Three-dimensional localization precision of the double-helix point spread function versus astigmatism and biplane

Wide-field microscopy with a double-helix point spread function (DH-PSF) provides three-dimensional (3D) position information beyond the optical diffraction limit. We compare the theoretical localization precision for an unbiased estimator of the DH-PSF to that for 3D localization by astigmatic and biplane imaging using Fisher information analysis including pixelation and varying levels of background. The DH-PSF results in almost constant localization precision in all three dimensions for a $2μm$ thick depth of field while astigmatism and biplane improve the axial localization precision over smaller axial ranges. For high signal-to-background ratio, the DH-PSF on average achieves better localization precision.