can provide a sensitive probe for the structure of biological objects with diameters much smaller than the wavelength of light.