3D Refractive Index Distribution Research Articles

Realization of volume optical computerized tomography by circular gratings

Volume optical computerized tomography (VOCT) combining moiré deflectometry is superior in studying the spatial characteristics of flow field for its strong anti-disturbing capability, wide measurement range and three-dimensional (3D) measurement. However, 3D filtered back-projection (FBP) reconstruction algorithm of reconstructing the refractive index distribution requires the radial second-order derivative of projection wave front. Taking it into account, the moiré effect of two identical concentric circular gratings is utilized to obtain the radial first-order derivative of wave front directly. Besides, based on the explicit analytical relation between moiré fringes and tested wave front, a modified Fourier-transform method is applied to extract the wave front's radial first-order derivative from moiré fringes. These methods are approved efficient by measuring the 3D refractive index distribution of an axial symmetry flame.

Contribution of the gradient refractive index and shape to the crystalline lens spherical aberration and astigmatism

The optical properties of the crystalline lens are determined by its shape and refractive index distribution. However, to date, those properties have not been measured together in the same lens, and therefore their relative contributions to optical aberrations are not fully understood. The shape, the optical path difference, and the focal length of ten porcine lenses (age around 6 months) were measured in vitro using Optical Coherence Tomography and laser ray tracing. The 3D Gradient Refractive Index distribution (GRIN) was reconstructed by means of an optimization method based on genetic algorithms. The optimization method searched for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens in 18 different meridians. Spherical aberration and astigmatism of the lenses were estimated using computational ray tracing, with the reconstructed GRIN lens and an equivalent homogeneous refractive index. For all lenses the posterior radius of curvature was systematically steeper than the anterior one, and the conic constant of both the anterior and posterior positive surfaces was positive. In average, the measured focal length increased with increasing pupil diameter, consistent with a crystalline lens negative spherical aberration. The refractive index of nucleus and surface was reconstructed to an average value of 1.427 and 1.364, respectively, for 633 nm. The results of the GRIN reconstruction showed a wide distribution of the index in all lens samples. The GRIN shifted spherical aberration towards negative values when compared to a homogeneous index. A negative spherical aberration with GRIN was found in 8 of the 10 lenses. The presence of GRIN also produced a decrease in the total amount of lens astigmatism in most lenses, while the axis of astigmatism was only little influenced by the presence of GRIN. To our knowledge, this study is the first systematic experimental study of the relative contribution of geometry and GRIN to the aberrations in a mammal lens.

Digital holographic microtomography for high‐resolution refractive index mapping of live cells

Quantification of three-dimensional (3D) refractive index (RI) with sub-cellular resolution is achieved by digital holographic microtomography (DHμT) using quantitative phase images measured at multiple illumination angles. The DHμT system achieves sensitive and fast phase measurements based on iterative phase extraction algorithm and asynchronous phase shifting interferometry without any phase monitoring or active control mechanism. A reconstruction algorithm, optical diffraction tomography with projection on convex sets and total variation minimization, is implemented to substantially reduce the number of angular scattered fields needed for reconstruction without sacrificing the accuracy and quality of the reconstructed 3D RI distribution. Tomogram of a living CA9-22 cell is presented to demonstrate the performance of the method. Further, a statistical analysis of the average RI of the nucleoli, the nucleus excluding the nucleoli and the cytoplasm of twenty CA9-22 cells is performed.

Three-dimensional refractive index reconstruction of red blood cells with one-dimensional moving based on local plane wave approximation

To simplify the reconstruction optical system, an improved method is developed to reconstruct the three-dimensional (3D) quantitative refractive index of live cells based on a local plane wave approximation. In this method, the cell is illuminated by a convergent beam whose cross section is much larger than the cell, so the beam passing through the cell can be treated as a local plane wave. With the one-dimensional moving of cells in the beam cross section, multi-directional phase projections can be obtained using a Mach–Zehnder interferometer and the Hilbert transform phase retrieval algorithm. An inverse Radon–Radon iterative algorithm is used to reconstruct the 3D refractive index distribution which is verified by a simulation reconstruction. The corresponding set-up is applied to obtain the multi-directional phase projections and reconstruct the 3D refractive index of red blood cells (RBCs). The results show that only with a simple device could the method measure the 3D refractive index of cells with high precision. The reconstruction method could also be applied in opto-fluidic microscopy to fabricate a compact on-chip opto-fluidic tomographic microscope.

Probing Cell Nanoscale Structural Properties Using Intrinsic Contrast of Light Scattering

There has been a pressing need to quantify the cellular and sub-cellular structures at the nanoscale in its natural environment. Light scattering represents the pre-dominant intrinsic light interaction with cells. The fundamental diffraction barrier often prevents the access to the structural components approximately less than the scale of the wavelength. The complex structure of an object can be described by 3D refractive index distribution (i.e., scattering potential) or its Fourier spectrum (spatial frequency). Based on the analysis of the spectral-spatial properties of scattered light during light-structure interaction, we introduce a new physical approach to probe the complex structural characteristics at the nanoscale with scattered light. Our approach encodes a specific spatial frequency with a corresponding wavelength, which produces a super-resolved microscopic image and allows structural quantification of a sub-cellular component with nanoscale sensitivity and accuracy. We first validated the feasibility of this approach to probe nanoscale structural properties using model systems. Then we investigated the nano-structural properties from cell nucleus during the cell cycle. The translational potential of this approach was also demonstrated for early cancer detection using clinical cell specimens from patients with pre-cancerous lesions.

Higher‐order phase shift reconstruction approach

Biological soft tissues encountered in clinical and preclinical imaging mainly consists of atoms of light elements with low atomic numbers and their elemental composition is nearly uniform with little density variation. Hence, x-ray attenuation contrast is relatively poor and cannot achieve satisfactory sensitivity and specificity. In contrast, x-ray phase-contrast provides a new mechanism for soft tissue imaging. The x-ray phase shift of soft tissues is about a thousand times greater than the x-ray absorption over the diagnostic x-ray energy range, yielding a higher signal-to-noise ratio than the attenuation contrast counterpart. Thus, phase-contrast imaging is a promising technique to reveal detailed structural variation in soft tissues, offering a high contrast resolution between healthy and malignant tissues. Here the authors develop a novel phase retrieval method to reconstruct the phase image on the object plane from the intensity measurements. The reconstructed phase image is a projection of the phase shift induced by an object and serves as input to reconstruct the 3D refractive index distribution inside the object using a tomographic reconstruction algorithm. Such x-ray refractive index images can reveal structural features in soft tissues, with excellent resolution differentiating healthy and malignant tissues. A novel phase retrieval approach is proposed to reconstruct an x-ray phase image of an object based on the paraxial Fresnel-Kirchhoff diffraction theory. A primary advantage of the authors' approach is higher-order accuracy over that with the conventional linear approximation models, relaxing the current restriction of slow phase variation. The nonlinear terms in the autocorrelation equation of the Fresnel diffraction pattern are eliminated using intensity images measured at different distances in the Fresnel diffraction region, simplifying the phase reconstruction to a linear inverse problem. Numerical experiments are performed to demonstrate the accuracy and stability of the proposed approach. The proposed reconstruction formula is a generalization of the transport of intensity equation (TIE). It has the second-order accuracy compared to the linear model used in the conventional phase retrieval approach. The numerical experiments demonstrate that the accuracy and stability of the proposed phase reconstruction method outperforms the TIE-based reconstruction method. A novel approach has been proposed to retrieve an x-ray phase shift image induced by an object from intensity images measured at different distances in the Fresnel diffraction region. The authors' approach has the second-order accuracy and is able to retrieve the phase shift of an object stably, overcoming the restriction of slow phase variation assumed by the conventional phase retrieval techniques.

Influence of tapering process on changes of optical fiber refractive index distribution along a structure

AbstractInvestigations of internal structure changes along an optical fiber during the manufacture of biconical taper have been described. Basing on the constant volume theory, classification of biconical structures manufactured on a special set-up is presented and discussed. The interferometric tomography method has been used for determination of 3D geometry and refractive index distribution in manufactured optical fiber tapers. The experiments provide detailed information on external (diameter of cladding) as well as internal (core diameter and refractive index profile) changes along the taper region. The results have been discussed in relation to the parameters of the manufacturing process.

Investigation of the refractive index distribution in precision compression glass molding by use of 3D tomography

Compression molding of glass optical components is a high volume near net-shape precision fabrication method. In the compression molding process, refractive index variation is often introduced in glass during cooling. The variation of the refractive index in a molded glass lens is an important parameter that can influence its optical performance, especially for lenses used in high precision optical systems. In this research, the three-dimensional (3D) refractive index distribution in molded glass lenses was studied using an optical setup based on the Mach–Zehnder interferometer and filtered back-projection reconstruction algorithm. Specifically, phase information was first evaluated by measuring interferometric fringes using a digital camera at pre-determined discrete locations. The 3D refractive index distribution inside the molded glass lens was then calculated from the phase information.

Cone-beam tomography of propagation-based imaging

A tomography algorithm is proposed for the reconstruction of the three-dimensional (3D) distribution of the real refractive index of a pure phase sample from the projections of cone-beam propagation-based imaging (PBI). The algorithm first retrieves the integral of the real refractive index based on the formula described in this letter, and then a conventional computed tomography algorithm is performed to reconstruct the 3D distribution of the real refractive index of the sample. The computer simulations show that this method is effective for PBI tomography.

Field-based angle-resolved light-scattering study of single live cells

We perform field-based angle-resolved light-scattering measurements from single live cells. We use a laser interferometer to acquire phase and amplitude images of cells at the image plane. The angular scattering spectrum is calculated from the Fourier transform of the field transmitted through the cells. A concurrent 3D refractive index distribution of the same cells is measured using tomographic phase microscopy. By measuring transient increases in light scattering by single cells during exposure to acetic acid, we correlate the scattering properties of single cells with their refractive index distributions and show that results are in good agreement with a model based on the Born approximation.

Three‐dimensional refractive index reconstruction with quantitative phase tomography

Optical tomography based on quantitative phase microscopy is used to determine nondestructively and with high spatial resolution the three-dimensional (3D) refractive index distributions within optical fiber devices. After obtaining a series of phase images of the fiber as it is rotated around its longitudinal axis at regularly-spaced angular positions, filtered backprojection is used to reconstruct a 3D map of the refractive index. The 3D refractive index distribution of the join region between two fusion spliced optical fibers is reconstructed with accuracy better than 10(-3).

A Method for Measuring the Three-Dimensional Refractive-Index Distribution of Single Cells Using Proximal Two-Beam Optical Tweezers and a Phase-Shifting Mach—Zehnder Interferometer

This paper describes a method for measuring the three-dimensional (3D) refractive-index distribution in a single cell. The method can be used to observe the distribution of cell components without fluorescence staining. The two-dimensional optical path length distributions from multiple directions are obtained by non-contact rotation of the cell. These optical path lengths are converted into the line integrals of the refractive index, and the 3D refractive-index distribution is reconstructed by means of computed tomography. The refractive-index distribution in a breast cancer cell can be measured using a phase-shifting Mach—Zehnder interferometer in conjunction with proximal two-beam optical tweezers.

Surface plasmon interferometric microscopy for three-dimensional imaging of dynamic processes

A method, which we named surface plasmon interferometric microscopy, for real-time displaying of the dynamic evolution of the refractive index (RI) of a sample in three-dimensions is demonstrated experimentally. The Fourier fringe analysis technique is employed to get the phase variations of the samples by demodulating the interference patterns captured by a CCD camera, and the 3D RI distribution can be obtained through numerical interpolation from the relation between the phase and the RI of the samples. Our method may provide an interesting way to monitor fast dynamics of physical, biological, and chemical processes in real time.

The mechanism of aqueous outflow in primates, lower mammals and birds: a comparative study

The optical properties of the crystalline lens are determined by its shape and refractive index distribution. However, to date, those properties have not been measured together in the same lens, and therefore their relative contributions to optical aberrations are not fully understood. The shape, the optical path difference, and the focal length of ten porcine lenses (age around 6 months) were measured in vitro using Optical Coherence Tomography and laser ray tracing. The 3D Gradient Refractive Index distribution (GRIN) was reconstructed by means of an optimization method based on genetic algorithms. The optimization method searched for the parameters of a 4-variable GRIN model that best fits the distorted posterior surface of the lens in 18 different meridians. Spherical aberration and astigmatism of the lenses were estimated using computational ray tracing, with the reconstructed GRIN lens and an equivalent homogeneous refractive index. For all lenses the posterior radius of curvature was systematically steeper than the anterior one, and the conic constant of both the anterior and posterior positive surfaces was positive. In average, the measured focal length increased with increasing pupil diameter, consistent with a crystalline lens negative spherical aberration. The refractive index of nucleus and surface was reconstructed to an average value of 1.427 and 1.364, respectively, for 633 nm. The results of the GRIN reconstruction showed a wide distribution of the index in all lens samples. The GRIN shifted spherical aberration towards negative values when compared to a homogeneous index. A negative spherical aberration with GRIN was found in 8 of the 10 lenses. The presence of GRIN also produced a decrease in the total amount of lens astigmatism in most lenses, while the axis of astigmatism was only little influenced by the presence of GRIN. To our knowledge, this study is the first systematic experimental study of the relative contribution of geometry and GRIN to the aberrations in a mammal lens.