Quantitative Phase Imaging (QPI) provides unique means for the imaging of biological or technical microstructures, merging beneficial features identified with microscopy, interferometry, holography, and numerical computations. This roadmap article reviews several digital holography-based QPI approaches developed by prominent research groups. It also briefly discusses the present and future perspectives of 2D and 3D QPI research based on digital holographic microscopy, holographic tomography, and their applications.

Digital holographic microtomography is a promising technique for three-dimensional (3D) measurement of the refractive index (RI) profiles of biological specimens. Measurement of the RI distribution of a free-floating single living cell with an isotropic superresolution had not previously been accomplished. To the best of our knowledge, this is the first study focusing on the development of an integrated dual-tomographic (IDT) imaging system for RI measurement of an unlabelled free-floating single living cell with an isotropic superresolution by combining the spatial frequencies of full-angle specimen rotation with those of beam rotation. A novel ‘UFO’ (unidentified flying object) like shaped coherent transfer function is obtained. The IDT imaging system does not require any complex image-processing algorithm for 3D reconstruction. The working principle was successfully demonstrated and a 3D RI profile of a single living cell, Candida rugosa, was obtained with an isotropic superresolution. This technology is expected to set a benchmark for free-floating single live sample measurements without labeling or any special sample preparations for the experiments.

This study presents a novel tomographic imaging technique for living biomedical samples using an optically driven full-angle rotation scheme based on digital holographic microscopy, in which the three-dimensional refractive index distribution inside the sample can be measured and analyzed. To accomplish the full-angle sample rotation, two optical traps are driven by highly focused spots on the top and bottom of the sample. The rim image of the sample outside the focal depth at the different rotation angles and propagation distances can be corrected and compensated, respectively, via numerical focusing; therefore, tomographic imaging of the sample can be conducted. The proposed approach shows that an entire symmetric spectrum can be acquired for tomographic reconstruction without the missing apple core problem as in traditional sample-rotation schemes. The three-dimensional refractive index of living yeast in a fluid medium is measured and verified.

The properties of a low-coherence phase-shifting digital holographic microscope are first studied and analyzed. We then demonstrate en face imaging with transverse resolution of $3\mathrm{\mu m}$ and axial resolution of $10\mathrm{\mu m}$ through a thickness of $300\mathrm{\mu m}$ onion membrane. In addition, with the above said resolu tions, optical sectioning of the eye and spine of a live zebra fish has been demonstrated. To the best of our knowledge, this is the first time that a short coherence phase-shifting holographic micro scope has been applied to the internal structure visualization of a biological specimen under an in vivo environment.

Holographic optical tweezers (HOT) is a programmable technique used for manipulation of microsized samples. In combination with computer-generation holography (CGH), a spatial light modulator reshapes the light distribution within the focal area of the optical tweezers. HOT can be used to realize real-time multiple-point manipulation in fluid, and this is useful in biological research. In this article, we summarize the HOT technique, discuss its recent developments, and present an overview of its biological applications.

This paper proposes a coded aperture structured illumination (CASI) technique in digital holographic microscopy (DHM). A CASI wave is generated using two binary phase codes (0° and 120°) for spatial phase shifting. The generated CASI wave then interferes with a reference wave to form a coded Fresnel hologram at a single exposure with compressive sensing (CS) to avoid the temporal phase-shifting process of the structured illumination (SI). The CS algorithm is applied to retrieve the missing data of decoded phase-shifted SI-modulated waves, which are used to separate overlapped spatial frequencies for obtaining a larger spatial frequency coverage to provide superresolution imaging. Two phase-only spatial light modulators are applied to generate a directional SI pattern for obtaining a coded aperture with a suitable size to perform one-shot acquisition in the DHM system.