Measuring the translational and rotational velocity of particles in helical motion using structured light

Abstract: We measure the rotational and translational velocity components of particles moving in helical motion using the frequency shift they induced to the structured light beam illuminating them. Under Laguerre-Gaussian mode illumination, a particle with a helical motion reflects light that acquires an additional frequency shift proportional to the angular velocity of rotation in the transverse plane, on top of the usual frequency shift due to the longitudinal motion. We determined both the translational and rotational velocities of the particles by switching between two modes: by illuminating with a Gaussian beam, we can isolate the longitudinal frequency shift; and by using a Laguerre-Gaussian mode, the frequency shift due to the rotation can be determined. Our technique can be used to characterize the motility of microorganisms with a full three-dimensional movement.