Three-dimensional Refractive Index Distribution Research Articles

Alternating projection combined with fast gradient projection (FGP-AP) method for intensity-only measurement optical diffraction tomography in LED array microscopy.

Optical diffraction tomography (ODT) is a powerful label-free measurement tool that can quantitatively image the three-dimensional (3D) refractive index (RI) distribution of samples. However, the inherent "missing cone problem," limited illumination angles, and dependence on intensity-only measurements in a simplified imaging setup can all lead to insufficient information mapping in the Fourier domain, affecting 3D reconstruction results. In this paper, we propose the alternating projection combined with the fast gradient projection (FGP-AP) method to compensate for the above problem, which effectively reconstructs the 3D RI distribution of samples using intensity-only images captured from LED array microscopy. The FGP-AP method employs the alternating projection (AP) algorithm for gradient descent and the fast gradient projection (FGP) algorithm for regularization constraints. This approach is equivalent to incorporating prior knowledge of sample non-negativity and smoothness into the 3D reconstruction process. Simulations demonstrate that the FGP-AP method improves reconstruction quality compared to the original AP method, particularly in the presence of noise. Experimental results, obtained from mouse kidney cells and label-free blood cells, further affirm the superior 3D imaging efficacy of the FGP-AP method.

Spatial Fluctuations of Optical Turbulence Strength in a Laboratory Turbulence Simulator

Controlled turbulence simulators in the laboratory have been extensively employed to investigate turbulence effects on light propagation in the atmosphere, driven by some advanced optical engineering such as remote sensing, energy-delivery systems, and free-space optical communication systems. Many studies have achieved rich results on the optical turbulence intensity, scintillation index, and power spectral density characteristics of the light propagation path in the center of a turbulence simulator, but a comprehensive analysis of the optical turbulence characteristics for different spatial locations is still lacking. We simulate turbulence with air as the medium in a classical convective Rayleigh–Bénard turbulence simulator through high-resolution computational fluid dynamics methods, the three-dimensional refractive index distribution is obtained, and the optical properties are analyzed comprehensively. It is found that the hot and cold plumes and the large-scale circulation strongly influence the inhomogeneity of Cn2 in the turbulence tank, making it weak in the middle and strong near the boundary. The refractive index power spectral density at different heights is centrally symmetric, with the slope gradually deviating from the −5/3 scaling power with increasing distance from the central region. Under the log-log plot, the variation of the refractive index variance with height exhibits a three-segmented feature, showing in order: a stable region, a logarithmic profile, and a power-law profile, in the region close to the boundary. These results will contribute to the construction of a suitable turbulence simulator for optical engineering applications.

Quantitative real-time phase microscopy for extended depth-of-field imaging based on the 3D single-shot differential phase contrast (ssDPC) imaging method.

Optical diffraction tomography (ODT) is a promising label-free imaging method capable of quantitatively measuring the three-dimensional (3D) refractive index distribution of transparent samples. In recent years, partially coherent ODT (PC-ODT) has attracted increasing attention due to its system simplicity and absence of laser speckle noise. Quantitative phase imaging (QPI) technologies represented by Fourier ptychographic microscopy (FPM), differential phase contrast (DPC) imaging and intensity diffraction tomography (IDT) need to collect several or hundreds of intensity images, which usually introduce motion artifacts when shooting fast-moving targets, leading to a decrease in image quality. Hence, a quantitative real-time phase microscopy (qRPM) for extended depth of field (DOF) imaging based on 3D single-shot differential phase contrast (ssDPC) imaging method is proposed in this research study. qRPM incorporates a microlens array (MLA) to simultaneously collect spatial information and angular information. In subsequent optical information processing, a deconvolution method is used to obtain intensity stacks under different illumination angles in a raw light field image. Importing the obtained intensity stack into the 3D DPC imaging model is able to finally obtain the 3D refractive index distribution. The captured four-dimensional light field information enables the reconstruction of 3D information in a single snapshot and extending the DOF of qRPM. The imaging capability of the proposed qRPM system is experimental verified on different samples, achieve single-exposure 3D label-free imaging with an extended DOF for 160 µm which is nearly 30 times higher than the traditional microscope system.

Enhanced functionalities of immune cells separated by a microfluidic lattice: assessment based on holotomography.

The isolation of white blood cells (WBCs) from whole blood constitutes a pivotal process for immunological studies, diagnosis of hematologic disorders, and the facilitation of immunotherapy. Despite the ubiquity of density gradient centrifugation in WBC isolation, its influence on WBC functionality remains inadequately understood. This research employs holotomography to explore the effects of two distinct WBC separation techniques, namely conventional centrifugation and microfluidic separation, on the functionality of the isolated cells. We utilize three-dimensional refractive index distribution and time-lapse dynamics to analyze individual WBCs in-depth, focusing on their morphology, motility, and phagocytic capabilities. Our observations highlight that centrifugal processes negatively impact WBC motility and phagocytic capacity, whereas microfluidic separation yields a more favorable outcome in preserving WBC functionality. These findings emphasize the potential of microfluidic separation techniques as a viable alternative to traditional centrifugation for WBC isolation, potentially enabling more precise analyses in immunology research and improving the accuracy of hematologic disorder diagnoses.

A Coaxial Dual-Waveguide Fiber Coupler

We demonstrate a method to fabricate an in-fiber integrated multi-waveguide fiber coupler based on thermal diffusion technology to achieve stable and efficient coupling of a single-mode fiber to a multi-waveguide fiber. Simulation results show that the efficient coupling of a single-mode fiber and a multi-waveguide fiber can be realized by introducing double-clad fiber into single-mode fiber and multi-waveguide fiber. A coaxial dual-waveguide fiber coupler was fabricated based on thermal diffusion technology. The measurement results of the three-dimensional refractive index distribution of the coaxial dual-waveguide fiber coupler verified the feasibility of the thermal diffusion technology to fabricate the multi-waveguide fiber coupler. The insertion loss of the thermally diffused coaxial dual-waveguide fiber coupler was tested, and its performance was better than that of the fusion tapered coupler. The multi-waveguide fiber coupler fabricated by thermal diffusion technology allows for an all-fiber setup with coupling efficiency as high as 98%, achieves a relatively stable fundamental mode excitation in multi-waveguide fiber, requires minimal maintenance, and will accelerate the translation toward particle trapping, spectral detection, and optical communication.

Machine-learning-based diagnosis of thyroid fine-needle aspiration biopsy synergistically by Papanicolaou staining and refractive index distribution

We developed a machine learning algorithm (MLA) that can classify human thyroid cell clusters by exploiting both Papanicolaou staining and intrinsic refractive index (RI) as correlative imaging contrasts and evaluated the effects of this combination on diagnostic performance. Thyroid fine-needle aspiration biopsy (FNAB) specimens were analyzed using correlative optical diffraction tomography, which can simultaneously measure both, the color brightfield of Papanicolaou staining and three-dimensional RI distribution. The MLA was designed to classify benign and malignant cell clusters using color images, RI images, or both. We included 1535 thyroid cell clusters (benign: malignancy = 1128:407) from 124 patients. Accuracies of MLA classifiers using color images, RI images, and both were 98.0%, 98.0%, and 100%, respectively. As information for classification, the nucleus size was mainly used in the color image; however, detailed morphological information of the nucleus was also used in the RI image. We demonstrate that the present MLA and correlative FNAB imaging approach has the potential for diagnosing thyroid cancer, and complementary information from color and RI images can improve the performance of the MLA.

Quasi-Isotropic High-Resolution Fourier Ptychographic Diffraction Tomography with Opposite Illuminations

Optical diffraction tomography (ODT) is a powerful tool for the study of unlabeled biological cells thanks to its unique capability of measuring the three-dimensional (3D) refractive index (RI) distribution of samples quantitatively and noninvasively. In conventional transmission ODT, however, certain spatial frequency components along the optical axis cannot be measured due to the limited angular coverage of the incident beam, resulting in a poor axial resolution several times worse than the lateral one. In this Letter we propose a new type of ODT method, termed opposite illumination Fourier ptychographic diffraction tomography (OI-FPDT), which produces almost isotropic resolution by combining transmissive angle-scanning and reflective wavelength-scanning. Without resorting to interferometric detection, OI-FPDT requires an intensity-only measurement, and the forward and backward scattered intensity images are synthesized in the Fourier space to recover the 3D RI distribution of samples based on an iterative ptychographic reconstruction algorithm. To the best of our knowledge, this is the first time that near-isotropic resolution (∼ 274 nm) of ODT result is obtained in a non-interferometric and sample motion-free manner. Results of simulated cell phantom, tailor-made fiberglass, and onion epidermal cell samples confirm the validity of the proposed method.

Parallel synthetic aperture transport-of-intensity diffraction tomography with annular illumination.

Transport-of-intensity diffraction tomography (TIDT) is a recently developed label-free computational microscopy technique that retrieves high-resolution three-dimensional (3D) refractive index (RI) distribution of biological specimens from 3D intensity-only measurements. However, the non-interferometric synthetic aperture in TIDT is generally achieved sequentially through the acquisition of a large number of through-focus intensity stacks captured at different illumination angles, resulting in a very cumbersome and redundant data acquisition process. To this end, we present a parallel implementation of a synthetic aperture in TIDT (PSA-TIDT) with annular illumination. We found that the matched annular illumination provides a mirror-symmetric 3D optical transfer function, indicating the analyticity in the upper half-plane of the complex phase function, which allows for recovery of the 3D RI from a single intensity stack. We experimentally validated PSA-TIDT by conducting high-resolution tomographic imaging of various unlabeled biological samples, including human breast cancer cell lines (MCF-7), human hepatocyte carcinoma cell lines (HepG2), Henrietta Lacks (HeLa) cells, and red blood cells (RBCs).

Squid Skin Cell-Inspired Refractive Index Mapping of Cells, Vesicles, and Nanostructures

The fascination with the optical properties of naturally occurring systems has been driven in part by nature's ability to produce a diverse palette of vibrant colors from a relatively small number of common structural motifs. Within this context, some cephalopod species have evolved skin cells called iridophores and leucophores whose constituent ultrastructures reflect light in different ways but are composed of the same high refractive index material─a protein called reflectin. Although such natural optical systems have attracted much research interest, measuring the refractive indices of biomaterial-based structures across multiple different environments and establishing theoretical frameworks for accurately describing the obtained refractive index values has proven challenging. Herein, we employ a synergistic combination of experimental and computational methodologies to systematically map the three-dimensional refractive index distributions of model self-assembled reflectin-based structures both in vivo and in vitro. When considered together, our findings may improve understanding of squid skin cell functionality, augment existing methods for characterizing protein-based optical materials, and expand the utility of emerging holotomographic microscopy techniques.

Standardizing image assessment in optical diffraction tomography.

Optical diffraction tomography (ODT) has gradually become a popular label-free imaging technique that offers diffraction-limited resolution by mapping an object's three-dimensional (3D) refractive index (RI) distribution. However, there is a lack of comprehensive quantitative image assessment metrics in ODT for studying how various experimental conditions influence image quality, and subsequently optimizing the experimental conditions. In this Letter, we propose to standardize the image assessment in ODT by proposing a set of metrics, including signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and structural distinguishability (SD). To test the feasibility of the metrics, we performed experiments on angle-scanning ODT by varying the number of illumination angles, RI contrast of samples, sample feature sizes, and sample types (e.g., standard polystyrene beads and 3D printed structures) and evaluated the RI tomograms with SNR, CNR, and SD. We further quantitatively studied how image quality can be improved, and tested the image assessment metrics on subcellular structures of living cells. We envision the proposed image assessment metrics may greatly benefit end-users for assessing the RI tomograms, as well as experimentalists for optimizing ODT instruments.

Near-infrared, wavelength, and illumination scanning holographic tomography.

We present a holographic tomography technique in which the projections are acquired using both wavelength and illumination scanning in the near-infrared region. We show how to process the acquired data to obtain correct values of three-dimensional refractive index distributions in both single-wavelength and multi-wavelength data acquisition schemes and how to properly account for the dispersion of the sample. We perform numerical and experimental comparisons of different illumination scenarios to determine the most efficient measurement protocol. We show that the multi-wavelength protocol is advantageous in terms of signal-to-noise ratio and contrast-to-noise ratio over single-wavelength protocols, even for the same number of projections used for reconstructions. Finally, we show that this approach is suitable for providing high-quality refractive index distributions of relatively thick colon cancer samples.

Recovery of continuous 3D refractive index maps from discrete intensity-only measurements using neural fields

Intensity diffraction tomography (IDT) refers to a class of optical microscopy techniques for imaging the three-dimensional refractive index (RI) distribution of a sample from a set of two-dimensional intensity-only measurements. The reconstruction of artefact-free RI maps is a fundamental challenge in IDT due to the loss of phase information and the missing-cone problem. Neural fields has recently emerged as a new deep learning approach for learning continuous representations of physical fields. The technique uses a coordinate-based neural network to represent the field by mapping the spatial coordinates to the corresponding physical quantities, in our case the complex-valued refractive index values. We present Deep Continuous Artefact-free RI Field (DeCAF) as a neural-fields-based IDT method that can learn a high-quality continuous representation of a RI volume from its intensity-only and limited-angle measurements. The representation in DeCAF is learned directly from the measurements of the test sample by using the IDT forward model without any ground-truth RI maps. We qualitatively and quantitatively evaluate DeCAF on the simulated and experimental biological samples. Our results show that DeCAF can generate high-contrast and artefact-free RI maps and lead to an up to 2.1-fold reduction in the mean squared error over existing methods. Producing high-quality 3D refractive index maps from 2D intensity-only measurements is a long-standing objective in computational microscopy, with many applications involving the visualization of cellular and subcellular structures. A new method can reconstruct high-contrast and artefact-free images by employing the neural fields technique, which can learn a continuous 3D representation using a neural network that maps spatial coordinates to the refractive index values.

Freeform gradient-index media: a new frontier in freeform optics.

Freeform optics enable irregular system geometries and high optical performance by leveraging rotational variance. To this point, for both imaging and illumination, freeform optics has largely been synonymous with freeform surfaces. Here a new frontier in freeform optics is surveyed in the form of freeform gradient-index (F-GRIN) media. F-GRIN leverages arbitrary three-dimensional refractive index distributions to impart unique optical influence. When transversely variant, F-GRIN behaves similarly to freeform surfaces. By introducing a longitudinal refractive index variation as well, F-GRIN optical behavior deviates from that of freeform surfaces due to the effect of volume propagation. F-GRIN is a useful design tool that offers vast degrees of freedom and serves as an important complement to freeform surfaces in the design of advanced optical systems for both imaging and illumination.

Continuous-wave terahertz diffraction tomography for measuring three-dimensional refractive index maps

Three-dimensional (3D) refractive index (RI) distribution is important to reveal the object’s inner structure. We implemented terahertz (THz) diffraction tomography with a continuous-wave single-frequency THz source for measuring 3D RI maps. The off-axis holographic interference configuration was employed to obtain the quantitative scattered field of the object under each rotation angle. The 3D reconstruction algorithm adopted the filtered backpropagation method, which can theoretically calculate the exact scattering potential from the measured scattered field. Based on the Rytov approximation, the 3D RI distribution of polystyrene foam spheres was achieved with high fidelity, which verified the feasibility of the proposed method.

Rolling angle recovery of flowing cells in holographic tomography exploiting the phase similarity.

Holographic tomography allows the 3D mapping of the refractive index of biological samples thanks to reconstruction methods based on the knowledge of illumination directions or rotation angles of the imaged sample. Recently, phase contrast tomographic flow cytometry by digital holography has been demonstrated to reconstruct the three-dimensional refractive index distribution of single cells while they are flowing along microfluidic channels. In this system, the illumination direction is fixed while the sample's rotation is not deterministically known a priori but induced by hydrodynamic forces. We propose here a technique to retrieve the rolling angles, based on a new phase images similarity metric that is capable of identifying a cell's orientations from its 3D positioning while it is flowing along the microfluidic channel. The method is experimentally tested and also validated through appropriate numerical simulations. We provide demonstration of concept by achieving reconstruction of breast cancer cells tomography.

Three-dimensional tomography of red blood cells using deep learning

We accurately reconstruct three-dimensional (3-D) refractive index (RI) distributions from highly ill-posed two-dimensional (2-D) measurements using a deep neural network (DNN). Strong distortions are introduced on reconstructions obtained by the Wolf transform inversion method due to the ill-posed measurements acquired from the limited numerical apertures (NAs) of the optical system. Despite the recent success of DNNs in solving ill-posed inverse problems, the application to 3-D optical imaging is particularly challenging due to the lack of the ground truth. We overcome this limitation by generating digital phantoms that serve as samples for the discrete dipole approximation (DDA) to generate multiple 2-D projection maps for a limited range of illumination angles. The presented samples are red blood cells (RBCs), which are highly affected by the ill-posed problems due to their morphology. The trained network using synthetic measurements from the digital phantoms successfully eliminates the introduced distortions. Most importantly, we obtain high fidelity reconstructions from experimentally recorded projections of real RBC sample using the network that was trained on digitally generated RBC phantoms. Finally, we confirm the reconstruction accuracy using the DDA to calculate the 2-D projections of the 3-D reconstructions and compare them to the experimentally recorded projections.

Polymer optical bridges for efficient splicing of optical fibers

We present an application of optonumerical methodology for improvement of functional parameters of polymer optical bridges that connect two optical fibers. To fully determine and improve the properties of this kind of microstructure, experimental methods are combined with numerical modeling. The parameters describing the functionality of the polymer optical bridges are optical losses (insertion and return), which determine the usability of those elements as optical fiber splices. These parameters are the function of such features as refractive index distribution, microstructure geometry, and propagation of the light wavelength. To analyze the relation of those features on the functional parameters of the studied microstructures, the experimental results are compared to the ones obtained with simulations. Numerical modeling of the aforementioned optical bridges is performed by means of the finite-difference time-domain method. Experimental methods consist of optical diffraction tomography, which is used to obtain a full three-dimensional refractive index distribution of optical bridge, and measurement of optical losses. Implementation of the proposed methodology in iterative procedure allows the optimization of the fabrication procedure to produce efficient and reliable optical splices with desired functional parameters—insertion loss at the level of 0.2 dB and return loss above 60 dB.

Разработка алгоритмов сегментации в голографической микроскопии и томографии для определения морфологических параметров клеток

The paper presents development of cell segmentation algorithms on two-dimensional phase images and three-dimensional refractive index distributions obtained, respectively, by means of digital holographic microscopy and tomography. The algorithms were optimized for measurements of cells morphological parameters: volume, projected area and membrane area. The developed segmentation algorithms were validated and volume calculation error was estimated by comparison with the values obtained using confocal fluorescence tomography.

Super-resolution three-dimensional fluorescence and optical diffraction tomography of live cells using structured illumination generated by a digital micromirror device

We present a multimodal approach for measuring the three-dimensional (3D) refractive index (RI) and fluorescence distributions of live cells by combining optical diffraction tomography (ODT) and 3D structured illumination microscopy (SIM). A digital micromirror device is utilized to generate structured illumination patterns for both ODT and SIM, which enables fast and stable measurements. To verify its feasibility and applicability, the proposed method is used to measure the 3D RI distribution and 3D fluorescence image of various samples, including a cluster of fluorescent beads, and the time-lapse 3D RI dynamics of fluorescent beads inside a HeLa cell, from which the trajectory of the beads in the HeLa cell is analyzed using spatiotemporal correlations.

GPU-based deep convolutional neural network for tomographic phase microscopy with ℓ1 fitting and regularization.

Tomographic phase microscopy (TPM) is a unique imaging modality to measure the three-dimensional refractive index distribution of transparent and semitransparent samples. However, the requirement of the dense sampling in a large range of incident angles restricts its temporal resolution and prevents its application in dynamic scenes. Here, we propose a graphics processing unit-based implementation of a deep convolutional neural network to improve the performance of phase tomography, especially with much fewer incident angles. As a loss function for the regularized TPM, the ℓ1-norm sparsity constraint is introduced for both data-fidelity term and gradient-domain regularizer in the multislice beam propagation model. We compare our method with several state-of-the-art algorithms and obtain at least 14dB improvement in signal-to-noise ratio. Experimental results on HeLa cells are also shown with different levels of data reduction.