Abstract

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.

Highlights

  • The refractive index (RI) of biological cells and tissues contain important biophysical information about shapes, sizes, volumes and dry mass, and these characteristics are crucial for the morphological detection and diagnosis of disease

  • Three lateral spatial frequency positions are selected for comparison, and the frequency components mainly contributed by annular illumination aperture are marked with yellow line. (b) Ideal low-pass phase optical transfer functions (POTF) determined by the nonzero region of entire volume transmitted through the incoherent system. (c) The profiles of combined POTF and ideal low-pass one

  • We demonstrate a novel tomographic technique termed MFC-optical diffraction tomography (ODT) by combining different frequency components corresponding to different illumination apertures in a traditional bright-field transmission microscope with partially coherent illuminations

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Summary

Introduction

The refractive index (RI) of biological cells and tissues contain important biophysical information about shapes, sizes, volumes and dry mass, and these characteristics are crucial for the morphological detection and diagnosis of disease. There are numerous variants of non-interferometric phase retrieval approaches, like transport of intensity equation (TIE) [7,8,9,10,11,12] and differential phase contrast (DPC) [13], which provide promising QPI results under both coherent illumination and partially coherent illumination. The optimal frequency components of 3D POTF corresponding to multiple illumination apertures are combined together by utilizing linear least-squares method, and a more accurate 3D reconstruction result with imaging resolution up to the incoherent diffraction limit can be obtained. Many previous works have provided complete theories about 3D POTF for PC-ODT [35, 37] and demonstrated promising 3D RI experimental results [38,39,40] based on circular illumination aperture, the tradeoff between the intensity contrast and the maximum theoretical resolution has not been overcome yet in PC-ODT.

Numerical expression of 3D POTF for arbitrary illumination aperture
Characterization of 3D POTF for partially coherent illumination
Multi-frequency combination of 3D POTFs
Implementation of MFC-ODT technique
Objective
Experimental results
Conclusion and discussion
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