Geometrical Optics Theory Research Articles

Optical nano-imaging via microsphere compound lenses working in non-contact mode.

Microsphere lens for nano-imaging has been widely studied because of its superior resolving power, real-time imaging characteristic, and wide applicability on diverse samples. However, the further development of the microsphere microscope has been restricted by its limited magnification and small field-of-view. In this paper, the microsphere compound lenses (MCL) which allow enlarged magnification and field-of-view simultaneously in non-contact imaging mode have been demonstrated. A theoretical model involving wave-optics effects is established to guide the design of MCL for different magnifications and imaging configurations, which is more precise compared with common geometric optics theory. Experimentally, using MCL to image the specimen with a tunable magnification from 2.8× to 10.3× is realized. Due to the enlarged magnification, a high-resolution target with 137 nm line width can be resolved by a 10× objective. Besides, the field-of-view of MCL is larger than that of a single microsphere and can be further increased through scanning working manner, which has been demonstrated by imaging a sample with ∼76 nm minimum feature size in a large area. Prospectively, the well-designed MCL will become irreplaceable components to improve the imaging performances of microsphere microscope just like the compound lens in the conventional macroscopic imaging system.

A new model for explanation and generation of branched flow of light

In this paper, a quasiparticle concept was proposed to understand the branched flow of light phenomenon. Combined with the geometrical optical theory, we successfully established a model to simulate the branched flow of light with this novel perspective. Our model owns an intuitive physics picture, without losing generality. Moreover, we demonstrated that a special structure with the fixed position and specific refractive value of quasiparticles can be designed, a controllable branched flow pattern of light will be correspondingly attained for future experimental guidance.

Investigation of the stripe patterns from X-ray reflection optics.

X-ray beams reflected from a single layer or multilayer coating are widely used for X-ray tomography, holography, and X-ray phase contrast imaging. However, the observed irregular stripe patterns from either unfocused or defocused beams often cause disturbing artifacts and seriously deteriorate the image quality. In this work, we investigate the origin of these irregular fine structures using the wave optics theory. The connection to similar results obtained by the geometric optics theory is also presented. The proposed relation between the second derivative of the wavefront and the irregular structures was then verified by conducting at-wavelength metrology with the speckle-based wavefront sensing technique. This work will not only help to understand the formation of these irregular structures but also provide the basis for manufacturing future 'stripe-free' refection optics.

Design and optimization method of a convex blazed grating in the Offner imaging spectrometer

The convex reflective diffraction grating is an essential optical component in Offner systems, which has been widely used in imaging spectrometers. We propose a new design and optimization method for the convex blazed grating in the Offner imaging spectrometer. The method integrates the macro- and microdesign of the optical system, and it can be used to design and optimize the convex blazed grating with high diffraction efficiency. Traditional geometric optics theory and image quality evaluation methods are used to design the macro-optical structure parameters of the Offner system. And then the incident ray information, such as the incident angle and the polarization states are calculated by using the three-dimensional polarization ray-tracing method. To improve the diffraction efficiency, we combine rigorous coupled wave analysis and a particle swarm optimization algorithm to optimize the microstructure parameters of the convex-blazed grating. Further, a convex-blazed grating in a mid-wave infrared Offner imaging spectrometer is designed as an example to illustrate our design method in detail. The design results indicate that the Offner imaging spectrometer has good imaging quality, and the average diffraction efficiency of the -1st diffraction order of the convex-blazed grating in the spectral coverage 3-5 µm is 82.24%. Compared to the traditional design method, the lowest spectral diffraction efficiency is improved from 59.88% to 69.24%, the highest spectral diffraction efficiency is improved from 90.45% to 91.84%, and the standard deviation is reduced from 7.82 to 6.62.

Optimization of the optical particle counter for online particle measurement in pressure-changing natural gas.

Online measurement of particulate matter in high-pressure natural gas is of great significance to the purification process and safe operation of long-distance pipelines. However, pressure changes in high-pressure natural gas pipelines are complicated. The optical particle counter (OPC) is affected by the change in the refractive index of natural gas, which causes an error of the measured particle size. In order to solve this problem, based on the theory of geometric optics, an optimization model of the aerosol tube spherical window regarding the refractive index was established. This optimization basically eliminates the influence of gas refractive index on the OPC beam characteristics, so that OPC has the same performance under any high-pressure conditions as under normal pressure. The problem of the optical sensor being unsuitable for high-pressure conditions in which it is difficult to be calibrated in atmospheric air is solved, and the accuracy of the online particle test in the high-pressure natural gas pipeline is greatly improved. The influence of window thickness and installation error on the optimization model is analyzed, which provides references for improving the accuracy of optical sensors and application design in higher-pressure environments. Finally, the feasibility, reliability, and accuracy of the method are analyzed and verified by experiments.

Study on a gyrotron quasi-optical mode converter for terahertz imaging

In this paper, a quasi-optical mode converter for terahertz imaging is presented. This design is based on a 0.22 THz TE03 gyrotron oscillator. It includes a Vlasov launcher, an elliptical reflector and a parabolic reflector, which is used to convert TE03 cylindrical waveguide mode to a Gaussian-like beam. The quasi-optical system is analyzed in terms of geometric optics theory and the vector diffraction theory. Numerical optimization code is programmed by MATLAB software for analyzing the quasi-optical system. Simulation results show that the power transmission efficiency of the operating cavity mode to a fundamental Gaussian distribution is 82.14%, the output Gaussian beam can be propagated over 0.8 m without divergence and the scalar Gaussian mode content is 98.2%. A cold test experiment platform is built up to verify the design based on numerical calculation. In experiment, the scalar Gaussian mode content of 97.0% is measured which shows good agreement with numerical calculation.

Comparison of Experimental STEM Conditions for Fluctuation Electron Microscopy.

Variable-resolution fluctuation electron microscopy (VR-FEM) data from measurements on amorphous silicon and PdNiP have been obtained at varying experimental conditions. Measurements have been conducted at identical total electron dose and with an identical electron dose normalized to the respective probe size. STEM probes of different sizes have been created by variation of the semi-convergence angle or by defocus. The results show that defocus yields a reduced normalized variance compared to data from probes created by convergence angle variation. Moreover, the trend of the normalized variance upon probe size variation differs between the two methods. Beam coherence, which affects FEM data, has been analyzed theoretically using geometrical optics on a multi-lens setup and linked to the illumination conditions. Fits to several experimental beam profiles support our geometrical optics theory regarding probe coherence. The normalized variance can be further optimized if one determines the optimal exposure time for the nanobeam diffraction patterns.

The Effects of Tree Trunks on the Directional Emissivity and Brightness Temperatures of a Leaf-Off Forest Using a Geometric Optical Model

As a surface component, the tree trunk affects the top-of-canopy (TOC) emissivity and thermal infrared (TIR) radiance over a forest with fewer leaves, which is important for the inversion of land surface temperatures (LSTs) and further applications such as predicting forest fires and monitoring drought conditions. Therefore, the tree trunk effect was analyzed in this article using a thermal radiation directionality model, in which the forest structure was considered by the geometric optical (GO) theory and the spectral invariance theory was introduced into the GO framework for the single-scattering effect between components. The model used was evaluated using unmanned aerial vehicle (UAV)-based measurements with root-mean-square errors (RMSEs) lower than 0.25 °C for directional anisotropies (DAs) of brightness temperatures (BTs). Comparison with a 3-D radiative transfer model, discrete anisotropic radiative transfer (DART), also indicated an acceptable tool of the proposed model for the trunk effect with RMSEs lower than 0.003 °C and 1.2 °C for DAs of emissivity and BTs, respectively. In this study, the root-mean-squared difference (RMSD) levels between the vegetation-soil and vegetation-trunk-soil canopies, which were viewed as an equivalent indicator of the trunk effect, were provided for the TOC emissivity and BTs as well as their DAs, by combination with the changes in the leaf area index (LAI), stand density, trunk shape, and component temperatures, which can help identify the cases in which the trunk effect should be considered. According to a comprehensive analysis, for cases with sparse stand density ( α <; <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</b> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">.</b> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">04</b> ), the tree trunk should be considered for a BT RMSD level lower than 0.5 °C when the LAI value was lower than 0.6. The corresponding LAI value was 0.8 for an RMSD level of BT DA lower than 0.3 °C. Moreover, for the cases with low soil emissivity, the difference in the TOC emissivity with and without trunk can reach up to 0.035, and the RMSD was still larger than 0.01 when the stand density and LAI were 0.05 and 0.6, respectively.

The Impact of Resonance on the Light Extraction Efficiency of Single Nanowire Ultraviolet Light Emitting Diodes

Fabricating the nanowire ultraviolet light emitting diodes (UV LEDs) has been a promising candidate to dramatically enhance the external quantum efficiency (EQE) of UV LEDs. For a great luminescent performance, it is necessary to understand the propagating features of light inside the nanowire. The relationship between the resonance inside the nanowire, the light extraction efficiency (LEE) and the far-field distribution of nanowire UV LEDs, as well as the geometrical parameters of the nanowire and the impact of surrounding index has been discussed in this paper. It is shown that the resonance plays an important role to enhance the LEE at various parameters. The study on the far-field distribution indicates that the variation of far-field patterns at different conditions can be conveniently explained by the geometrical optics theory. This deep understanding provides benefits to design the nanowire UV LEDs.

Effects of size, volume fraction, and orientation of metallic flake particles on infrared radiation characteristics of Al/acrylic resin composite coatings

The composite functional coating containing micro-nano flake particles is a kind of classic thin-layer structural material, which has excellent photothermal properties. In this paper, a model of random distributed flake particles system is established, and then combining with the geometrical optics theory, the spectral radiation transfer model of the composite functional coating containing micro-nano flake particles is built by the Monte Carlo ray-tracing method (MCRT). After verifying the reliability of the model, the effect of the distribution characteristics, particle size parameters, volume fraction and other parameters of random distributed flake particles system on the spectral radiation characteristics of the coating in 8∼14 μm infrared window is investigated. The results indicate that the spectral emissivity of the coating enhances about 9 % at most when particle radius increases from 5 μm to 15 μm, decreases about 60 % at most when volume fraction of particle system increases from 10 % to 30 %, and goes up about 74.5 % when the flake particles change form horizontal arrangement to orientation range is 0°∼60°.

A Channel Model for Polarized Off-Body Communications With Dynamic Users

This paper presents an off-body channel model for polarized communications with dynamic users. The model is based on Geometrical Optics and Uniform Theory of Diffraction and accounts for free space propagation, reflections, and diffractions. It allows for arbitrary antennas’ polarizations and gain patterns and supports a number of on-body antenna placements. In order to take the influence of users’ motion into account, a mobility model for wearable antennas on dynamic users is used. Signal depolarization mechanisms are identified, and simulations are performed to analyze the influence of user dynamics on the channel. The results show that significant polarization mismatch losses occur due to wearable antenna rotations, resulting in received power variations up to 37.5 dB for the line-of-sight component and 41.4 dB for the scattered one. The importance of taking signal polarization into account is demonstrated by comparing the simulation results between polarized and nonpolarized channel models in a free space propagation scenario, where a difference up to 53 dB in between the two is observed.

Binocular Light-Field: Imaging Theory and Occlusion-Robust Depth Perception Application.

Binocular stereo vision (SV) has been widely used to reconstruct the depth information, but it is quite vulnerable to scenes with strong occlusions. As an emerging computational photography technology, light-field (LF) imaging brings about a novel solution to passive depth perception by recording multiple angular views in a single exposure. In this paper, we explore binocular SV and LF imaging to form the binocular-LF imaging system. An imaging theory is derived by modeling the imaging process and analyzing disparity properties based on the geometrical optics theory. Then an accurate occlusion-robust depth estimation algorithm is proposed by exploiting multibaseline stereo matching cues and defocus cues. The occlusions caused by binocular SV and LF imaging are detected and handled to eliminate the matching ambiguities and outliers. Finally, we develop a binocular-LF database and capture realworld scenes by our binocular-LF system to test the accuracy and robustness. The experimental results demonstrate that the proposed algorithm definitely recovers high quality depth maps with smooth surfaces and precise geometric shapes, which tackles the drawbacks of binocular SV and LF imaging simultaneously.

Multidimensional nonlinear geometric optics for transport operators with applications to stable shock formation

In $n \geq 1$ spatial dimensions, we study the Cauchy problem for a quasilinear transport equation coupled to a quasilinear symmetric hyperbolic subsystem of a rather general type. For an open set (relative to a suitable Sobolev topology) of regular initial data that are close to the data of a simple plane wave, we give a sharp, constructive proof of shock formation in which the transport variable remains bounded but its first-order Cartesian coordinate partial derivatives blow up in finite time. Moreover, we prove that the singularity does not propagate into the symmetric hyperbolic variables: they and their first-order Cartesian coordinate partial derivatives remain bounded, even though they interact with the transport variable all the way up to its singularity. The formation of the singularity is tied to the finite-time degeneration, relative to the Cartesian coordinates, of a system of geometric coordinates adapted to the characteristics of the transport operator. Two crucial features of the proof are that relative to the geometric coordinates, all solution variables remain smooth, and that the finite-time degeneration coincides with the intersection of the characteristics. Compared to prior shock formation results in more than one spatial dimension, in which the blowup occurred in solutions to wave equations, the main new features of the present work are: i) we develop a theory of nonlinear geometric optics for transport operators, which is compatible with the coupling and which allows us to implement a quasilinear geometric vectorfield method, even though the regularity properties of the corresponding eikonal function are less favorable compared to the wave equation case and ii) we allow for a full quasilinear coupling, i.e., the principal coefficients in all equations are allowed to depend on all solution variables.

Mesoscale modeling of polycrystalline light transmission

Recent advances in polycrystalline ceramic synthesis have established fabrication routes for producing dense ceramics with grain size on the order of few nanometers. Light transmission properties and, specifically, the high transparency of birefringent nanocrystalline ceramics cannot be captured by classical geometrical optics theory. In this investigation, we combine the Raman-Viswanathan wave-retardation theory with finite element method (FEM) based numerical simulations to develop an approach for predicting the refractive index variation within and real in-line transmission through relevant optical materials. This approach is validated on non-cubic (and, therefore birefringent) Al2O3 and MgF2 polycrystalline ceramics, by comparing the computed light transmission to experimental transmission measurements. For both of the considered ceramics systems, the developed numerical model effectively reproduces the experimentally measured transmission as a function of average grain size and incident light wavelength, showing improvement over the original approach of Raman and Viswanathan and a recent particle-scattering based adaptation of geometrical optics theory by Apetz and van Bruggen. The same modeling framework can also simulate the effects of applied elastic and electric fields, allowing for the design and predictive evaluation of functional optical properties in piezoelectric ceramics.

Generation of Non-diffraction Vortex Beam and Its Application in Digital Communication

An axicon-frustum basin-type Bessel resonator is designed for generating non-diffraction vortex beams with opposite propagation directions under different conditions. Based on the theory of geometric optics, the principle of creating vortex beams is analyzed in this axicon-frustum basin-shaped resonant cavity. It is shown that a non-diffraction vortex beam can be produced in the cavity under high-order beam stimulation. In the terahertz wavebands, the dyadic Green's function algorithm is used to numerically evaluate the electromagnetic characteristics in the cavity, and the numerical results demonstrate that the conclusion of the principle analysis is valid. Finally, the application of non-diffraction vortex beams in digital communication is explored.

Thin-disk laser resonator design: The dioptric power variation of thin-disk and the beam quality factor

This paper investigates the general limitations of thin-disk laser (TDL) resonators due to the dioptric power variation of thin-disk (TD) crystal to attain the good beam quality. For this reason, the generalized formulation of TDL resonator in geometric optics theory is analytically derived. The analytical model is developed by considering two general configurations of stable resonators based on the position of the TD crystal inside the resonator; end-disk and fold-disk resonators. The calculation results reveal best M2 factor at operation pump power (OPP) from a specified disk is proportional to the variation interval of the dioptric power of the TD and it depends on the general configuration of resonator. For each configuration, the initial radius of curvature of the TD determines the resonator shape to attain the minimum acceptable M2 factor.

Optimization of the optical particle counter for online particle measurement in high-pressure gas.

With the aim to achieve fast and accurate online measurement of particle size and concentration in different high-pressure gas, the application of an optical particle counter (OPC) is extended from atmospheric pressure to high-pressure conditions (more than 2MPa). But with the increase of the gas pressure, the performance of the OPC is reduced, resulting in the error of the tested particle size. In order to resolve this problem, an optimization model of optical window thickness is established for the optical sensor of the OPC based on the geometric optics theory. The effects of gas pressure, temperature, and medium on the optimized model are analyzed, which are helpful to improve the accuracy of the optical sensor. Finally, the feasibility, reliability, and accuracy of the method are verified through experiments.

The influence of pressure on optical particle measurement

In this study, the effects of pressure on the optical sensor in an on-line particle measurement system were investigated in detail based on the quantum theory and kinetic theory of gas. The results show that pressure alters the divergent light angle by altering the density and refractive index of the gas, so that the focused beam position is offset from the center of the aerosol tube; this causes the intensity per cross-section area of the optical measurement volume (OMV) to change, creating a significant deviation in the measurement result relative to the actual sample. Theoretical and experimental dynamic models were established based on the geometric optics theory and the geometric mathematical relation to analyze these variations. The results show that OMV size increases as pressure and divergent light angle increase. During an actual particle measurement process, the dynamic models proposed here can be used to effectively adjust and reconstruct the optical sensor, which can substantially improve the precision and accuracy of the measurement results.

Estimating axial resolution with diffraction theory.

Depth estimation is a classic machine vision and image processing problem aiming at mapping the distances of objects from the camera. The accuracy of this depth map depends on the axial resolution achieved by the system, which is usually estimated using geometrical optics theory. This paper proposes a novel formula using diffraction theory. A comparison with the geometrical approach for estimating the axial resolution is provided, and results for several simulations are discussed.

Multi-scale structure patterning by digital-mask projective lithography with an alterable projective scaling system

We report a flexible and efficient method to pattern two-dimensional (2D) multi-scale structures by digital-mask projective lithography (DMPL) with an alterable projective scaling system. In the developed DMPL system, femtosecond laser was modulated by digital micromirror device (DMD) to generate a designable intensity distribution with digital image information. The projective law of this DMPL system based on the geometric optics theory verified for different projective scaling lens systematically has been studied. With the combination of the customizable DMD elements and alterable projective scaling system, 2D designable patterned microstructures with multi-scale size range from millimeter to hundred nanometer have been achieved by a single exposure. In addition, an engineered Fresnel zone plate (FZP) with numerical aperture (NA) of 0.36 and focal length of 114 μm has been achieved by a single exposure of 1.2 s. The acquisition of the array of FZP lens shows the stability and efficiency of the pattern process. The proposed method could be expected to play an important role in the flexible and efficient fabrication of engineered 2D multi-scale structures.