3D Refractive Index Research Articles

Continuous-wave terahertz in-line holographic diffraction tomography with the scattering fields reconstructed by a physics-enhanced deep neural network

Diffraction tomography is a promising, quantitative, and nondestructive three-dimensional (3D) imaging method that enables us to obtain the complex refractive index distribution of a sample. The acquisition of the scattered fields under the different illumination angles is a key issue, where the complex scattered fields need to be retrieved. Presently, in order to develop terahertz (THz) diffraction tomography, the advanced acquisition of the scattered fields is desired. In this paper, a THz in-line digital holographic diffraction tomography (THz-IDHDT) is proposed with an extremely compact optical configuration and implemented for the first time, to the best of our knowledge. A learning-based phase retrieval algorithm by combining the physical model and the convolution neural networks, named the physics-enhanced deep neural network (PhysenNet), is applied to reconstruct the THz in-line digital hologram, and obtain the complex amplitude distribution of the sample with high fidelity. The advantages of the PhysenNet are that there is no need for pretraining by using a large set of labeled data, and it can also work for thick samples. Experimentally with a continuous-wave THz laser, the PhysenNet is first demonstrated by using the thin samples and exhibits superiority in terms of imaging quality. More importantly, with regard to the thick samples, PhysenNet still works well, and can offer 2D complex scattered fields for diffraction tomography. Furthermore, the 3D refractive index maps of two types of foam sphere samples are successfully reconstructed by the proposed method. For a single foam sphere, the relative error of the average refractive index value is only 0.17%, compared to the commercial THz time-domain spectroscopy system. This demonstrates the feasibility and high accuracy of the THz-IDHDT, and the idea can be applied to other wavebands as well.

Label-Free Intracellular Multi-Specificity in Yeast Cells by Phase-Contrast Tomographic Flow Cytometry.

In-flow phase-contrast tomography provides a 3D refractive index of label-free cells in cytometry systems. Its major limitation, as with any quantitative phase imaging approach, is the lack of specificity compared to fluorescence microscopy, thus restraining its huge potentialities in single-cell analysis and diagnostics. Remarkable results in introducing specificity are obtained through artificial intelligence (AI), but only for adherent cells. However, accessing the 3D fluorescence ground truth and obtaining accurate voxel-level co-registration of image pairs for AI training is not viable for high-throughput cytometry. The recent statistical inference approach is a significant step forward for label-free specificity but remains limited to cells' nuclei. Here, a generalized computational strategy based on a self-consistent statistical inference to achieve intracellular multi-specificity is shown. Various subcellular compartments (i.e., nuclei, cytoplasmic vacuoles, the peri-vacuolar membrane area, cytoplasm, vacuole-nucleus contact site) can be identified and characterized quantitatively at different phases of the cells life cycle by using yeast cells as a biological model. Moreover, for the first time, virtual reality is introduced for handling the information content of multi-specificity in single cells. Full fruition is proofed for exploring and interacting with 3D quantitative biophysical parameters of the identified compartments on demand, thus opening the route to a metaverse for 3D microscopy.

LED array microscopy system correction method with comprehensive error parameters optimized by phase smoothing criterion.

LED array microscopy is a novel computational imaging technique that can achieve two-dimensional (2D) phase imaging and three-dimensional (3D) refractive index imaging with both high resolution and a large field of view. Although its experimental setup is simple, the errors caused by LED array position and light source central wavelength obviously decrease the quality of reconstructed results. To solve this problem, comprehensive error parameters optimized by the phase smoothing criterion are put forward in this paper. The central wavelength error and 3D misalignment model with six freedom degree errors of LED array are considered as the comprehensive error parameters when the spatial positional and optical features of arbitrarily placed LED array are unknown. Phase smoothing criterion is also introduced to the cost function for optimizing comprehensive error parameters to improve the convergence results. Compared with current system correction methods, the simulation and experimental results show that the proposed method in this paper has the best reconstruction accuracy, which can be well applied to an LED array microscope system with unknown positional and optical features of the LED array.

Three-dimensional refractive index estimation based on deep-inverse non-interferometric optical diffraction tomography (ODT-Deep).

Optical diffraction tomography (ODT) solves an inverse scattering problem to obtain label-free, 3D refractive index (RI) estimation of biological specimens. This work demonstrates 3D RI retrieval methods suitable for partially-coherent ODT systems supported by intensity-only measurements consisting of axial and angular illumination scanning. This framework allows for access to 3D quantitative RI contrast using a simplified non-interferometric technique. We consider a traditional iterative tomographic solver based on a multiple in-plane representation of the optical scattering process and gradient descent optimization adapted for focus-scanning systems, as well as an approach that relies solely on 3D convolutional neural networks (CNNs) to invert the scattering process. The approaches are validated using simulations of the 3D scattering potential for weak phase 3D biological samples.

Tuning 3D refractive indices via constrained uniaxial stretch in cellulose triacetate films plasticized with triethyl citrate

Tuning 3D refractive indices of polymers is urgently needed for optical films, but it is quite challenging. Here, we proposed a simple constrained uniaxial stretch method that successfully tuned the 3D refractive indices in cellulose triacetate (TAC) films plasticized with triethyl citrate (TEC). Our results suggest that, under constrained uniaxial stretch, the main chains and side groups prefer to orientate in the stretch direction and the constrained direction, respectively. Such a unique chain arrangement differentiates the refractive indices in three directions of the film. The branched small molecule TEC is also crucial for tuning refractive indices, which promotes chain activity and enhances the chain orientation under stretching, leading to a considerable change in refractive indices before samples fracture. The polymer film we fabricated possesses a direction-dependent optical performance, where the refractive index in the film thickness direction is between that of the stretch direction and constrained direction. This work provides a fundamental understanding on the chain structure and optical performance of polymer films. The constrained uniaxial stretch method, in general, should also be applicable to tuning other 3D physical properties through tuning the direction-dependent orientation of polymers.

Electronic band structures and optical properties of 2D XOF (X = Ga or In) oxyfluoride monolayers using density functional theory and GW approximation

The class of two-dimensional oxyfluoride monolayers is currently considered one of the most attractive nanomaterials for enhancing design and pushing the limits of different cutting-edge technologies. Two-dimensional semiconductor materials are the most promising systems for various applications in optoelectronic devices because they have a unique optical properties. We continue in this way by investigating the GW band structures and optical properties of unique 2D XOF (X = Ga or In) oxyfluoride monolayers, involving absorption, conductivity, refractive index, and dielectric function. We find no imaginary frequencies in the computed phonon spectra, indicating that these systems are dynamically stable. Furthermore, GaOF and InOF stay stable for temperatures T ≤ 840 K. The band gap of GaOF obtained with the single shot (G0W0) is larger than the band gap energy Eg of InOF. Where the direct band gap energies of GaOF and InOF are 6.1 eV and 4.8 eV, respectively. Our GW(PBE) numerical simulations demonstrate that the GaOF monolayer moves transparent once the frequency of the incoming light exceeds the plasma frequency (35.00 eV). Furthermore, InOF switches transparently once the incident light frequency exceeds the plasma frequency ∼ 35.00 eV. Interestingly, we obtain that these 2D sheets have a strong absorption coefficient in the range of ∼ 3.00–60.00 eV. They are emerging as a potential for the building blocks of the nano-size and ultra-thin optoelectronics of the future since they productively emit and absorb light.

All-dielectric terahertz wave metagrating lens based on 3D printing low refractive index material

A metagrating lens with a high numerical aperture (NA = 0.9) is designed based on the grating diffraction principle and the unit structure of the asymmetric scattering mode. The metagrating lens is composed of all-dielectric material with low refractive index and achieves good focusing at an operating frequency of 0.1 THz. In our experiments, we used 3D printing technology to fabricate the metagrating lens to further reduce the fabrication cost of the metalens and avoid the disadvantages of conventional optical devices that are large and costly.

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.

Single‐Step 3D Printing of Micro‐Optics with Adjustable Refractive Index by Ultrafast Laser Nanolithography

AbstractLaser exposure defines voxel's dimensions as essential building blocks in direct write 3D nanolithography. However, the exposure conditions not only influence the size of the produced features but also their optical properties. This empowers the realization of an adjustable refractive index out of single material by varying the writing strategy while preserving laser 3D nanolithography's flexibility in geometry and high resolution. Here, the refractive index for the 450–1600 nm spectral range of the micro‐optics out of SZ2080 hybrid polymer is systematically studied by applying ray and wave optics approaches followed by optical resolution analysis. It reveals the exact value of the laser‐printed components instead of the determination assessed by other techniques measuring thin films or bulky volumes of the investigated substance. The studied micro‐lenses are of below 100 µm in dimensions and a clear distinction in their performance on low and high exposure doses is found by analyzing it in all different approaches and validating using different lithography setups. Findings reveal the complexity of the refractive index of the 3D micro‐optics which is influenced by the material density and morphology. A route for freedom in 3D printing shape and refractive index can be realized by the technological optimization of delicate exposure control in ultrafast laser nanolithography.

Development of a 3D ultrafast laser written near-infrared spectro-interferometer.

Direct ultrafast laser photoinscription of transparent materials is a powerful technique for the development of embedded 3D photonics. This is particularly adaptable for astrophotonic devices when a number of inputs are required. The process relies essentially on volume fabrication of waveguiding structures in flexible 3D designs and refractive index contrast parameters adjustable for specific spectral ranges. This enables 3D geometry and thus avoids in-plane crossings of waveguides that can induce losses and cross talk in multi-telescope beam combiners. The additional novel capability of the technique allows for the fabrication of high aspect ratio nanostructures nonperturbatively sampling the optical field. Combining ultrafast laser micro- and nanoprocessing with engineered beams, we present here results for the development of chip-sized silica glass integrated robust 3D three-telescope beam combiners in the near-IR range, as well as embedded diffraction gratings, for phase closure analysis and spectro-interferometry applications in astronomy.

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.

Partially coherent broadband 3D optical transfer functions with arbitrary temporal and angular power spectra.

Optical diffraction tomography is a powerful technique to produce 3D volumetric images of biological samples using contrast produced by variations in the index of refraction in an unlabeled specimen. While this is typically performed with coherent illumination from a variety of angles, interest has grown in partially coherent methods due to the simplicity of the illumination and the computation-free axial sectioning provided by the coherence window of the source. However, such methods rely on the symmetry or discretization of a source to facilitate quantitative analysis and are unable to efficiently handle arbitrary illumination that may vary asymmetrically in angle and continuously in the spectrum, such as diffusely scattered or thermal sources. A general broadband theory may expand the scope of illumination methods available for quantitative analysis, as partially coherent sources are commonly available and may benefit from the effects of spatial and temporal incoherence. In this work, we investigate partially coherent tomographic phase microscopy from arbitrary sources regardless of angular distribution and spectrum by unifying the effects of spatial and temporal coherence into a single formulation. This approach further yields a method for efficient computation of the overall systems' optical transfer function, which scales with O(n 3), down from O(mn 4) for existing convolutional methods, where n 3 is the number of spatial voxels in 3D space and m is the number of discrete wavelengths in the illumination spectrum. This work has important implications for enabling partially coherent 3D quantitative phase microscopy and refractive index tomography in virtually any transmission or epi-illumination microscope.

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.

Bond-selective intensity diffraction tomography

Recovering molecular information remains a grand challenge in the widely used holographic and computational imaging technologies. To address this challenge, we developed a computational mid-infrared photothermal microscope, termed Bond-selective Intensity Diffraction Tomography (BS-IDT). Based on a low-cost brightfield microscope with an add-on pulsed light source, BS-IDT recovers both infrared spectra and bond-selective 3D refractive index maps from intensity-only measurements. High-fidelity infrared fingerprint spectra extraction is validated. Volumetric chemical imaging of biological cells is demonstrated at a speed of ~20 s per volume, with a lateral and axial resolution of ~350 nm and ~1.1 µm, respectively. BS-IDT’s application potential is investigated by chemically quantifying lipids stored in cancer cells and volumetric chemical imaging on Caenorhabditis elegans with a large field of view (~100 µm x 100 µm).

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.