Operator Based Aberration Correction for Improved Colloidal Particle Characterization

The characterization of the properties of micron sized particles is limited by physical aberration-based distortions. Lie algebra operators come out of geometric optics and can be used to model these distortions, producing propagation and refraction aberrations. The Hermitian and Unitary properties of these operators allow them to correct the aberration. Previous work shows experimentally that a spatially varying multiplicative phase factor could be used to model spherical aberrations, increasing the accuracy of particle characterization. We show a rigorous mathematical framework of the operators used to model these aberrations. We go beyond spherical aberrations to show Lie operators which approximate other aberration types and give experimental evidence demonstrating the increased accuracy of particle characterisation using these Lie operators to correct aberrations.