Single-molecule orientation measurements with a quadrated pupil

We present a means of measuring the dipole orientation of a fluorescent, rotationally fixed single molecule (SM), using a specially designed phase mask, termed a "quadrated pupil," conjugate to the back focal plane of a conventional widefield microscope. In comparison to image-fitting techniques that infer orientation by matching simulations to defocused or excessively magnified images, the quadrated pupil approach is more robust to minor modeling discrepancies, defocus, and optical aberrations. Precision on the order of 1 degrees-5 degrees is achieved in proof-of-concept experiments for both azimuthal (phi) and polar (theta) angles. Since the phase mask is implemented on a liquid-crystal spatial light modulator (SLM) that may be deactivated without any mechanical perturbation of the sample or imaging system, the technique may be readily integrated into conventional imaging studies.