Resistance to optical distortions in three-dimensional interferometric temporal focusing microscopy

We analyze how optical distortions in deep imaging or dense scattering media influence three-dimensional interferometric temporal focusing (3D-ITF) imaging, and derive the distorted point spread function (PSF) and optical transfer function (OTF). Upon this, we find that 3D-ITF microscopy is less affected by optical distortions in terms of spatial resolution, artifacts and sectioning ability. Temporal focusing (TF) illumination supports a robust spatial modulation in 3D-ITF microscopy with distorted optics. As the modulation spatial frequencies are unique, they offer a redundancy in 3D-ITF microscopy. The redundancy in the spatial frequency of 3D-ITF images compensates for the loss of spatial frequency caused by the optical distortion in the emission OTF. The redundancy recovers the high spatial frequencies to prevent the degradation of spatial resolution. Moreover, the redundancy recovers the distortion in the emission OTF spectrum, which causes distorted shapes in the PSF such as side lobes and double peaks. Thus, there is a relatively lossless OTF spectrum in 3D-ITF compared to TF, and this leads to better trade-off between remaining noise artifacts and resolution after the Wiener filter correction.