Effect of double-helix point-spread functions on 3D imaging in the presence of spherical aberrations

Double Helix point-spread functions (DH-PSFs), the result of PSF engineering, are used for super resolution microscopy. The DH-PSF design features two dominant lobes in the image plane which rotate with the change in axial (z) position of the light point source. The center of the DH-PSF gives the precise XY location of the point source, while the orientation of the lobes gives the axial location. In this paper we investigate the effect of spherical aberrations on the DH-PSF. Physical parameters such as the lens used, the size of the particle, refractive index of medium, and depth i.e., location within the underlying object, contribute to the amount of spherical aberration. DH-PSFs with spherical aberrations are computed for different imaging conditions. Three-dimensional images were generated of computer-generated objects using both space-invariant and depth-variant approach. Different approaches to estimate intensity and location of points from these images were investigated. Our results show that the DH-PSFs are susceptible to spherical aberration leading to an apparent shift in the location of the point source with increasing spherical aberrations which is comparable to the conventional PSF. Estimation algorithms like the depth variant expectation maximization (DVEM) can be used to obtain estimates of the true underlying object from the image obtained with DH-PSFs.