Comparison of two structured illumination techniques based on different 3D illumination patterns

Manipulating the excitation pattern in optical microscopy has led to several super-resolution techniques. Among different patterns, the lateral sinusoidal excitation was used for the first demonstration of structured illumination microscopy (SIM), which provides the fastest SIM acquisition system (based on the number of raw images required) compared to the multi-spot illumination approach. Moreover, 3D patterns that include lateral and axial variations in the illumination have attracted more attention recently as they address resolution enhancement in three dimensions. A threewave (3W) interference technique based on coherent illumination has already been shown to provide super-resolution and optical sectioning in 3D-SIM. In this paper, we investigate a novel tunable technique that creates a 3D pattern from a set of multiple incoherently illuminated parallel slits that act as light sources for a Fresnel biprism. This setup is able to modulate the illumination pattern in the object space both axially and laterally with adjustable modulation frequencies. The 3D forward model for the new system is developed here to consider the effect of the axial modulation due to the 3D patterned illumination. The performance of 3D-SIM based on 3W interference and the tunable system are investigated in simulation and compared based on two different criteria. First, restored images obtained for both 3D-SIM systems using a generalized Wiener filter are compared to determine the effect of the illumination pattern on the reconstruction. Second, the effective frequency response of both systems is studied to determine the axial and lateral resolution enhancement that is obtained in each case.