Reconstruction Of Refractive Index Research Articles

Integrated Optical Waveguide Electric Field Sensors Based on Bismuth Germanate.

Bismuth germanate (Bi4Ge3O12, BGO) is a widely used optical sensing material with a high electro-optic coefficient, ideal for optical electric field sensors. Achieving high precision in electric field sensing requires fabricating optical waveguides on BGO. Traditional waveguide writing methods face challenges with this material. This study explores using femtosecond laser writing technology for preparing waveguides on BGO, leveraging ultrafast optical fields for superior material modification. Our experimental analysis shows that a cladding-type waveguide, written with a femtosecond laser at 200 kHz repetition frequency and 10.15 mW average power (pulse energy of 50.8 nJ), exhibits excellent light-guiding characteristics. Simulations of near-field optical intensity distribution and refractive index variations using the refractive index reconstruction method demonstrate that the refractive index modulation ensures single-mode transmission and effectively confines light to the core layer. In situ refractive index characterization confirms the feasibility of fabricating a waveguide with a refractive index reduction on BGO. The resulting waveguide has a loss per unit length of approximately 1.2 dB/cm, marking a successful fabrication. Additionally, we design an antenna electrode, analyze sensor performance indicators, and integrate a preparation process plan for the antenna electrode. This achievement establishes a solid experimental foundation for future studies on BGO crystal waveguides in electric field measurement applications.

Bidirectional in-silico clearing approach for deep refractive-index tomography using a sparsely sampled transmission matrix.

Optical diffraction tomography (ODT) enables the label-free volumetric imaging of biological specimens by mapping their three-dimensional refractive index (RI) distribution. However, the depth of imaging achievable is restricted due to spatially inhomogeneous RI distributions that induce multiple scattering. In this study, we introduce a novel ODT technique named bidirectional in-silico clearing RI tomography. This method incorporates both forward and reversed in-silico clearing. For the reversed in-silico clearing, we have integrated an ODT reconstruction framework with a transmission matrix approach, which enables RI reconstruction and wave backpropagation from the illumination side without necessitating modifications to the conventional ODT setup. Furthermore, the framework employs a sparsely sampled transmission matrix, significantly reducing the requisite number of measurements and computational expenses. Employing this proposed technique, we successfully imaged a spheroid with a thickness of 263 µm, corresponding to 11.4 scattering mean free paths. This method was successfully applied to various biological specimens, including liver and colon spheroids, demonstrating consistent imaging performance across samples with varied morphologies.

Возможность применения метода Гершберга-Папулиса в задаче реконструкции фазовой структуры по малоракурсным гильбертограммам

The possibility of processing small-view hilbertograms by the Gershberg-Papulis method to restore the refractive index of phase objects is discussed. The method consists in iterative transitions from estimating a function in the Fourier plane to estimating it in a coordinate space with an adjustment using a priori information. The spectrum of the function is determined on the entire frequency plane as an iterative process result Numerical simulation of the refractive index reconstruction for various test functions was performed using the Gershberg-Papulis method using Radon data known for four angles. Experimental studies on the Hilbert diagnostics example of reacting media (flames) in a high-speed shooting mode (up to 2000 frames per second) were performed using a four-angle tomographic complex implemented on the basis of an upgraded IAB-463M shadow device.

Quantitative parameter reconstruction from optical coherence tomographic data

Quantitative tissue information, like the light scattering properties, is considered as a key player in the detection of cancerous cells in medical diagnosis. A promising method to obtain these data is optical coherence tomography (OCT). In this article, we will therefore discuss the refractive index reconstruction from OCT data, employing a Gaussian beam based forward model. We consider in particular samples with a layered structure, meaning that the refractive index as a function of depth is well approximated by a piecewise constant function. For the reconstruction, we present a layer-by-layer method where in every step the refractive index is obtained via a discretized least squares minimization. For an approximated form of the minimization problem, we present an existence and uniqueness result. The applicability of the proposed method is then verified by reconstructing refractive indices of layered media from both simulated and experimental OCT data.

Three-dimensional refractive index microscopy based on the multi-layer propagation model with obliquity factor correction

Multi-layer propagation model-based intensity diffraction tomography (IDT) is a three-dimensional (3D) microscopy imaging technique to reveal the structural information of optically thick or multiple scattering samples. However, the performance of existing multi-layer propagation models deteriorates with increasing illumination angle, which can prevent good 3D refractive index (RI) imaging. To overcome this limitation, we incorporate the obliquity factor (OF) into the multi-layer propagation model. Numerical simulation validates that the forward propagation and the RI reconstruction both can be considerably improved. Then, the 3D RI reconstruction performance is quantitatively and qualitatively validated by optical experiments on polystyrene microspheres and peony pollen grains, respectively. In addition, excellent optical sectioning and high spatial resolution are experimentally demonstrated on various unlabeled fixed and living samples, including an Arabidopsis root, HeLa and HCT-116 cells. Time-lapse 3D imaging of living samples is performed for the first time for multi-layer propagation model-based IDT, demonstrating its potential application to some biological and medical studies.

3D refractive index reconstruction from phaseless coherent optical microscopy data using multiple scattering-based inverse solvers—a study

Reconstructing 3D refractive index profile of scatterers using optical microscopy measurements presents several challenges over the conventional microwave and RF domain measurement scenario. These include phaseless and polarization-insensitive measurements, small numerical aperture, as well as a Green’s function where spatial frequencies are integrated in a weighted manner such that far-field angular spectrum cannot be probed and high spatial frequencies that permit better resolution are weighed down. As a result of these factors, the non-linearity and the ill-posedness of the inverse problem are quite severe. These limitations have imposed that inverse scattering problems in the microscopy domain largely consider scalar wave approximations and neglect multiple scattering. Here, we present first inverse scattering results for optical microscopy setup where full-wave vectorial formulation and multiple scattering is incorporated. We present (a) how three popular inverse scattering solvers from microwave domain can be adapted for the present inverse problem, (b) the opportunities and challenges presented by each of these solvers, (c) a comparative insight into these solvers and contrast with the simpler Born approximation approach, and (d) potential routes to improve the performance of these solvers for the hard inverse problem of optical microscopy.

In-silico clearing approach for deep refractive index tomography by partial reconstruction and wave-backpropagation

Refractive index (RI) is considered to be a fundamental physical and biophysical parameter in biological imaging, as it governs light-matter interactions and light propagation while reflecting cellular properties. RI tomography enables volumetric visualization of RI distribution, allowing biologically relevant analysis of a sample. However, multiple scattering (MS) and sample-induced aberration (SIA) caused by the inhomogeneity in RI distribution of a thick sample make its visualization challenging. This paper proposes a deep RI tomographic approach to overcome MS and SIA and allow the enhanced reconstruction of thick samples compared to that enabled by conventional linear-model-based RI tomography. The proposed approach consists of partial RI reconstruction using multiple holograms acquired with angular diversity and their backpropagation using the reconstructed partial RI map, which unambiguously reconstructs the next partial volume. Repeating this operation efficiently reconstructs the entire RI tomogram while suppressing MS and SIA. We visualized a multicellular spheroid of diameter 140 µm within minutes of reconstruction, thereby demonstrating the enhanced deep visualization capability and computational efficiency of the proposed method compared to those of conventional RI tomography. Furthermore, we quantified the high-RI structures and morphological changes inside multicellular spheroids, indicating that the proposed method can retrieve biologically relevant information from the RI distribution. Benefitting from the excellent biological interpretability of RI distributions, the label-free deep visualization capability of the proposed method facilitates a noninvasive understanding of the architecture and time-course morphological changes of thick multicellular specimens.

High-fidelity optical diffraction tomography of live organisms using iodixanol refractive index matching.

Optical diffraction tomography (ODT) enables the three-dimensional (3D) refractive index (RI) reconstruction. However, when the RI difference between a sample and a medium increases, the effects of light scattering become significant, preventing the acquisition of high-quality and accurate RI reconstructions. Herein, we present a method for high-fidelity ODT by introducing non-toxic RI matching media. Optimally reducing the RI contrast enhances the fidelity and accuracy of 3D RI reconstruction, enabling visualization of the morphology and intra-organization of live biological samples without producing toxic effects. We validate our method using various biological organisms, including C. albicans and C. elegans.

Broadband spectroscopy of astrophysical ice analogues

Context. Broadband optical constants of astrophysical ice analogues in the infrared (IR) and terahertz (THz) ranges are required for modeling the dust continuum emission and radiative transfer in dense and cold regions, where thick icy mantles are formed on the surface of dust grains. Such data are still missing from the literature, which can be attributed to the lack of appropriate spectroscopic systems and methods for laboratory studies. Aims. In this paper, the THz time-domain spectroscopy (TDS) and the Fourier-transform IR spectroscopy (FTIR) are combined to study optical constants of CO and CO2 ices in the broad THz-IR spectral range. Methods. The measured ices were grown at cryogenic temperatures by gas deposition on a cold silicon window. We developed a method to quantify the broadband THz-IR optical constants of ices, based on the direct reconstruction of the complex refractive index of ices in the THz range from the TDS data and the use of the Kramers-Kronig relation in the IR range for the reconstruction from the FTIR data. Uncertainties introduced by the Kramers-Kronig relations were eliminated by merging the THz and IR spectra. Finally, the reconstructed THz-IR response was analyzed using classical models of complex dielectric permittivity. Results. The complex refractive index of CO and CO2 ices deposited at the temperature of 28 K was obtained in the range of 0.312.0 THz and fitted using the analytical Lorentz model. Based on the measured dielectric constants, opacities of the astrophysical dust with CO and CO2 icy mantles were computed. Conclusions. The method developed in this work can be used for a model-independent reconstructions of optical constants of various astrophysical ice analogs in a broad THz-IR range. Such data can provide important benchmarks for interpreting broadband observations from existing and future ground-based facilities and space telescopes. The reported results will be useful in modeling sources that exhibit a drastic molecular freeze-out, such as the central regions of prestellar cores and mid-planes of protoplanetary disks, as well as CO and CO2 snow lines in disks.

Absorption and phase decoupling in transport of intensity diffraction tomography

Here we report a valid reconstruction approach to decouple the phase and absorption components of complex refractive index in the transport of intensity diffraction tomography (TIDT) microscopy. Within the existed diffraction tomographic reconstruction framework, the objects refractive index (RI) and absorption components are usually intertwined with each other in the scattering field, complicating the complex refractive index reconstruction process. With the closed-form deconvolution solution and two intensity image datasets captured through focus, we realize the decoupling of the RI part of the specimens and the absorption part in TIDT without pure phase approximation or linearized weak absorption. The difference between the RI and absorption parts of the complex refractive index reconstruction reveals the optical properties of the different components of the object. Simulation and experiments are both performed to validate our decoupling approach based on the simulated 3D resolution target, human breast cancer cell lines MCF-7 and Thalassiosira diatom. The results of the simulations and experiments suggest that the proposed approach is successful and effective for investigating the structural diversity of biological cells at the subcellular level.

High-resolution 3D Fourier ptychographic reconstruction using a hemispherical illumination source with multiplexed-coded strategy.

Fourier ptychography is a promising and flexible imaging technique that can achieve 2D quantitative reconstruction with higher resolution beyond the limitation of the system. Meanwhile, by using different imaging models, the same platform can be applied to achieve 3D refractive index reconstruction. To improve the illumination NA as much as possible while reducing the intensity attenuation problem caused by the LED board used in the traditional FP platform, we apply a hemispherical lighting structure and design a new LED arrangement according to 3D Fourier diffraction theory. Therefore, we could obtain the illumination of 0.98NA using 187 LEDs and achieve imaging half-pitch resolutions of ∼174 nm and ∼524 nm for the lateral and axial directions respectively, using a 40×/0.6NA objective lens. Furthermore, to reduce the number of captured images required and realize real-time data collection, we apply the multiplexed-coded illumination strategy and compare several coded patterns through simulation and experiment. Through comparison, we determined a radial-coded illumination pattern that could achieve more similar results as sequential scanning and increase the acquisition speed to above 1 Hz. Therefore, this paper provides the possibility of this technique in real-time 3D observation of in vitro live samples.

Femtosecond laser inscribed Yb:LuAG waveguides: guiding performance, micro-spectroscopy characterizations, and refractive index reconstruction

We report on fabrication of dual-line waveguides in Yb:LuAG crystal by 1030-nm femtosecond laser inscription, 450 fs pulses at a 100 kHz repetition rate. The efficient single-mode guidance is demonstrated in the type II waveguide structures when propagating light along both TE and TM polarization at 632.8 nm and 1064 nm. Based on the configuration, the minimum propagation loss of the 18-µm width waveguide is determined to be 0.55 dB/cm at wavelength of 632.8 nm. Both the lattice-damaged tracks and strain-affected regions are characterized by means of the confocal micro-Raman spectroscopy. In combination with beam propagation calculations, we quantitatively determine the corresponding contribution of each effect to the refractive-index field of the fabricated waveguides.

Multiple-scattering suppressive refractive index tomography for the label-free quantitative assessment of multicellular spheroids.

Refractive index (RI) tomography is a quantitative tomographic technique used to visualize the intrinsic contrast of unlabeled biological samples. Conventional RI reconstruction algorithms are based on weak-scattering approximation, such as the Born or Rytov approximation. Although these linear algorithms are computationally efficient, they are invalid when the fields are strongly distorted by multiple scattering (MS) of specimens. Herein, we propose an approach to reconstruct the RI distributions of MS objects even under weak-scattering approximation using an MS-suppressive operation. The operation converts the distorted fields into MS-suppressed fields, where weak-scattering approximation is applicable. Using this approach, we reconstructed a whole multicellular spheroid and successfully visualized its internal subcellular structures. Our work facilitates the realization of RI tomography of MS specimens and label-free quantitative analysis of 3D multicellular specimens.

Optical Diffraction Tomography Using Nearly In-Line Holography with a Broadband LED Source

We present optical tomography methods for a 3D refractive index reconstruction of weakly scattering objects using LED light sources. We are able to record holograms by minimizing the optical path difference between the signal and reference beams while separating the scattered field from its twin image. We recorded multiple holograms by illuminating the LEDs sequentially and reconstructed the 3D refractive index reconstruction of the sample. The reconstructions show high signal-to-noise ratio in which the effect of speckle artifacts is highly minimized due to the partially incoherent illumination of the LEDs. Results from combining different illumination wavelengths are also described demonstrating higher acquisition speed.

Tomographic refractive index profiling of direct laser written waveguides.

The fabrication of complex integrated photonic devices via direct laser writing is a powerful and rapidly developing technology. However, the approach is still facing several challenges. One of them is the reliable quantitative characterization of refractive index (RI) changes induced upon laser exposure. To this end, we develop a tomographic reconstruction algorithm following a modern optimization approach, relying on accelerated proximal gradient descent, based on intensity images only. Very recently, such algorithms have become the state of the art in the community of bioimaging, but have never been applied to direct laser written structures such as waveguides. We adapt the algorithm to our concern of characterizing these translation-invariant structures and extend it in order to jointly estimate the aberrations introduced by the imaging system. We show that a correct estimation of these aberrations is necessary to make use of data recorded at larger angles and that it can increase the fidelity of the reconstructed RI profiles. Moreover, we present a method allowing to cross-validate the RI reconstructions by comparing en-face widefield images of thin waveguide sections with matching simulations based on the retrieved RI profile.

Reconstruction and modeling of the complex refractive index of nonlinear glasses from terahertz to optical frequencies.

The linear complex refractive index of a set of borosilicate and tellurite as well as heavy metal oxide silicate, germanate and fluoride glasses has been determined using the Kramers-Kronig analysis on combined data from terahertz time domain (THz-TD) and Fourier transform infrared (FTIR) spectrometers in the ultrabroadband range of 0.15 THz to 200 THz. Debye, Lorentz and shape language modeling (SLM) approaches are applied. Far-infrared absorption power-law model parameters are determined via searching for the largest frequency range that minimizes the root mean squared error (RMSE) of a linear least squares fit for the set of glasses and other glass literature data. Relationships between the absorption parameters, glass properties and compositions are explored.

Measurement of discharge channel based on background oriented schlieren technique using an optimized algorithm

Thermal ionization is the main characteristic of long air gap breakdown. Using the thermal characteristics of the discharge channel can not only analyze the formation and development mechanism of the leader discharge but also better reflect the insulation recovery process of the discharge channel. The background oriented schlieren (BOS) technique is a method generally used for diagnosing flow fields. It can also be used to extract the gradient profile of the refractive index field in long-gap discharge channels, which can then be inverted to yield the temperature field. Based on the BOS, a 1-m rod–plate gap discharge observation system was built and the discharge test was carried out. By optimizing the refractive index reconstruction algorithm, a more accurate temperature field distribution of the discharge channel was obtained. By analyzing the evolution process of the discharge channel, the shock wave radius variation law and insulation recovery time of the channel were obtained, which had a guiding significance for the reclosing time setting.

Limited-angle tomographic phase microscopy utilizing confocal scanning fluorescence microscopy.

We present a multimodal imaging technique, combining tomographic phase microscopy with limited angular projection range and number, and two-channel spinning-disk confocal scanning fluorescence microscopy. This technique allows high-accuracy 3D refractive index (RI) profiling of live cells in spite of the missing projections. The cellular outer shape and its interior organelles measured by the confocal fluorescence imaging not only specify the cell in molecular levels, but also provide the 3D distributions of the whole cell as well as its organelles. We take these additional 3D morphological details as constraints in Gerchberg-Papoulis-based optical diffraction tomography algorithm. We then obtain an accurate 3D RI tomogram, even with a sparse angular range having a small number of perspective projections, otherwise providing low-accuracy RI reconstruction. Then, we obtain both cellular molecular specificity and inner RI values of the cell and its organelles. We compare the reconstructed 3D RI profiles of various samples, demonstrating the superiority of the proposed technique.

3D reconstruction of weakly scattering objects from 2D intensity-only measurements using the Wolf transform.

A new approach to optical diffraction tomography (ODT) based on intensity measurements is presented. By applying the Wolf transform directly to intensity measurements, we observed unexpected behavior in the 3D reconstruction of the sample. Such a reconstruction does not explicitly represent a quantitative measure of the refractive index of the sample; however, it contains interesting qualitative information. This 3D reconstruction exhibits edge enhancement and contrast enhancement for nanostructures compared with the conventional 3D refractive index reconstruction and thus could be used to localize nanoparticles such as lipids inside a biological sample.

The Conjugate Gradient Least Square Algorithm in Terahertz Tomography

Terahertz tomography allows for non-contact tomographic inspection of dielectric materials without the need for radiation protection measures. Terahertz tomography offers the opportunity to inspect such objects from multiple angles not only by measuring the absorption but also by acquiring the time-of-flight of the radiation. Hence, this technique facilitates the reconstruction of the complete complex refractive index of a sample under test. Even complicated surface structures can be imaged, provided the feature size is above the diffraction limit roughly given by the wavelength of the terahertz radiation in use. For industrial applications, computational efficiency and imaging performance are crucial. Therefore, we apply the iterative conjugate gradient least square (CGLS) algorithm to reconstruct images from terahertz tomography data. To ensure reliable convergence of this semi-convergent CGLS algorithm a stopping mechanism based on the L-curve criterion is implemented. The result is a fast-converging, parallelizable method, which offers the flexibility to adapt to the specifics of terahertz tomography. As an example of this adaptability, we implement a non-negativity constraint, suppressing noise in the image and significantly enhancing reconstruction quality.