Imaging the 3D internal structure of an object is a fundamental problem. 3D quantitative phase imaging (QPI) is a non-invasive technique that measures the refractive index distribution without staining or labeling. In contrast to commercial phase contrast modes, QPI measurement is directly related to material properties, facilitating quantitative studies. Despite many promising applications in biomedical imaging, diagnostics, metrology and inspection, the adoption of existing 3D QPI techniques have been limited partly because of the system complexity and cost that arise from the use of a high coherence source, interferometric system and customized optomechanical unit. QPI techniques that are both simple and easily adaptable to existing commercial systems are particularly attractive for wide-scale adoptions.

In this Applied Optics article, Jenkins and Gaylord propose a new 3D QPI technique, tomographic deconvolution phase microscopy, that uses only commercial microscopy hardware. The simplification is enabled by jointly designing the ‘indirect’ measurements and reconstruction algorithm, a common philosophy used in the emerging field of ‘computational imaging’.
The authors start by implementing a QPI technique that eliminates the need for both coherent source and interferometric measurement. The propagation-based QPI technique works by simply taking a series of through-focus intensity measurements. The spatially extended source is incorporated in the forward (image formation) model, enabling the use of a standard brightfield microscope source. The authors further show that the forward model is linear and valid under the 1st Born and Rytov approximations, a good assumption for both biological samples and optical fibers. To capture 3D phase information with isotropic spatial resolution, the authors repeat the through-focus measurements at multiple angles by rotating the object. Next, the 3D refractive index distribution is recovered using a holistic approach, in which a minimization problem relates all the intensity measurements to the unknown 3D distribution. The authors demonstrate that the reconstruction procedure involves only linear deconvolution, which means that it can be realized using computationally efficient algorithms based on the Fast Fourier Transform (FFT).

The 3D QPI technique introduced here is a great example of how synergies between optics and algorithms allows simple and yet powerful imaging systems. The authors point out that the current technique is still limited due to requirement of 3D fixation and culture if applied to biological samples. It is highly possible that innovations in computational imaging will enable 3D phase tomography techniques that have all the desired properties, e.g. motion-free, high-resolution, and easy sample preparation, to name a few.

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