Three-dimensional tomographic microscopy technique with multi-frequency combination with partially coherent illuminations.

We demonstrate a three-dimensional (3D) optical diffraction tomographic technique with multi-frequency combination (MFC-ODT) for the 3D quantitative phase imaging of unlabeled specimens. Three sets of through-focus intensity images are captured under an annular aperture and two circular apertures with different coherence parameters. The 3D phase optical transfer functions (POTF) corresponding to different illumination apertures are combined to obtain a synthesized frequency response, achieving high-quality, low-noise 3D reconstructions with imaging resolution up to the incoherent diffraction limit. Besides, the expression of 3D POTF for arbitrary illumination pupils is derived and analyzed, and the 3D imaging performance of annular illumination is explored. It is shown that the phase-contrast washout effect in high-NA circular apertures can be effectively addressed by introducing a complementary annular aperture, which strongly boosts the phase contrast and improves the imaging resolution. By incorporating high-NA illumination as well as high-NA detection, MFC-ODT can achieve a theoretical transverse resolution up to 200 nm and an axial resolution of 645 nm. To test the feasibility of the proposed MFC-ODT technique, the 3D refractive index reconstruction results are based on a simulated 3D resolution target and experimental investigations of micro polystyrene bead and unstained biological samples are presented. Due to its capability for high-resolution 3D phase imaging as well as the compatibility with a widely available commercial microscope, the MFC-ODT is expected to find versatile applications in biological and biomedical research.