Two-photon microscopy (TPM) is one of the most important imaging techniques in biological imaging since it was invented in 1990s. Due to its unique capabilities, this technique enables noninvasive study of scattering biological specimens in three dimensions with submicrometer resolution and penetration depth up to a few hundred micrometers. Focal modulation microscopy (FMM) provides sub-cellular spatial resolution at large penetration depths in tissue samples by rejecting out-of-focus signal. Combined with focal modulation techniques, this paper proposes two-photon focal modulation microscopy (TPFMM) to further enhance penetration depth by bringing a spatiotemporal phase modulator (STPM) in the TPM. The STPM is equivalent to a time-dependent phase-only pupil filter that alternates between a homogeneous filter and an inhomogeneous filter. When the STPM is homogeneous, the excitation beam is properly focused into the focal volume by the objective lens. The inhomogeneous filter is so designed that it leads to redistribution of the excitation beam and minimize the focal intensity, which can be binary phase and continuous phase distribution. Using the vectorial diffraction theory, we have theoretically demonstrated that TPFMM with the designed STPM can significantly suppress the background contribution from out-of-focus ballistic excitation and achieve almost the same resolution as TPM. The improved background rejection of this imaging modality, enabled by focal modulation, are quantified with three dimensional imaging data obtained from fluorescent beads and fixed tissue samples using a home-made TPFMM. These investigations have its potential to extend the penetration depth of nonlinear microscopy in imaging multiple-scattering biological tissues, such as mouse brain.
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