3D Refractive Index Distribution Research Articles

Deep-learning based 3D birefringence image generation using 2D multi-view holographic images

Refractive index stands as an inherent characteristic of a material, allowing non-invasive exploration of the three-dimensional (3D) interior of the material. Certain materials with different refractive indices produce a birefringence phenomenon in which incident light is split into two polarization components when it passes through the materials. Representative birefringent materials appear in calcite crystals, liquid crystals (LCs), biological tissues, silk fibers, polymer films, etc. If the internal 3D shape of these materials can be visually expressed through a non-invasive method, it can greatly contribute to the semiconductor, display industry, optical components and devices, and biomedical diagnosis. This paper introduces a novel approach employing deep learning to generate 3D birefringence images using multi-viewed holographic interference images. First, we acquired a set of multi-viewed holographic interference pattern images and a 3D volume image of birefringence directly from a polarizing DTT (dielectric tensor tomography)-based microscope system about each LC droplet sample. The proposed model was trained to generate the 3D volume images of birefringence using the two-dimensional (2D) interference pattern image set. Performance evaluations were conducted against the ground truth images obtained directly from the DTT microscopy. Visualization techniques were applied to describe the refractive index distribution in the generated 3D images of birefringence. The results show the proposed method’s efficiency in generating the 3D refractive index distribution from multi-viewed holographic interference images, presenting a novel data-driven alternative to traditional methods from the DTT devices.

3D Measurements and Characterizations of Refractive Index Distributions of Volume Holographic Gratings Using Low‐Coherence Holotomography

AbstractHolographic Optical Elements (HOEs) employ refractive index (RI) modulation to manipulate light, establishing their widespread application in augmented and virtual reality technologies. Despite significant strides in HOEs' fabrication, a comprehensive 3D examination and measurement of these elements remain largely unexplored. This study targets this void by conducting an in‐depth exploration of the 3D RI distributions of volume holographic gratings (VHGs), a quintessential representative of HOEs. Direct tomographic measurements of the 3D RI distributions within millimeter‐scale VHGs are performed at a spatial resolution of 156 nm × 156 nm × 1.2 µm and an RI precision of 2×10−4. This level of precision facilitates a systematic high‐resolution characterization of VHGs. The findings present a substantial evolution from traditional measurement techniques and promise to considerably advance the evaluation of intricate HOE structures and refine the corresponding fabrication processes.

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.

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.

Multi-harmonic structured illumination-based optical diffraction tomography

Imaging speed and spatial resolution are key factors in optical diffraction tomography (ODT), while they are mutually exclusive in 3D refractive index imaging. This paper presents a multi-harmonic structured illumination-based optical diffraction tomography (MHSI-ODT) to acquire 3D refractive index (RI) maps of transparent samples. MHSI-ODT utilizes a digital micromirror device (DMD) to generate structured illumination containing multiple harmonics. For each structured illumination orientation, four spherical spectral crowns are solved from five phase-shifted holograms, meaning that the acquisition of each spectral crown costs 1.25 raw images. Compared to conventional SI-ODT, which retrieves two spectral crowns from three phase-shifted raw images, MHSI-ODT enhances the imaging speed by 16.7% in 3D RI imaging. Meanwhile, MHSI-ODT exploits both the 1st-order and the 2nd-order harmonics; therefore, it has a better intensity utilization of structured illumination. We demonstrated the performance of MHSI-ODT by rendering the 3D RI distributions of 5 µm polystyrene (PS) microspheres and biological samples.

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.

Efficient and accurate intensity diffraction tomography of multiple-scattering samples.

Optical Diffraction Tomography (ODT) is a label-free method to quantitatively estimate the 3D refractive index (RI) distributions of microscopic samples. Recently, significant efforts were directed towards methods to model multiple-scattering objects. The fidelity of reconstructions rely on accurately modelling light-matter interactions, but the efficient simulation of light propagation through high-RI structures over a large range of illumination angles is still challenging. Here we present a solution dealing with these problems, proposing a method that allows one to efficiently model the tomographic image formation for strongly scattering objects illuminated over a wide range of angles. Instead of propagating tilted plane waves we apply rotations on the illuminated object and optical field and formulate a new and robust multi-slice model suitable for high-RI contrast structures. We test reconstructions made by our approach against simulations and experiments, using rigorous solutions to Maxwell's equations as ground truth. We find the proposed method to produce reconstructions of higher fidelity compared to conventional multi-slice methods, especially for the challenging case of strongly scattering samples where conventional reconstruction methods fail.

Influence of Yokukansan on the refractive index of neuroblastoma cells.

Yokukansan (YKS) is a traditional Japanese herbal medicine that is increasingly being studied for its effects on neurodegenerative diseases. In our study, we presented a novel methodology for a multimodal analysis of the effects of YKS on nerve cells. The measurements of 3D refractive index distribution and its changes performed by holographic tomography were supported with an investigation by Raman micro-spectroscopy and fluorescence microscopy to gather complementary morphological and chemical information about cells and YKS influence. It was shown that at the concentrations tested, YKS inhibits proliferation, possibly involving reactive oxygen species. Also substantial changes in the cell RI after few hours of YKS exposure were detected, followed by longer-term changes in cell lipid composition and chromatin state.

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).

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.

Loss Minimized Data Reduction in Single-Cell Tomographic Phase Microscopy Using 3D Zernike Descriptors

Tomographic phase microscopy (TPM) in flow cytometry is one of the most promising computational imaging techniques for the quantitative 3-dimensional (3D) analysis of unstained single cells. Continuous cells’ flow, combined with the stain-free mode, can assure the high-throughput collection of quantitative and informative 3D data. TPM promises to allow rapid cells’ screening by a nondestructive technique and with statistically relevant data. The current leading-edge research aimed at developing TPM systems in flow cytometry has already demonstrated the possibility of acquiring thousands of single-cell tomograms. Nevertheless, a key unsolved problem exists about the efficient storage and easy handling of such a huge amount of 3D data that prevents rapid analysis for cell diagnosis. Here, we show, for the first time, an effective encoding strategy of single-cell tomograms that can completely overcome this critical bottleneck. Essentially, by using the 3D version of Zernike polynomials, we demonstrate that the 3D refractive index distribution of a cell can be straightforwardly encoded in 1D with negligible information loss (<1%), thus greatly streamlining the data handling and storage. The performance analysis of the proposed method has been first assessed on simulated tomographic cell phantom, while the experimental validation has been extensively proofed on tomographic data from experiments with different cell lines. The results achieved here imply an intriguing breakthrough for TPM that promises to unlock computational pipelines for analyzing 3D data that were unattainable until now.

Refractive index dispersion measurement in the short-wave infrared range using synthetic phase microscopy.

Refractive index is an optical property explored in the light scattering measurement of micro- and nano-particles as well as in label-free imaging of cells and tissues. Because the refractive index value is a major input to the characterization and quantification of the analyzed specimens, various methods have been developed targeting at different sample types. In this paper, we demonstrate a technique for the refractive index measurement of homogeneous microspheres and liquids in the short-wave infrared (SWIR) range. We use synthetic phase microscopy (SPM), which records a scattering-corrected projection of the 3D refractive index distribution, in combination with a least-squares fitting to a theoretical model of a sphere. Using the method, we determine the refractive index dispersion of two polymer microspheres (polymethyl methacrylate and polystyrene), two glass microspheres (silica and soda lime), and three microscopy mounting media (glycerol, FluorSave, and Eukitt) in the SWIR range of 1100-1650 nm.

Transport-of-intensity Fourier ptychographic diffraction tomography: defying the matched illumination condition

Optical diffraction tomography (ODT) is a promising label-free three-dimensional (3D) microscopic method capable of measuring the 3D refractive index (RI) distribution of optically transparent samples (e.g., unlabeled biological cells). In recent years, non-interferometric ODT techniques have received increasing attention for their system simplicity, speckle-free imaging quality, and compatibility with existing microscopes. However, ODT methods for implementing non-interferometric measurements in high numerical aperture (NA) microscopy systems are often plagued by low-frequency missing problems—a consequence of violating the matched illumination condition. Here, we present transport-of-intensity Fourier ptychographic diffraction tomography (TI-FPDT) to address this challenging issue by combining ptychographic angular diversity with additional “transport of intensity” measurements. TI-FPDT exploits the defocused phase contrast to circumvent the stringent requirement on the illumination NA imposed by the matched illumination condition. It effectively overcomes the reconstruction quality deterioration and RI underestimation problems in conventional FPDT, as demonstrated by high-resolution tomographic imaging of various unlabeled transparent samples (including microspheres, USAF targets, HeLa cells, and C2C12 cells). Due to its simplicity and effectiveness, TI-FPDT is anticipated to open new possibilities for label-free 3D microscopy in various biomedical applications.

Characterization of two-photon photopolymerization fabrication using high-speed optical diffraction tomography

Two-photon photopolymerization (TPP) has recently become a popular method for the fabrication of three-dimensional (3D) micro- and nanostructures. The reproduction fidelity of the designed micro- and nanostructures is influenced by experimental writing conditions, including laser power, exposure time, etc. To determine the appropriate writing parameters, characterization of morphological features and surface roughness during the experiment is needed. Traditional characterization methods for TPP, e.g., scanning electron microscopy and atomic force microscopy, have limited speed and cannot study internal structures without invasive approaches. Optical diffraction tomography (ODT) is an emerging label-free 3D imaging technique based on reconstructing the object’s 3D refractive index (RI) distribution with diffraction-limited resolution. Here, we propose a non-invasive solution to fully characterize the TPP-fabricated structures using a high-speed ODT technique, which can eliminate the need for complex sample preparation, such as fluorescence labelling or metal-coating, and achieve a full 3D measurement time of 6 ms. By visualizing and studying different TPP-fabricated structures, including embedded spirals and cubes, via the ODT system, the fabrication quality, including 3D morphological features, exposure levels, and surface roughness, can be examined quantitatively. The results suggest our method can effectively improve the fabrication quality and reproducibility of TPP, generating impacts on the nanofabrication community.

Quantitative refractive index tomography of millimeter-scale objects using single-pixel wavefront sampling

Optical diffraction tomography (ODT) is broadly employed to study 3D structures of transparent objects in a stain-free manner. ODT is commonly implemented with an interferometric setup, but its applications on mesoscopic objects have been challenging due to its limited phase detection range. We introduce an ODT method capable of producing 3D refractive index (RI) distribution via a single-pixel detector. Our method exploits a single-pixel wavefront sensor to measure two-dimensional complex information of millimeter-scale weakly absorbing objects at various projection angles. The application of the Fourier diffraction (or slice) theorem to the acquired complex images results in an RI tomogram of transparent objects. The experiments with calibrated objects and zebrafish larvae demonstrate its promise for measuring the RI tomogram of large and weakly absorbing objects beyond the visible spectral range.

High-fidelity intensity diffraction tomography with a non-paraxial multiple-scattering model.

We propose a novel intensity diffraction tomography (IDT) reconstruction algorithm based on the split-step non-paraxial (SSNP) model for recovering the 3D refractive index (RI) distribution of multiple-scattering biological samples. High-quality IDT reconstruction requires high-angle illumination to encode both low- and high- spatial frequency information of the 3D biological sample. We show that our SSNP model can more accurately compute multiple scattering from high-angle illumination compared to paraxial approximation-based multiple-scattering models. We apply this SSNP model to both sequential and multiplexed IDT techniques. We develop a unified reconstruction algorithm for both IDT modalities that is highly computationally efficient and is implemented by a modular automatic differentiation framework. We demonstrate the capability of our reconstruction algorithm on both weakly scattering buccal epithelial cells and strongly scattering live C. elegans worms and live C. elegans embryos.

Developing a Reliable Holographic Flow Cyto-Tomography Apparatus by Optimizing the Experimental Layout and Computational Processing.

Digital Holographic Tomography (DHT) has recently been established as a means of retrieving the 3D refractive index mapping of single cells. To make DHT a viable system, it is necessary to develop a reliable and robust holographic apparatus in order that such technology can be utilized outside of specialized optics laboratories and operated in the in-flow modality. In this paper, we propose a quasi-common-path lateral-shearing holographic optical set-up to be used, for the first time, for DHT in a flow-cytometer modality. The proposed solution is able to withstand environmental vibrations that can severely affect the interference process. Furthermore, we have scaled down the system while ensuring that a full 360° rotation of the cells occurs in the field-of-view, in order to retrieve 3D phase-contrast tomograms of single cells flowing along a microfluidic channel. This was achieved by setting the camera sensor at 45° with respect to the microfluidic direction. Additional optimizations were made to the computational elements to ensure the reliable retrieval of 3D refractive index distributions by demonstrating an effective method of tomographic reconstruction, based on high-order total variation. The results were first demonstrated using realistic 3D numerical phantom cells to assess the performance of the proposed high-order total variation method in comparison with the gold-standard algorithm for tomographic reconstructions: namely, filtered back projection. Then, the proposed DHT system and the processing pipeline were experimentally validated for monocytes and mouse embryonic fibroblast NIH-3T3 cells lines. Moreover, the repeatability of these tomographic measurements was also investigated by recording the same cell multiple times and quantifying the ability to provide reliable and comparable tomographic reconstructions, as confirmed by a correlation coefficient greater than 95%. The reported results represent various steps forward in several key aspects of in-flow DHT, thus paving the way for its use in real-world applications.

Multimodal image reconstruction from tomographic diffraction microscopy data.

Tomographic diffraction microscopy (TDM) is a tool of choice for high-resolution, marker-less 3D imaging of biological samples. Based on a generalization of digital holographic microscopy with full control of the sample's illumination, TDM measures, from many illumination directions, the diffracted fields in both phase and amplitude. Photon budget associated to TDM imaging is low. Therefore, TDM is not limited by phototoxicity issues. The recorded information makes it possible to reconstruct 3D refractive index distribution (with both refraction and absorption contributions) of the object under scrutiny, without any staining. In this contribution, we show an alternate use of this information. A tutorial for multimodal image reconstruction is proposed. Both intensity contrasts and phase contrasts are proposed, from the image formation model to the final reconstruction with both 2D and 3D rendering, turning TDM into a kind of 'universal' digitalmicroscope.

Transport of intensity diffraction tomography with non-interferometric synthetic aperture for three-dimensional label-free microscopy

We present a new label-free three-dimensional (3D) microscopy technique, termed transport of intensity diffraction tomography with non-interferometric synthetic aperture (TIDT-NSA). Without resorting to interferometric detection, TIDT-NSA retrieves the 3D refractive index (RI) distribution of biological specimens from 3D intensity-only measurements at various illumination angles, allowing incoherent-diffraction-limited quantitative 3D phase-contrast imaging. 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. Based on an off-the-shelf bright-field microscope with a programmable light-emitting-diode (LED) illumination source, TIDT-NSA achieves an imaging resolution of 206 nm laterally and 520 nm axially with a high-NA oil immersion objective. We validate the 3D RI tomographic imaging performance on various unlabeled fixed and live samples, including human breast cancer cell lines MCF-7, human hepatocyte carcinoma cell lines HepG2, mouse macrophage cell lines RAW 264.7, Caenorhabditis elegans (C. elegans), and live Henrietta Lacks (HeLa) cells. These results establish TIDT-NSA as a new non-interferometric approach to optical diffraction tomography and 3D label-free microscopy, permitting quantitative characterization of cell morphology and time-dependent subcellular changes for widespread biological and medical applications.

Crescent-shaped shadow of second harmonic generation in dielectric microsphere/TMD monolayer heterostructure

For heterointerfaces at micro/nano scales, extremely-space-confined second harmonic generation (SHG) of transition metal dichalcogenide (TMD) monolayers can facilitate the extraction of TMD monolayers’ 3D dielectric environment. Here, we construct SiO2 microsphere/MoS2 monolayer (3D/2D) heterostructures and spatially resolve their SHG distributions via pixel-to-pixel spatial mapping. Asymmetric 3D refractive index distribution of the microsphere is successfully projected to 2D plane of TMD monolayer and visualized by corresponding 2D image of SHG intensity distribution, which presents a crescent-shaped shadow. Out results open up new possibilities for 3D interfacial sensing and imaging with SHG of 2D monolayers.