Determination of rotation in the pitch degree of freedom for a spherical birefringent particle

A three dimensional rigid spherical microscopic object can rotate in either the pitch, yaw or roll fashion. Among these, yaw motion has been conventionally studied using the intensity of the scattered light from birefringent microspheres through crossed polarizers. So far, however, there is no way to study the pitch rotational motion in spherical microspheres. Here we suggest a new method towards the study of such pitch motion in birefringent microspheres under crossed polarizers by measuring the 2-fold asymmetry in the scattered signal using video microscopy. We show a simple example of pitch rotation determination using video microscopy for a microsphere attached with a kinesin molecule while moving along a microtubule. It can also be extended to optical tweezers.