Refractive Index Field Research Articles

Tomographic reconstruction of the refractive index with hard X-rays: an efficient method based on the gradient vector-field approach

The refractive-index gradient vector field approach establishes a connection between a tomographic data set of differential phase contrast images and the distribution of the partial spatial derivatives of the refractive index in an object. The reconstruction of the refractive index in a plane requires the integration of its gradient field. This work shows how this integration can be efficiently performed by converting the problem to the Poisson equation, which can be accurately solved even in the case of noisy and large datasets. The performance of the suggested method is discussed and demonstrated experimentally by computing the refractive index distribution in both a simple plastic phantom and a complex biological sample. The quality of the reconstruction is evaluated through the direct comparison with other commonly used methods. To this end, the refractive index is retrieved from the same data set using also (1) the filtered backprojection algorithm for gradient projections, and (2) the regularized phase-retrieval procedure. Results show that the gradient vector field approach combined with the developed integration technique provides a very accurate depiction of the sample internal structure. Contrary to the two other techniques, the considered method does not require a preliminary phase-retrieval and can be implemented with any advanced computer tomography algorithm. In this work, analyzer-based phase contrast images are used for demonstration. Results, however, are generally valid and can be applied for processing differential phase-contrast tomographic data sets obtained with other phase-contrast imaging techniques.

Fiber Bragg gratings in optical microfibers

Microfiber Bragg gratings (mFBGs) are of great promise due to their compactness, large evanescent field effect, low stiffness, and good flexibility. A lot of researches related to the fabrication and the potential applications of mFBGs in sensing and communication have been made in the past. This review begins from the theoretical analysis based on the mode coupling effect. Then, the fabrication techniques for the refractive index-changed and the structural mFBGs are described. The sensing applications for the measurands of refractive index, force, and magnetic field, and the applications for realizing functional devices, including optical tunable filters, temperature-compensated filters, and Fabry-Perot cavities are discussed.

Computational Schlieren Photography with Light Field Probes

We introduce a new approach to capturing refraction in transparent media, which we call light field background oriented Schlieren photography. By optically coding the locations and directions of light rays emerging from a light field probe, we can capture changes of the refractive index field between the probe and a camera or an observer. Our prototype capture setup consists of inexpensive off-the-shelf hardware, including inkjet-printed transparencies, lenslet arrays, and a conventional camera. By carefully encoding the color and intensity variations of 4D light field probes, we show how to code both spatial and angular information of refractive phenomena. Such coding schemes are demonstrated to allow for a new, single image approach to reconstructing transparent surfaces, such as thin solids or surfaces of fluids. The captured visual information is used to reconstruct refractive surface normals and a sparse set of control points independently from a single photograph.

Hydrodynamics of the turbulent point-spread function

We derive hydrodynamic equations for the point-spread function of an imaging system looking through atmospheric turbulence at an incoherent object. These are derived from the hydrodynamics of the index of refraction of the air. We use the path integral representation of the paraxial approximation for wave propagation through turbulence. We then study the case of a frozen turbulent refractive index field being advected past the imaging system with a constant wind and discuss the implications for optical flow estimation. We conclude by discussing possible directions for future work.

Structure of the refractive index distribution of the supersonic turbulent boundary layer

The refractive index field of supersonic turbulent boundary layer with Mach number 3 is measured with the nanoparticle-based planar laser scattering technique, and its structure is investigated from the viewpoints of power spectrum, structure function and correlation function. The power spectrum along streamwise direction shows evident power behavior in a broad region of wavenumber, and the power exponent varies from −1.9 to −1.7 in the logarithmic region. The dominant structures is revealed using the pre-multiplied spectrum, and the length of the largest structure is about 1.2δ (δ is the thickness of the boundary layer). The structure function of the refractive index along streamwise direction is computed and an analytic expression is suggested to fit the experimental results, which is a modification of the Tatraski model. The power spectrum is computed with the fitting expression and its behavior is analyzed. The characteristic length along normal direction is studied with the linking equation in aero-optics. This length is defined with normal integral of correlation coefficient, and the results with two slightly different definitions of correlation coefficient are compared.

Light Polarization-Assisted Sensing with Tilted Fiber Bragg Gratings

Tilted fiber Bragg gratings (TFBGs) are short-period gratings for which the refractive index modulation of the fiber core is angled by a few degrees with respect to the perpendicular to the propagation axis. They induce two kinds of light coupling: the self-backward coupling of the core mode at the Bragg wavelength and the backward coupling between the core mode and several tens of cladding modes, each with its own effective refractive index and mode field shape. The information contained in their spectral content is such that they inherently provide novel sensing modalities and improve the sensitivity in comparison to uniform fiber Bragg gratings. In particular, TFBGs are intrinsically temperature- insensitive by referencing spectral measurements to the wavelength and power level of the core mode resonance. As the tilt angle breaks the circular symmetry of the optical fiber cross-section, TFBGs are strongly dependent on light polariza- tion effects, which can be advantageously used when they are coated with nanoscale metal coatings or thin films. In this review, we report the latest achievements obtained with bare and coated TFBGs used for high-resolution refractometry and biochemical sensing through surface Plasmon wave generation.

μ-Raman spectroscopy characterization of LiNbO3 femtosecond laser written waveguides

In this paper, we present an iterative method which merges experimental μ-Raman measurements and numerical simulations to describe femtosecond written waveguides in LiNbO3 crystals. This method is based on the deformation potential theory, and uses the finite element method to analyze elastic deformations after femtosecond laser micro-explosions in x-cut Mg:LiNbO3 crystals. The resultant strain and refractive index field after laser interaction were estimated and yielded similar values to those obtained in other works. The LiNbO3 Raman deformation potential constants were also estimated in this work.

MATFESA: strain and refractive index field estimation after femtosecond laser interaction with transparent material

In this paper we present the development of an open code (“MATFESA”) based on the Finite Element Method (FEM) which can be used to estimate the strain and refractive index fields after femtosecond laser writing process by means of an iterative analysis. The fs-laser pulse residual stress control is the key to obtain high performance guiding structures for photonics.

Optical distortion evaluation of an aerodynamically heated window, based on the higher-order singular value decomposition with the influence of elasto-optical effect excluded

The higher-order singular value decomposition (HOSVD) was used to reconstruct the three-dimensional (3D) refractive index field of an aerodynamically heated window. The numerical 3D optical distortion was evaluated for both the reconstructed and the exact refractive index fields of the window, excluding the influence of the elasto-optical effect. The method based on the HOSVD truncation was shown to reduce the refractive index information required to capture the major optical distortion of the window. The refractive index information was reduced by reconstructing the refractive index field of the window using the truncated n-mode singular matrices. The method can also be used to evaluate the optical distortion of the window.

Numerical study using angular spectrum propagation model for aero optical imaging

When the interceptors with optical detector onboard fly at supersonic speeds, aero-optical effects (AOEs) will occur and have bad influence on the accuracy of image navigation and eventually decrease the operational effectiveness. Thus, it is crucial for precise image navigation to do research on prediction of the performance of aero optical imaging. This paper employs a method based on the model of angular spectrum propagation to study the light transmission through the supersonic flowfields and aero optical imaging. First, the density fields are translated into the refractive index fields through the Gladstone–Dale (G–D) relationship. In this paper, each CFD grid is viewed as a uniform and isotropic cell, and it is assumed that the optical waves are propagating cell by cell. According to the angular spectrum propagation, each CFD grid is thought of as a linear spatial filter (LPF), and the supersonic flowfields are regarded as the combinations of these LPFs. The different spatial frequencies brought about by the different densities are used to analyze the influences of the density distribution on the light propagation. The proposed method can calculate the optical transformation function (OTF) and directly use it for modeling the aero optical image. In the end, the aero optical images are simulated and the centroid offsets of aero optical imaging are calculated. The results show that the proposed approach is reasonable.

Nano-lens diffraction around a single heated nano particle

The action of a nanoscopic spherically symmetric refractive index profile on a focused Gaussian beam may easily be envisaged as the action of a phase-modifying element, i.e. a lens: Rays traversing the inhomogeneous refractive index field n(r) collect an additional phase along their trajectory which advances or retards their phase with respect to the unperturbed ray. This lens-like action has long been understood as being the mechanism behind the signal of thin sample photothermal absorption measurements [Appl. Opt. 34, 41-50 (1995)], [Jpn. J. Appl. Phys. 45, 7141-7151 (2006)], where a cylindrical symmetry and a different lengthscale is present. In photothermal single (nano-)particle microscopy, however, a complicated, though prediction-wise limited, electrodynamic scattering treatment was established [Phys. Rev. B 73, 045424 (2006)] during the emergence of this new technique. Our recent study [ACS Nano, DOI: 10.1021/nn300181h] extended this approach into a full ab-initio model and showed for the first time that the mechanism behind the signal, despite its nanoscopic origin, is also the lens-like action of the induced refractive index profile only hidden in the complicated guise of the theoretical generalized Mie-like framework. The diffraction model proposed here yields succinct analytical expressions for the axial photothermal signal shape and magnitude and its angular distribution, all showing the clear lens-signature. It is further demonstrated, that the Gouy-phase of a Gaussian beam does not contribute to the relative photothermal signal in forward direction, a fact which is not easily evident from the more rigorous EM treatment. The presented model may thus be used to estimate the signal shape and magnitude in photothermal single particle microscopy.

Tomographic reconstruction of three-dimensional refractive index fields by use of a regularized phase-tracking technique and a polynomial approximation method

We present a complete data-processing procedure for quantitative reconstruction of three-dimensional (3D) refractive index fields from limited multidirectional interferometric data. The proposed procedure includes two parts: (1) extraction of the projection data from limited multidirectional interferograms by a regularized phase-tracking technique and wavefront fitting and (2) reconstruction of the 3D refractive index fields by a modified polynomial approximation method. It has been shown that the procedure gives a satisfactory solution to the reconstruction issue in interferometric tomography, from the initial projection data extraction to the final image reconstruction. Computer simulation and experimental results are both presented.

Polynomial approximation method for tomographic reconstruction of three-dimensional refractive index fields with limited data

We propose a polynomial approximation method (PAM) for reconstruction of three-dimensional refractive index fields by interferometric tomography using limited data. Based on the assumption that the fields to be reconstructed are usually smooth and can be decomposed into a finite order of (orthogonal) polynomials, a set of linear equations can be constructed using both the measured projection data and the Radon transform of the basis functions. By solving these equations, the least-squares solutions of expansion coefficients can be obtained and then substituted back to yield the desired fields. Numerical results have demonstrated that the proposed method is fast, robust to noise and can achieve satisfactory results for refractive index fields with limited projection views and large opaque objects.

Meteorological information in GPS-RO reflected signals

Abstract. Vertical profiles of the atmosphere can be obtained globally with the radio-occultation technique. However, the lowest layers of the atmosphere are less accurately extracted. A good description of these layers is important for the good performance of Numerical Weather Prediction (NWP) systems, and an improvement of the observational data available for the low troposphere would thus be of great interest for data assimilation. We outline here how supplemental meteorological information close to the surface can be extracted whenever reflected signals are available. We separate the reflected signal through a radioholographic filter, and we interpret it with a ray tracing procedure, analyzing the trajectories of the electromagnetic waves over a 3-D field of refractive index. A perturbation approach is then used to perform an inversion, identifying the relevant contribution of the lowest layers of the atmosphere to the properties of the reflected signal, and extracting some supplemental information to the solution of the inversion of the direct propagation signals. It is found that there is a significant amount of useful information in the reflected signal, which is sufficient to extract a stand-alone profile of the low atmosphere, with a precision of approximately 0.1 %. The methodology is applied to one reflection case.

A simple model to estimate turbulent density fluctuation and associated optical distortion over hydro-dynamically rough surfaces

Here we develop an analysis to estimate root-mean-square (RMS) turbulent density fluctuation over hydro-dynamically rough plates and cones for compressible flows. This information is then used to estimate standard aero-optical quantities such as the mean square random phase error and the Strehl ratio. To compute the density fluctuation, a closed-form analytical model has been developed using classical (inner-law) boundary layer results. The model estimates local compressible (adiabatic) skin friction, equivalent (Van Driest) log-law velocity profiles and boundary layer thickness and, via the Crocco–Busemann energy integral (assuming for simplicity adiabatic conditions) temperature fluctuations. Finally, using state and appropriate closures for the turbulent pressure fluctuation and Reynolds stresses, we arrive at an RMS turbulent density fluctuation result. This result is compared to experimental and semi-empirical models and shows reasonable agreement. The density fluctuation is of particular interest since it can be directly related to estimate the local refractive index associated with the flow through the Gladstone–Dale constant. The refractive index field provides the basis for aero-optical modeling of a particular system, with a particular focus on beam path bending, the mean square random phase error and the related Strehl ratio.

Optical distortion evaluation of an aerodynamically heated window using the interfacial fluid thickness concept

The interfacial fluid thickness (IFT) concept was used to develop a harmonic-mean refractive index gradient magnitude threshold to retrieve the high refractive index gradient regions of an aerodynamically heated window. The retrieved high-gradient regions were used to reconstruct the refractive index field of the window. The numerical three-dimensional optical distortion evaluation was conducted for both the reconstructed and the original refractive index fields of the window using the ray-tracing program based on a recursive algorithm. Wave aberration results show that the methodology based on the IFT concept reduces the refractive index information required to capture the essential optical distortion of the window. The method can also be used for numerically evaluating the optical distortion of the window.

Comparison of Fringe Displacement in Moiré Deflection Tomography Diagnosis between Flame and Arc Plasma

In this paper, an interesting optical phenomenon in flow fields' moiré deflection tomography diagnosis is presented. A flame and an arc plasma are chosen as two practical examples for comparative study, and 532 nm is chosen as the probe wavelength. The experimental results indicate that a higher temperature does not mean a larger moiré fringe displacement, which makes us realize that the refractive index gradient is not only determined by the temperature gradient of a flow field. The physical essence, that is, what determines a flow field's refractive index gradient, is proposed theoretically. The experimental phenomenon can be well explained using the theoretical analysis model, which implies the rationality of the physical essence proposed by us.

Oscillatory Lorentz-force-driven flows during potentiostatic current oscillations in magnetic fields

The velocity and refractive index fields during potentiostatic current oscillations of iron electrode in H 2 S O 4 with applied magnetic fields were measured by a combination of particle image velocimetry and interferometry. Depending on the magnetic field orientation differently oriented swirling flows around the electrode were observed in the activation phase. The resulting secondary flows crucially affect the concentration boundary layer thickness at the iron electrode, which finally strongly influences the duration of the passivation phase.

Refractive index imaging from radiative transfer equation-based reconstruction algorithm: Fundamentals

We present the first reconstruction algorithm for refractive index imaging, which is based on the radiative transfer equation (RTE). An objective function is iteratively minimized to find a solution to the problem of inversion of the refractive index field. The function describes the discrepancies of the emerging light measurements on the surface of the sample to be probed with predicted data from the corresponding numerical model. The unknown refractive index field is updated within each reconstruction iteration according to a search direction on the index distribution given by the adjoint model to the RTE. In this paper, emphasis is placed on the theoretical aspects. Preliminary tests are demonstrated on generic phantoms.

Dynamics of dissipative spatial solitons over a sharp potential

We analyze various scenarios of the dynamics of a spatial soliton interacting with a sharp potential barrier (SPB) in the complex Ginzburg–Landau model with the cubic-quintic nonlinearity. In optical realizations of the model, the SPB corresponds to a local notch in the refractive-index field. Possible outcomes of the interaction include splitting of the soliton, its lateral drift, formation of tree-like multi-jet patterns, and destruction of the soliton. The results suggest applications to the design of two- and multi-route splitters of light beams.