Determination of pitch rotation in a spherical birefringent microparticle

Rotational motion of a three dimensional spherical microscopic object can happen either in pitch, yaw or roll fashion. Among these, the yaw motion has been conventionally studied using the intensity of scattered light from birefringent microspheres through crossed polarizers. Up until now, however, there is no way to study the pitch motion in spherical microspheres. Here, we suggest a new method to study the pitch motion of birefringent microspheres under crossed polarizers by measuring the 2-fold asymmetry in the scattered signal either using video microscopy or with optical tweezers. We show a couple of simple examples of pitch rotation determination using video microscopy for a microsphere attached with a kinesin molecule while moving along a microtubule and of a particle diffusing freely in water.