Refractive Geometry Research Articles

Analytical equation for camera imaging with refractive interfaces

Camera imaging through refractive interfaces is a crucial issue in photogrammetric measurements. Most past studies adopted numerical optimization algorithms based on refractive ray tracing procedures. In these studies, the camera and interface parameters are usually calculated iteratively with numerical optimization algorithms. Inappropriate initial values can cause iterations to diverge. Meanwhile, these iterations cannot efficiently reveal the accurate nature of refractive imaging. Therefore, obtaining camera calibration results that are both flexible and physically interpretable continues to be challenging. Consequently, in this study, we modeled refractive imaging by employing ray transfer matrix analysis. Subsequently, we deduced an analytical refractive imaging (ARI) equation that explicitly describes the refractive geometry in a matrix form. Although this equation is built upon the paraxial approximation, we executed a numerical experiment that shows that the developed analytical equation can accurately illustrate refractive imaging with a considerable object distance and a slightly tilted angle of the flat interface. This ARI equation can be used to define the expansion center and the normal vector of the flat interface. Finally, we also propose a flexible measurement method to determine the orientation of the flat interface, wherein the orientation can be measured rather than calculated by iterative procedures.

A refractive three-dimensional reconstruction method for fringe projection with a planar medium

In special measurement situations, a vision measurement system needs to measure objects through a viewing observation window made of a planar transparent medium. The refraction at the interface between a medium and air leads to large measurement errors in the pin-hole imaging model. Most existing solutions require complex processes of calculating refracted light equations and/or matching stereo images. Here, we propose a refractive three-dimensional (3D) reconstruction method for fringe projection with a planar medium. We derive a coordinate conversion relationship from a pseudo-object point caused by light refraction to a real-object point based on flat refractive geometry. Then, we integrate the relationship into regular fringe projection framework for unbiased 3D reconstruction. Two experiments, including 3D shape measurements of a step and a regular sphere are performed. The results verify the effectiveness and accuracy of the proposed refractive 3D reconstruction method.

Calibration of a Structured Light Imaging System in Two-Layer Flat Refractive Geometry for Underwater Imaging.

The development of a robust 3D imaging system for underwater applications is a crucial process in underwater imaging where the physical properties of the underwater environment make the implementation of such systems challenging. Calibration is an essential step in the application of such imaging systems and is performed to acquire the parameters of the image formation model and to enable 3D reconstruction. We present a novel calibration method for an underwater 3D imaging system comprising a pair of cameras, of a projector, and of a single glass interface that is shared between cameras and projector(s). The image formation model is based on the axial camera model. The proposed calibration uses a numerical optimization of a 3D cost function to determine all system parameters, thus avoiding the minimization of re-projection errors which require numerically solving a 12th order polynomial equation multiple times for each observed point. We also propose a novel stable approach to estimate the axis of the axial camera model. The proposed calibration was experimentally evaluated on four different glass interfaces, wherein several quantitative results were reported, including the re-projection error. The achieved mean angular error of the system's axis was under 6∘, and the mean absolute errors for the reconstruction of a flat surface were 1.38 mm for normal glass interfaces and 2.82 mm for the laminated glass interface, which is more than sufficient for application.

SnO2/polyvinyl alcohol nanofibers wrapped tilted fiber grating for high-sensitive humidity sensing and fast human breath monitoring

A fiber-optic humidity sensor based on excessively tilted fiber grating (Ex-TFG) wrapped with tin dioxide (SnO2)/polyvinyl alcohol (PVA) hybrid nanofibers is presented. Relative humidity (RH) rise causes the changes both in refractive index (RI) and geometry size of the film. The transmitted spectrum of the Ex-TFG changes as a result, owing to the strong interaction of the excited forward propagating cladding modes to the surface coating. Experimental results demonstrate the maximum intensity sensitivity of 0.43 dB/%RH in RH range of 35%−75%. Compared with pure PVA film coated ones, the RH sensitivity of the SnO2/PVA wrapped grating is vastly enhanced by one order of magnitude. The reticular morphology of electrospun SnO2/PVA film around the Ex-TFG promises the unimpeded permeation of water molecules, and then the sensor exhibits an ultrafast response of ∼67 ms and recovery times of ∼83 ms, by monitoring the human breathing with different rhythms. Lastly, the negligible spectral deformation to temperature perturbations verifies the temperature de-correlation of the designed RH sensor. This work indicates that the proposed SnO2/PVA nanofibers wrapped Ex-TFG can provide a simple, robust and high-sensitive optic device for healthcare monitoring, environmental and biochemical sensing applications.

A three-point solution with scale estimation ability for two-view flat-refractive underwater photogrammetry

Underwater photogrammetry can efficiently document complex environments with limited accessibility. As the establishment of reference control networks is involved, using the relative two-view relation, which requires neither knowledge nor estimation of object-space coordinates, offers an attractive solution. In this paper, we study the two-view relation of underwater photogrammetry flat refractive geometry. Through its axial camera form, we show that the necessary correspondences to establish the relative orientation can be reduced to only three points. We also show that all six relative pose parameters can be estimated directly, where the baseline is estimated to its scale, with no external control. For the estimation, we propose direct models, and in seeking optimal minimization forms, we develop a closed-form expression for the epipolar curve. Thereby, we shed light on the epipolar geometry of the flat-refractive imaging system. For a complete evaluation, we also analyze the limits of the baseline estimation to its actual scale. In addition to our scale estimation ability, results show improved accuracy in the relative orientation parameters by order of magnitude or more compared to the state-of-the-art. Experiments demonstrate how our proposed model yields sub-millimeter levels of internal 3-space accuracy without introducing external knowledge.

Solar Angle Model for Daylight Redirection in Prismatic Panel

An advanced complex fenestration system can utilize uniform daylight. Nonetheless, an inefficient design would increase solar heat gain and indoor temperatures, besides uneven light distribution that would cause the "cave effect." Prismatic panels are widely used as complex fenestration systems, providing uniform daylight. This paper proposes a computational model that integrates optical principles like Snell's law with environmental variables and visualizes the performance of prismatic panels in terms of redirection angle while encountering the prism refractive index and geometry at the specified geographic location. The proposed model entails a prismatic panel as a daylight system for redirecting daylight. In contrast to detailed modeling needed for simulation in software programs like Radiance, this computational tool provides a more straightforward and efficient solution for the initial design of light redirection panels that rely on the principle of refraction and evaluate their annual performance based on the angle of deviation. The model's applicability has been demonstrated by utilizing various triangular prism design examples with diverse materials in Frankfurt and Helsinki.

Theory and Closed-Form Solutions for Three- and n-Layer Flat Refractive Geometry

Theory and Closed-Form Solutions for Three- and n-Layer Flat Refractive Geometry

Interconnection of Few-Mode Fibers and Photonic Integrated Circuits Using Mode-Field Adapters

We propose a detailed method for the interconnection between optical fibers and waveguides of photonic integrated circuits. Appropriate modal transmission is accomplished by matching the mode field diameters from both waveguide structures. Links from one structure to another are created by an interconnecting waveguide, maintaining a fixed coupling efficiency as its size is modified to adjust to the target waveguide core. This tailored transition acts as a mode field adapter, equalizing the transmission among multiple modes and reducing the mode-dependent losses while coupling. We present an algorithm to design the mode field adapter based on matching the effective mode areas using the power overlap integral. A study case considering a polymer photonic integrated device immediately connected to a few-mode fiber is analyzed. Coupling efficiencies over 90% for every transmitted mode are achieved, showing an evident improvement compared to typical approaches only matching core sizes. Detailed comparison of the results for each transmission mode is presented. This same procedure can be used to interconnect optical waveguides with different refractive index profiles and core geometry.

Optical and geometric parameter extraction for photonic integrated circuits.

We describe an in-situ technique to characterize the material refractive indices and waveguide geometry for photonic integrated circuits over hundreds of nanometers of optical bandwidth. By combining white light spectroscopy with unbalanced Mach-Zehnder interferometers, we can simultaneously and accurately extract the core thickness, core width, core refractive index, and cladding refractive index. This information is important for the technological maturation of photonic integrated circuit foundry fabrication. Capturing the inter-wafer and intra-wafer variation of these parameters is necessary to predict the yield of photonic components and for overall process quality control. Refractive indices are found with a 1-σ error of between 0.1% and 0.5%, and geometric parameters are found with an error of between 3 nm and 7 nm. Our analysis and validation are implemented and verified using the same waveguide layers as are used in the standard photonic wafer build, without any external techniques such as ellipsometry or microscopy.

Refractive geometry for underwater domes

Underwater cameras are typically placed behind glass windows to protect them from the water. Spherical glass, a dome port, is well suited for high water pressures at great depth, allows for a large field of view, and avoids refraction if a pinhole camera is positioned exactly at the sphere’s center. Adjusting a real lens perfectly to the dome center is a challenging task, both in terms of how to actually guide the centering process (e.g. visual servoing) and how to measure the alignment quality, but also, how to mechanically perform the alignment. Consequently, such systems are prone to being decentered by some offset, leading to challenging refraction patterns at the sphere that invalidate the pinhole camera model. We show that the overall camera system becomes an axial camera, even for thick domes as used for deep sea exploration and provide a non-iterative way to compute the center of refraction without requiring knowledge of exact air, glass or water properties. We also analyze the refractive geometry at the sphere, looking at effects such as forward- vs. backward decentering, iso-refraction curves and obtain a 6th-degree polynomial equation for forward projection of 3D points in thin domes. We then propose a pure underwater calibration procedure to estimate the decentering from multiple images. This estimate can either be used during adjustment to guide the mechanical position of the lens, or can be considered in photogrammetric underwater applications.

Underwater fuel assembly deformation measurement with multisensor dual-line structured light.

The fuel assembly is the core component of the nuclear energy system, and its excessive deformation will affect the normal insertion of the fuel rod and endanger safe operation of the reactor. In this paper, we present an underwater fuel assembly deformation measurement system based on 10 sets of visual measurement units. Benefitting from the waterproof design, the shielding-radiation design, the reflective structure design, the dual-optical line laser triangulation principle, and the underwater multilayer refractive geometry, the measurement system has shorter measurement time, higher measurement accuracy, and better environmental adaptability. Through the underwater field measurement and verification of the standard rod and fuel assembly, the bow deformation measurement accuracy of the measurement system is better than 0.3 mm, and the twist deformation measurement accuracy of the system is better than 0.15°. The proposed method allows transient and high-precision measurement in a certain irradiation dose and certain depth water, which provides a strong guarantee for measurement of fuel assembly deformation parameters in deep water and high radiation.

Neural complex luminaires

Complex luminaires, such as grand chandeliers, can be extremely costly to render because the light-emitting sources are typically encased in complex refractive geometry, creating difficult light paths that require many samples to evaluate with Monte Carlo approaches. Previous work has attempted to speed up this process, but the methods are either inaccurate, require the storage of very large lightfields, and/or do not fit well into modern path-tracing frameworks. Inspired by the success of deep networks, which can model complex relationships robustly and be evaluated efficiently, we propose to use a machine learning framework to compress a complex luminaire's lightfield into an implicit neural representation. Our approach can easily plug into conventional renderers, as it works with the standard techniques of path tracing and multiple importance sampling (MIS). Our solution is to train three networks to perform the essential operations for evaluating the complex luminaire at a specific point and view direction, importance sampling a point on the luminaire given a shading location, and blending to determine the transparency of luminaire queries to properly composite them with other scene elements. We perform favorably relative to state-of-the-art approaches and render final images that are close to the high-sample-count reference with only a fraction of the computation and storage costs, with no need to store the original luminaire geometry and materials.

Characterizing dynamic deformation of marine propeller blades with stroboscopic stereo digital image correlation

Stereo digital image correlation (stereo-DIC) technique shows a powerful capacity on full-field three-dimensional (3D) deformation measurement of rotary machine structures. However, it remains a challenge for underwater applications due to difficulties in imaging, stereo calibration, light refraction, and so on. In this paper, its potential in characterizing 3D dynamic deformation of the underwater rotor blades is shown by solving these problems. A stroboscopic stereo-DIC system is established to capture clear speckle images of a blade that rotates in the windowed cavitation tunnel under different flow speeds. To calibrate the stereo camera for underwater object measurement, an improved planar pattern-based calibration method and a globally optimal relative pose estimation algorithm are proposed to calibrate the intrinsic and extrinsic parameters of the stereo-DIC system separately. In particular, a novel refractive 3D reconstruction method for underwater objects is presented to recover the true 3D shape according to flat refraction geometry, ensuring the correctness and reliability of the measured 3D displacement fields. Several experiments demonstrated that the proposed stereo-DIC system and methods are feasible and accurate. Based on this, the measured dynamic displacement fields of a propeller blade are presented and discussed. Results herald a possibility for monitoring the full-field 3D dynamic response and structural health of underwater rotating structures by the proposed technique.

Refractive three-dimensional reconstruction for underwater stereo digital image correlation.

Measuring the three-dimensional (3D) deformation of submerged objects through different media with the stereo digital image correlation (stereo-DIC) method involves the refractive optical imaging problem where the non-linear transmission of light is induced by a change of medium density. The problem invalidates the underlying single viewpoint assumption of the perspective model in regular stereo-DIC, thereby resulting in erroneous measurements of 3D shape and deformation. In this work, we propose a refractive stereo-DIC method that overcomes the problem by considering light refraction in 3D reconstruction. We formulate a full refractive reconstruction geometry description based on Snell's law of flat refraction and the regular triangulation. This allows the true shape to be effectively reconstructed by tracing and establishing the refracted ray-paths based on the regular 3D reconstruction, without reformulating the camera model and image formation. The refractive stereo-DIC is finally established by integrating the refractive 3D reconstruction into the regular DIC framework for measuring accurate 3D shape and deformation of submerged objects. We experiment the proposed approach with underwater 3D shape and deformation measurements. Both results prove its feasibility and correctness, further heralding our approach as a flexible solution that could readily extend the stereo-DIC to fluid-immersed 3D deformation characterization.

Ultrasensitive temperature sensor based on a urethane acrylate-coated off-axis spiral long period fiber grating

We propose and experimentally demonstrate an ultra-high sensitivity fiber-optic sensor to measure temperature changes in order to establish a high-precision temperature model in the bio-fermentation process. The proposed sensor based on off-axis spiral long-period fiber grating (OAS-LPFG) is fabricated in a single mode fiber (SMF) by arc discharge technology. This kind of grating is distinguished in the refractive index (RI) modulation, geometry changes, and shear stress of a spiral structure. Because the RI of the urethane acrylate is close to that of the SMF cladding and has a high thermo-optic coefficient, the resonant wavelength of the OAS-LPFG dip has a high sensitivity to the temperature measurement. The response of the OAS-LPFG to environmental RI is analyzed by full vector complex coupling mode theory. In the experiment, the temperature sensitivity of the proposed sensor can be reached ∼-108.69 nm/°C over a range of 25.0 °C to 25.5 °C. Compared with other all-fiber-based temperature sensors, the sensor has higher sensitivity.

An analysis of the factors influencing the modeling accuracy of the invariant imbedding T-Matrix method and the optimal design of the parameter settings for particles with different geometrical and optical properties

The Invariant Imbedding (IIM) T-matrix method has been recognized as one of the most promising method to derive exact solution of the light scattering properties of the nonspherical atmospheric particles after the significant improvement by Bi L. and Yang P. Compared with DDA (Discrete Dipole Approximation) and the time domain methods, it can calculate the scattering properties of the random-oriented particles analytically once the T-matrix of the particle is obtained. In order to better understand the modeling capability of this model and optimize the parameter settings for the particles with different geometrical and optical properties, the factors influencing the modeling accuracy are systematically analyzed, which includes the discretization schemes of the radial integral, the discrete point numbers of the radial, zenith and azimuthal integrals. The results show that, the calculation accuracy of Gaussian quadrature technique is higher than that of the trapezoidal rule in the radial discretization. For particles with large size parameter or refractive index, the density of the discrete points (both for the radial discretization and the mesh generation of the zenith and azimuth angles) should be increased correspondingly to ensure the calculation accuracy. Finer discrete grids are also required for particles with extreme shapes (e.g., particles with large aspect ratios). Based on the analysis above, the method to determine the parameters of scattering simulation is further proposed for particles with different geometrical and optical properties, by which the discretization of the computational domain can be optimized once the refractive index and geometry of the particle are known. The method is also validated for cylinders and hexagonal prisms, the results shows that the optimization scheme can be applicable to particles with different shapes.

Using the Lens Paradox to Optimize an In Vivo MRI-Based Optical Model of the Aging Human Crystalline Lens.

PurposeTo optimize our in vivo magnetic resonance imaging (MRI)-based optical model of the human crystalline lens, developed with a small group of young adults, for a larger cohort spanning a wider age range.MethodsSubjective refraction and ocular biometry were measured in 57 healthy adults ages 18 to 86 years who were then scanned using 3T clinical magnetic resonance imaging (MRI) to obtain lens gradient of refractive index (GRIN) and geometry measurements. These parameters were combined with ocular biometric measurements to construct individualized Zemax eye models from which ocular refractive errors and lens powers were determined. Models were optimized by adding an age-dependent factor to the transverse relaxation time (T2)-refractive index (n) calibration to match model-calculated refractive errors with subjective refractions.ResultsIn our subject cohort, subjective refraction shifted toward hyperopia by 0.029 diopter/year as the lens grew larger and developed flatter GRINs with advancing age. Without model optimization, lens powers did not reproduce this clinically observed decrease, the so-called lens paradox, instead increasing by 0.055 diopter/year. However, modifying the T2-n calibration by including an age-dependent factor reproduced the decrease in lens power associated with the lens paradox.ConclusionsAfter accounting for age-related changes in lens physiology in the T2-n calibration, our model was capable of accurately measuring in vivo lens power across a wide age range. This study highlights the need for a better understanding of how age-dependent changes to the GRIN impact the refractive properties of the lens.Translational RelevanceMRI is applied clinically to calculate the effect of age-related refractive index changes in the lens paradox.

Agarose-based structured optical fibre

Biocompatible and resorbable optical fibres emerge as promising technologies for in vivo applications like imaging, light delivery for phototherapy and optogenetics, and localised drug-delivery, as well as for biochemical sensing, wherein the probe can be implanted and then completely absorbed by the organism. Biodegradable waveguides based on glasses, hydrogels, and silk have been reported, but most of these devices rely on complex fabrication procedures. In this sense, this paper proposes a novel structured optical fibre made of agarose, a transparent, edible material used in culture media and tissue engineering. The fibre is obtained by pouring food-grade agar into a mould with stacked rods, forming a solid core surrounded by air holes in which the refractive index and fibre geometry can be tailored by choosing the agarose solution composition and mould design, respectively. Besides exhibiting practical transmittance at 633 nm in relation to other hydrogel waveguides, the fibre is also validated for chemical sensing either by detecting volume changes due to agar swelling/dehydration or modulating the transmitted light by inserting fluids into the air holes. Therefore, the proposed agarose-based structured optical fibre is an easy-to-fabricate, versatile technology with possible applications for medical imaging and in vivo biochemical sensing.

Underwater image matching with efficient refractive-geometry estimation for measurement in glass-flume experiments

Computer vision technology has been employed in numerous ocean engineering experiments to measure motions and shapes of target objects. However, when dealing with underwater objects, conventional image matching strategies are less effective because of refractive distortions. In this paper, a new method is proposed for matching underwater images in glass-flume experiments. It leverages the estimation of refractive geometry to refine potential image correspondences that include mismatches and location errors. By analyzing the light paths, the relationship between corresponding points of underwater images is derived. Then, an efficient estimation algorithm is designed to compute the parameters of refractive planes from image correspondences. Finally, an improved matching process is presented by incorporating this algorithm into an outlier removal framework. Extensive experiments on synthetic data and real images demonstrate that the proposed method is effective in calculating the refractive geometry of glass-flume experiments and leads to significantly higher accuracies in underwater image matching.

Saturation and Refractive Index Geometry Effects on Localization of a Spatial Soliton in a Waveguide with Parabolic Rectangular Index Profile

In this paper, we have investigated the effects of well numbers, maximum refractive index variation Δn0, saturable nonlinearity β and soliton amplitude N on behavior of a spatial soliton propagating through a waveguide having a parabolic rectangular index profile. The aim of this work is to find the optimal values for these parameters in order to achieve the best soliton behavior. We found that the best system is one with N = 3, β = 0.4 and well number = 20. Knowing these optimal values helps experimenters to select the optimal system. In addition, to study the behavior of the propagating soliton, localization of the soliton was investigated under variations of a variety of the above-mentioned quantities. Our results show that localization of a soliton for the propagation distance z 10, the effective width (Weff) of the soliton shows an oscillatory behavior. The amplitude of Weff oscillations with increasing well number decreases, and the soliton becomes more localized. In contrast, with increase of β, Weff oscillations increase.