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Abstract Retrieving electrical impedance maps at the nanoscale rapidly via nondestructive inspection with a high signal-to-noise ratio is an unmet need, likely to impact various applications from biomedicine to energy conversion. In this study, we develop a multimodal functional imaging instrument that is characterized by the dual capability of impedance mapping and phase quantitation, high spatial resolution, and low temporal noise. To achieve this, we advance a quantitative phase imaging system, referred to as epi-magnified image spatial spectrum microscopy combined with electrical actuation, to provide complementary maps of the optical path and electrical impedance. We demonstrate our system with high-resolution maps of optical path differences and electrical impedance variations that can distinguish nanosized, semi-transparent, structured coatings involving two materials with relatively similar electrical properties. We map heterogeneous interfaces corresponding to an indium tin oxide layer exposed by holes with diameters as small as ~550 nm in a titanium (dioxide) over-layer deposited on a glass support. We show that electrical modulation during the phase imaging of a macro-electrode is decisive for retrieving electrical impedance distributions with submicron spatial resolution and beyond the limitations of electrode-based technologies (surface or scanning technologies). The findings, which are substantiated by a theoretical model that fits the experimental data very well enable achieving electro-optical maps with high spatial and temporal resolutions. The virtues and limitations of the novel optoelectrochemical method that provides grounds for a wider range of electrically modulated optical methods for measuring the electric field locally are critically discussed. 

Abstract In 1969, Emil Wolf proposed diffraction tomography using coherent holographic imaging to extract 3D information from transparent, inhomogeneous objects. In the same era, the Wolf equations were first used to describe the propagation correlations associated with partially coherent fields. Combining these two concepts, we present Wolf phase tomography (WPT), which is a method for performing diffraction tomography using partially coherent fields. WPT reconstruction works directly in the space–time domain, without the need for Fourier transformation, and decouples the refractive index (RI) distribution from the thickness of the sample. We demonstrate the WPT principle using the data acquired by a quantitative-phase-imaging method that upgrades an existing phase-contrast microscope by introducing controlled phase shifts between the incident and scattered fields. The illumination field in WPT is partially spatially coherent (emerging from a ring-shaped pupil function) and of low temporal coherence (white light), and as such, it is well suited for the Wolf equations. From three intensity measurements corresponding to different phase-contrast frames, the 3D RI distribution is obtained immediately by computing the Laplacian and second time derivative of the measured complex correlation function. We validate WPT with measurements of standard samples (microbeads), spermatozoa, and live neural cultures. The high throughput and simplicity of this method enables the study of 3D, dynamic events in living cells across the entire multiwell plate, with an RI sensitivity on the order of 10 −5 . 

Abstract Understanding the mechanisms by which neurons create or suppress connections to enable communication in brain-derived neuronal cultures can inform how learning, cognition and creative behavior emerge. While prior studies have shown that neuronal cultures possess self-organizing criticality properties, we further demonstrate that in vitro brain-derived neuronal cultures exhibit a self-optimization phenomenon. More precisely, we analyze the multiscale neural growth data obtained from label-free quantitative microscopic imaging experiments and reconstruct the in vitro neuronal culture networks (microscale) and neuronal culture cluster networks (mesoscale). We investigate the structure and evolution of neuronal culture networks and neuronal culture cluster networks by estimating the importance of each network node and their information flow. By analyzing the degree-, closeness-, and betweenness-centrality, the node-to-node degree distribution (informing on neuronal interconnection phenomena), the clustering coefficient/transitivity (assessing the “small-world” properties), and the multifractal spectrum, we demonstrate that murine neurons exhibit self-optimizing behavior over time with topological characteristics distinct from existing complex network models. The time-evolving interconnection among murine neurons optimizes the network information flow, network robustness, and self-organization degree. These findings have complex implications for modeling neuronal cultures and potentially on how to design biological inspired artificial intelligence. 

Tissue birefringence is an intrinsic marker of potential value for cancer diagnosis. Traditionally, birefringence properties have been studied by using intensity-based formalisms, through the Mueller matrix algebra. On the other hand, the Jones matrix description allows for a direct assessment of the sample’s anisotropic response. However, because Jones algebra is based on complex fields, requiring measurements of both phase and amplitude, it is less commonly used. Here we propose a real-time imaging method for measuring Jones matrices by quantitative phase imaging. We combine a broadband phase imaging system with a polarization-sensitive detector to obtain Jones matrices at each point in a megapixel scale image, with near video rate capture speeds. To validate the utility of our approach, we measured standard targets, partially birefringent samples, dynamic specimens, and thinly sliced histopathological tissue.