Fig. 1: Vortex PSF concept.

a A constrained dipole emitter is defined by the polar angle θ and azimuthal angle ϕ. The blue cone represents the degree of rotational constraint (g₂) of the dipole emitter and the red torus-like shape represents the dipole emission. The microscope, equipped with a vortex phase plate, induces a radial π phase difference in the Fourier plane of the emission path. This results in an asymmetric donut-like shape for fixed emitters on the camera which we call the Vortex PSF. b Simulated standard PSF of fixed emitters (g₂ = 1) with polar angles from left to right (10, 45, 80 degrees) and an azimuthal angle of 45 degrees. c Simulated Vortex PSF with the same angles and rotational constraint. d Phase profile of the vortex phase plate. e Azimuthal angle CRLB from simulated images as a function of the emitter polar angle (4000 signal photons, 10 background photons per pixel and g₂ = 1). f Polar angle CRLB as a function of the emitter polar angle with the same SBR and rotational constraint.