Fig. 4.

Simulated CRLBs (standard deviation) for (a) astigmatic, (b) conventional biplane, (c) four-phase dual-objective 4Pi, (d) four plane single-objective interference and (e, f, g) PSF engineered particle localization. The simulation for astigmatic imaging introduced a 340 nm offset between the x and y focal planes. The detection planes for conventional biplane imaging are simulated 380 nm apart. These separations were chosen for the most uniform z localization precision across the entire range. The simulation conditions for (d-g) are identical to those in Fig. 3a-d, except for that (g) used an image shift of 772 nm instead of 440 nm, which gives better CRLB. For the PSF engineered cases, we plotted the CRLB for 50% (dashed) and 100% (solid) photon recovery, representing a polarization dependent and a polarization independent SLM, respectively.