Fig. 1. Numerical simulation on a 0.75 NA imaging system over a depth range of 6 µm. (a) Diffraction-limited PSF; (b)–(d) geometric phase helical PSF of different lobe separation and rotation rate, with parameter L = 7, 11, and 14, respectively, and ϵ = 0.9. L1, L2 are labels for the LCP lobes and L3, L4 are labels for the RCP lobes.

Fig. 2. Experimental configuration. A 4f system is used to access the back focal plane of the objective where a geometric helical phase mask is placed. NA, 0.75; overall magnification, 60×. Focal length of lens 1, 200 mm; focal length of lenses 2 and 3, 300 mm. The phase mask generates opposite modulations on the LCP and RCP light. The two effective phase masks are divided into four regions (R1, R2, R3, R4), which account for the four lobes in the PSF.

Fig. 3. Experimental image stacks of the geometric phase helical PSF over a depth range of 6 µm. (a) Total intensity; (b) with RCP filtered out; and (c) with LCP filtered out.

Fig. 4. Calibration data for the geometric helical PSF rotation over a depth range of 4 µm. Two circular polarization components are plotted with magenta and cyan scatters being the experimental data, red and blue solid lines being the linear fit.

Fig. 5. Asymmetric designs of the geometric helical PSF. (a) LCP and RCP with opposite shifts in the y direction; (b) LCP and RCP with opposite shifts in the x direction.

Fig. 6. (a) Experimental results showing the variations in the PSF profile as the incident light changes its polarization orientation; (b) corresponding incident light orientation (note that the fast axis of the quarter-wave plate is along the vertical direction).

Fig. 7. Measured relative intensity in the PSF lobes (scatter plots) compared to theoretical results (solid lines); LCP data being the photon summation of the upper-right and lower-left lobes, normalized to total number of photons; and RCP data being the photon summation of the other two lobes, normalized to total number of photons.

Fig. 8. Estimated uncertainties for (a) spatial coordinates x, y, and z and (b) incident light polarization parameter θ.