A new paradigm for label-free 3D microscopy——Transport of intensity diffraction tomography

Fluorescence microscopy techniques are powerful tools for probing very small signals and revealing three-dimensional (3D) structural and functional properties of biological samples with high specificity. However, they require fluorescent dyes and proteins as biomarkers, and are thus ill-suited for samples that are non-fluorescent or cannot be fluorescently tagged. Besides, the excitation light and contrast agents can cause photobleaching, phototoxicity, and other adverse effects that prevent live-cell imaging over extended periods of time. These factors have pushed the need for label-free microscopy, where biological samples are studied in a non-invasive and label-free manner.

Although most biological cells are transparent and do not change the amplitude of the light passing through them, they introduce phase delays due to the inhomogeneous optical density of different structural regions. Therefore, phase contrast microscopy (e.g., Zernike phase contrast microscopy and differential interference contrast) offers simple and effective ways to directly visualize transparent cells and weakly absorbing samples under an optical microscope. The introduction of optical interferometry and holography into microscopy made it possible to measure tiny phase differences induced by the specimens, facilitating the evolution of phase imaging techniques from qualitative observation to quantitative measurement. By combining interferometric phase measurements with the concept of computed tomography (CT), optical diffraction tomography (ODT) allows depth-resolved 3D imaging of thick samples, just like confocal microscopy, but in a label-free manner. However, conventional ODT techniques require laser illumination, producing coherent imaging artifacts that prevent the formation of high-quality images. Moreover, most of them require a specialized interferometric setup with complicated beam scanning devices, which is not typically available to most biologists, prohibiting their widespread use in biological and medical science.

In a recent research paper published in Light Science & Application, the research teams led by Professor Chao Zuo from Smart Computational Imaging Laboratory (SCILab), Nanjing University of Science and Technology, China presented a new label-free 3D microscopy technique, termed transport of intensity diffraction tomography with non-interferometric synthetic aperture (TIDT-NSA). A unified theoretical framework for optical transfer functions and space-domain Kramers-Kronig relations is established, and the corresponding transfer functions for both non-interferometric 2D QPI and 3D diffraction tomography is derived as well. TIDT-NSA eliminated the need for the matched illumination condition (analyticity condition) as required in 2D Kramers-Kronig relations, and the resultant 3D Fourier spectrum of the intensity stack gives direct access to the object frequency content within the generalized aperture. By applying the direct non-interferometric 3D synthetic aperture in the Fourier domain, the incoherent-diffraction-limited quantitative 3D phase-contrast imaging is finally achieved.

Optical diffraction tomography can be realized by combining optical holography with computed tomography through either object rotation or illumination scanning to infer the volumetric RI distribution of biological specimens, extending quantitative phase imaging to three dimensions. However, most of them require a specialized interferometric setup with complicated laser beam scanning devices (e.g., scanning galvo-mirrors), hindering their widespread adoption in the biological and medical communities. On the other side, the QPI can be realized in a non-interferometric manner, such as transport of intensity equation (TIE), differential phase contrast microscopy (DPC), and Fourier ptychographic microscopy (FPM). Under angle-varied illuminations illumination, the optical transfer function of the imaging system is modulated by the incident beam, and the quantitative phase distribution of the sample can be recovered through the direct inversion of the transfer function or iterative phase retrieval algorithm. However, the phase reconstruction of these non-interferometric QPI methods suffers from the missing low-frequency problem induced by the violation of the matched illumination condition (i.e., the illumination aperture is smaller than the objective aperture). Such a matched illumination condition is essential for accurate phase recovery based on asymmetric-illumination-based non-interferometric QPI methods.

"However, the matched illumination condition is difficult to strictly fulfill in practice, especially when an oil-immersion objective lens is used. This prevents us from obtaining high-quality phase images," said Li, the first author of this work. "But we remove this limitation under the framework of TIDT-NSA, making 3D label-free imaging possible even under arbitrary illumination conditions."

In this work, scientists have found that the analytical properties of object function required in the Kramers-Kronig relations can always be satisfied at any illumination angle in 3D space. By extending the Kramers-Kronig relations from 2D to 3D and invoking the axial scanning, the restriction imposed by the matched illumination condition can be circumvented. "It's like we can travel into a hyperspace to find better solutions," said Li.

By further synthesizing the retrieved 3D complex phase functions at different illumination angles in the Fourier space, the object spectrum can be filled by the extracted generalized apertures, allowing for the reconstruction of the scattering potential of the 3D sample in a non-interferometric manner (Figure). The unique combination of z-scanning the sample with illumination angle diversity in TIDT-NSA provides strong defocus phase contrast and better optical sectioning capabilities suitable for high-resolution tomography of thick biological samples. 

"We validate the 3D RI tomographic imaging performance on various unlabeled fixed and live samples. These results establish TIDT-NSA as a new non-interferometric approach to optical diffraction tomography and 3D label-free microscopy," said Zuo, the research team leader. "We envision this approach being applied in a wide variety of biomedical imaging applications, permitting quantitative characterization of cell morphology and time-dependent subcellular changes over a long period of time."

The researchers are now exploring ways to address several remaining issues, including model optimization for multi-layer and multiple scattering samples, reducing the amount of data acquisition, and improving the imaging speed. Due to the lacking of specificity, the fluorescence-assisted TIDT-NSA will also be envisioned collaborating the advantages of specificity of fluorescence techniques and non-invasiveness of diffraction tomography, providing wider window and more insights to investigate biological processes.

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