Geometrical Optics Method Research Articles

Swift's Alberti? The Geometrical Comedy of Gulliver's Travels

This article propounds that Jonathan Swift’s Gulliver’s Travels develops a geometrical comedy in the Albertinian fashion. Starting with a specific reference to Momus in Puppet-Show, it will be maintained that Swift refers to an earlier tradition of criticism and transfers it to his prose writing. To explore this point, the article will draw on the Italian Renaissance humanist, satirist, and architect Leon Battista Alberti’s Momus and De Pictura. It will be suggested that there is a corollary between the exilic vision of the picaresque anti-hero and the definitive quality of the centric ray which establishes the centre of meaning in painting in Alberti. In accordance, it will be maintained that Swift adapts Alberti’s critical rendition of the Momus story as a geometrical metaphor for linear perspective. Although Momus does not directly appear as part of the dramatis personae in Gulliver’s Travels, Lemuel Gulliver emerges as an eighteenth-century successor to Alberti’s geometrical designs since Swift adapts the Renaissance humanist’s method of geometrical optics which reveres ocularcentrism. By these standards, it will be propounded that this method informs the comedic programme of Gulliver’s Travels. In accordance, the conclusion draws on the point that Swiftian comedy owes a considerable debt to the mimetic concerns of Renaissance humanism which signals at the birth of a post-humanist comedy through a re-mapping of Albertinian perspectivism.

Short vertical wavelength gravity waves in the Martian polar lower atmosphere observed by reanalysis of Mars Global Surveyor radio occultation data

This study investigated gravity waves in the Martian polar lower atmosphere using Mars Global Surveyor (MGS) radio occultation data from February 1998 to March 1999. In addition to the conventional geometrical optics method, Full Spectrum Inversion (FSI) was used to achieve a vertical resolution of ∼300 m in terms of the wavelength. In the polar night in the southern high latitude, wavelike structures with vertical wavelengths ranging from ∼1 km to several km extend from the surface to high altitudes. The positive static stability near the surface and the high terrain in the southern high latitude suggest the waves were topographically generated. The near-surface wind speed was estimated to be a few m s−1. In the midnight sun in the northern high latitude, waves show smaller amplitudes up to 10–15 km altitudes and attenuation above, which is attributable to reduced background stability. Near-neutral thin layers were ubiquitously observed in both groups, indicating the generation of turbulent layers by saturated gravity waves. It was shown that high-resolution radio occultations with radio holographic analysis offer a valuable tool for understanding atmosphere-solid planet interactions.

Analysis of Multiple Scattering Characteristics of Cable-Stayed Bridges with Multi-band SAR

Abstract. Accurate localization of multi-scattering features of cable-stayed bridges in multi-band Synthetic Aperture Radar (SAR) imagery is crucial for intelligent recognition of bridge targets within images, as well as for precise water level extraction. This study focuses on the Badong Yangtze River Bridge, utilizing Unmanned Aerial Vehicle (UAV) LiDAR data of the bridge, and analyzes the multi-scattering characteristics of different bridge structural targets based on Geometric Optics (GO) methods and the Range-Doppler principle. Furthermore, the study integrates LiDAR data of the bridge's cable-stays to examine their multi-scattering phenomena, finding that the undulations of the Yangtze River's surface waves significantly contribute to the pronounced double scattering features of the bridge's cable-stays. Additionally, statistical analysis of multi-source SAR data indicates that this phenomenon is not directly correlated with radar wavelength, implying no direct connection to surface roughness. Utilizing LiDAR point cloud data from the bridge's street lamps, this paper proposes a novel method for estimating water level elevation by identifying the center position of spots formed by double scattering from lamp posts. The results show that using TerraSAR ascending and descending orbit images, this method achieves a water level elevation accuracy of approximately 0.2 meters.

Intricate multiple scattering features of artificial facilities in X-Band SAR images

Abstract. Due to the intricate distortion and reflection geometry of the SAR signal, it is typically difficult to determine the multiple scattering of large artificial objects in SAR images. This work presents a scattering point path tracking model that utilizes the real three-dimensional dimensions of targets, based on the geometric optics method. Three different artificial structures, including light poles, cable stayed bridges, and power transmission lines, are carefully analysed in time-series SAR images with their simulated multiple scattering results. The results demonstrate that the routes determined by the model are consistent with the multiple scattering features on SAR images. Moreover, the time-series data demonstrate that ripples in the water's surface have a significant impact on the multi-scattering features of power lines and bridges. The double scattering features of the light pole provides a novel approach to the process of permanent scatterers (PS) in urban areas. The instances presented in this study demonstrate the effectiveness of the scattering point path tracking model in identifying the various artificial facility targets on different reflective surfaces. It will be a useful tool for deciphering the multiple scattering of large artificial structures when their 3D model is known.

Evaluation of the influence of distortions of the digital object model on the result of synthetic aperture radar image modelling

An essential problem in radar image processing is the synthesis of optimal and quasi-optimal algorithms for the formation of a vector of sufficient statistics and, as a consequence, for obtaining the features used to classify an object of observation. For this purpose it is required to consider the influence of distortions of digital three-dimensional models of objects on the results of modelling images obtained for synthetic aperture radar. Aim of article – to develop and evaluate the possibilities of the method of geometrical optics in the process of application of ray tracing apparatus for the cases of diffuse and specular reflection of waves from the surface of a reflecting object while evaluating the influence of angular distortions of a digital 3D model of an object on the results of modelling. The method of taking into account the theoretical relationship between the magnitude of coordinate distortions of the digital model and the magnitude of distortion of the received radar image is proposed. The paper evaluates the influence of distortions of digital models of three-dimensional (3D) objects on the results of modelling images obtained for synthetic aperture radar. The presented method of taking into account the influence of distortions of the digital 3D model of the object on the results of radar image modelling allows to estimate the conditions of applicability of the ray tracing method.

Modelling Optical Invisibility in a Lenticular Microlens array with methods of Geometrical Optics and Weber's Contrast

Though many advances have been made in exploring the ‘cloaking’ capabilities of metamaterials and optical systems in a wide range of the light spectrum, e.g. electromagnetic cloaking or paraxial ray optics, the phenomenon of unidirectional cloaking associated with ‘woodpile’ optical structures has not yet been widely discussed in the scope beyond experimental findings or digital integral cloaking; moreover, the relatively low cost of a lenticular array renders the investigation of its concealment properties in the visible regime of great interest for practical purposes. Thus, the following research paper provides an comprehensive theoretical model and analytical criterion for the phenomenon of unidirectional cloaking in the visible regime associated with a lenticular microlens array within the methods of computational ray optics (computing lens’s spherical aberration using governing ray optics equations) and Weber’s contrast (as perceived by the human eye) by considering the concealed object’s virtual image as seen through a lenticular lens. Having shown that the criterion for practical invisibility adheres to our experimental results in determining the boundary case of invisibility, we employed it to explore the effect system parameters have on the array’s cloaking capabilities. We established that the critical parameter for the array’s cloaking capability is the diverging angle of an array’s lenticular lens, the value of which positively correlates with the refraction index and the lens concave segment’s curvature. Therefore, a lenticular array with most prominent cloaking capabilities consists of lenses with the greatest admissible index of refraction and a arc measure for the lens’s concave segment.

Classical calculation of differential cross section for a beam deflected by a concentric refractive index field.

Ray tracing is a fundamental geometric-optics issue which gives a single ray path but seldom presents the collective behavior of light. The optical field distribution usually involves the calculation of an electromagnetic field and is rarely discussed from the perspective of geometric optics. However, in this paper, we show for a concentric medium with spherically symmetric refractive index, how the relative angular distribution of refractive beams can be obtained from the pure classical geometric optics method. As a measurement of the distribution, we introduce the concept of the differential cross section (DCS), which can be calculated from the relation between aiming distance and deflecting the angle of the ray. We present a general method to solve this relation from both Snell's law in a constant medium and the optical Binet equation (OBE) in a gradient-index (GRIN) medium. Even without observing the collective traces, the DCS can independently give a quantitative description for the deflected light density of concentric media at different directions. It may act as a reference index for the design of beam deflector.

Design of a high counting efficiency sensor for 1.0 cubic feet per minute laser particle counter.

Based on the theory of Mie scattering, an optical sensor for a 1.0 cubic feet per minute laser particle counter is developed in this paper. First, an illumination optical path relying on aspherical lens and cylindrical lens for laser shaping was designed, and a narrow optical spot with the illumination in the vertical direction of the photosensitive area approximately distributed as a flat top was obtained. Second, the scattering light path was designed by using the theory of Mie scattering and geometric optics method. Then, the structure of the sampling air path was designed with reference to the principle of Laval nozzle, and the particle flow trajectory was verified by simulation using the fluid dynamics software Ansys Fluent. Finally, the performance of the optical sensor was measured with polystyrene latex (PSL) particles, and the results showed that the counting efficiency of the 0.3μm particle size channel met the requirement of 50% ± 20% and the 0.5μm particle size channel met the requirement of 100% ± 10%, which complied with the ISO 21501-4 standard.

Using high-diffraction-efficiency holographic optical elements in a full-color augmented reality display system.

Holographic optical elements (HOEs) play an important role in augmented reality (AR) systems. However, the fabrication of full-color HOEs is difficult and the diffraction efficiency is low. In this paper, we use the time-scheduled iterative exposure method to fabricate full-color HOEs with high diffraction efficiency. Through this method, a full-color HOE with an average diffraction efficiency of 73.4% was implemented in a single photopolymer, the highest rate yet reported. In addition, the AR system is simulated by the geometric optics method combining k-vector circle and ray tracing and structured by combining laser micro-drop and high diffraction efficiency HOEs. A good color blending effect was achieved in a full-color AR system by using the reconstruction wavelength consistent with the recording light. It can present clear holographic images in a full-color AR display system.

Long Period Grating Imprinted on a Flat-Shaped Plastic Optical Fiber for Refractive Index Sensing

A corrugated surface long period grating (LPG) was fabricated on a flat-shaped plastic optical fiber (POF) as a refractive index (RI) sensor by a simple pressing with the heat pressure and mechanical die press print method. The light propagation characteristics of an LPG imprinted on a multi-mode POF were analyzed by the method of geometrical optics. Theoretical and experimental results showed that the structural parameters of the sensor affected the RI sensing performance, and the sensor with a thinner flat thickness, a deeper groove depth of the corrugated surface LPG, and a longer LPG exhibited better RI sensing performance. When the POF with a diameter of 1 mm was pressed with the heat pressure to a flat shape with a thickness of 600 µm, an LPG with a period of 300 µm, a groove depth of 200 µm, and a length of 6 cm was fabricated on it, and the RI sensitivity of 1447%/RIU was obtained with a resolution of 5.494×10−6 RIU. In addition, the influences of the POF cladding, tilting of LPG, and bending of the sensing structure were investigated. The results demonstrated that after removing the cladding and tilting or bending the LPG, the RI sensing performance was improved. When the LPG imprinted on the flat-shaped POF was bent with a curvature radius of 6/π cm, the highest sensitivity of 6 563%/RIU was achieved with a resolution of 2.487×10−9 RIU in the RI range of 1.3330–1.4230. The proposed sensor is a low-cost solution for RI measurement with the features of easy fabrication, high sensitivity, and intensity modulation at the visible wavelengths.

Dynamic sequential radar cross section properties of airborne corner reflector in array

AbstractWith the spread of airborne corner reflector (ACR) in the field of shipborne equipment, radar guided anti‐ship missile is facing new challenges. In order to achieve the mastery of the jamming principle of this apparatus, the paper studied its motion properties and sequential Radar Cross Section (RCS) properties. Firstly, the motion model of the ACR was obtained under certain constraints, by deriving the centroid dynamics equation and rotation dynamics equation according to the theoretical mechanics. Then, the dynamic sequential RCS model of ACR array was established by combining the motion model with the modified geometric optics method and coherent synthesis method. Through the simulation and analysis of the motion model, it was found that the flight process of the ACR can be divided into two stages: fast falling and steady falling. In the fast falling stage, the variables of the ACR system change rapidly, while the ACR rotates slowly and falls smoothly in the steady falling stage. From simulation of dynamic sequential RCS model, the results showed that the obvious depolarisation effect is occur in the fast falling stage. Further statistical analysis showed that, the omnidirectivity of single ACR is well from the dynamic perspective, meanwhile array placement can effectively enhance RCS amplitude and improve the probability density distribution.

Study on the Difference of Wavefront Distortion on Beams Caused by Wavelength Differences in Weak Turbulence Region

In dual-wavelength free-space optical communication systems, the wavefront distortion differences caused by the wavelength difference of the signal and beacon lights cannot be completely corrected. In this study, according to the method of geometric optics, the relationship between the wavefront phases of the signal and beacon lights is analyzed by establishing a mathematical model of the cross-correlation ratio of the arrival-angle fluctuation and phase relationship of different Gaussian-beam wavelengths under weak turbulence near the surface. The numerical results show that after Gaussian beams of different wavelengths propagate through the same atmospheric channel, the cross-correlation number of the arrival-angle fluctuation decreases with an increase in the wavelength difference, waist radius, and turbulence intensity, and increases with an increase in propagation distance. The beam-wavefront phase difference increases with an increasing wavelength difference. Finally, a wavefront distortion correction experiment of a dual-wavelength adaptive optical system verified the correctness of the wavefront phase-difference relationship between the signal light and beacon light established in this study.

On the relation between ice-crystal scattering phase function at 180° and particle size: implication to lidar-based remote sensing of cirrus clouds.

The lack of knowledge of the relation between a lidar backscatter signal and particle size makes it challenging to retrieve ice-cloud particle size from spaceborne lidar observations. This study employs a synergistic combination of the state-of-the-art invariant imbedding T-matrix method and the physical geometric-optics method (PGOM) to investigate the relation between the ice-crystal scattering phase function at 180° (P11(180°)) and particle size (L) for typical ice-crystal shapes. In particular, the P11(180°) -L relation is quantitatively analyzed. The dependence of the P11(180°) -L relation on particle shape can be used with spaceborne lidar observations to detect ice-cloud particle shapes.

Radiation modeling of microplasma UV lamps for design analysis and optimization

Microplasma UV lamps have recently emerged as viable excimer-based sources of UV radiation, garnering significant attention during the recent COVID-19 pandemic for their use in disinfection applications because of their ability to emit human-safe far-UVC (200–240 nm) spectrums. An accurate model to simulate the radiation profile of microplasma UV lamps is of paramount importance to develop efficient microplasma lamp-implemented systems. We developed a 3D numerical model of microplasma UV lamps using the ray optics method. The simulation results for lamp irradiance and fluence rate were experimentally validated with standard optical radiometry and actinometry measurements, respectively. To improve the optical efficiency of microplasma lamps, an in-depth analysis of radiation behavior inside the standard commercially available lamp was performed using the geometrical optics method, and several potential scenarios were explored. A 2D modeling of an individual microcavity indicated that the current common lamp design can be significantly improved by preventing radiation loss, and small modifications in optical design can greatly increase the energy performance of the system. Based on the findings of this study, several virtual design concepts were proposed, and their performances were numerically compared with that of the original design of commercial microplasma lamps. The developed model can potentially be integrated with hydrodynamic and kinetic models for the virtual prototyping of complex photoreactors operating with UV microplasma lamps.

Geometrical Optics Analysis of Diffraction in Patterned Cholesteric Liquid Crystals

A geometrical optics method is developed to analyze the diffraction in patterned cholesteric liquid crystals. We extend the equation for the center wavelength of selective reflection in a conventional cholesteric liquid crystal to the wavelength edges of the diffraction in patterned cholesteric liquid crystals. This method can be used to determine the reflection bandwidth and its wavelength edges of patterned cholesteric liquid crystals which depends on a slant angle and an incident angle. Furthermore, we also investigate a difference in the diffraction between planar and slanted patterned cholesteric liquid crystals using the geometrical optics method.

Statistical Characteristics of the Temporal Spectrum of Scattered Radiation in the Equatorial Ionosphere

On the basis of the solution of the space-time characteristic system by the method of geometric optics using symbolic calculations, analytical and numerical simulation of the propagation of the ordinary and extraordinary radio waves in the conducting equatorial ionospheric plasma was made considering the anisotropy of plasma irregularities and non-stationary nature of propagation medium. Broadening of the spectrum and the displacement of its maximum contain velocity of a turbulent plasma flow and parameters characterizing anisotropic plasmonic structures. Statistical moments of both radio waves do not depend on the absorption sign and are valid for both active and absorptive random media. Temporal pulsations and conductivity of a turbulent ionospheric plasma have an influence on the evaluation of the spectrum-varying propagation distances travelling by these waves. The new double-humped effect in the temporal spectrum has been revealed for the ordinary wave varying anisotropy coefficient and dip angle of stretched plasmonic structures. From a theoretical point of view, the algorithms developed in this work allow effective modelling of the propagation of both radio signals in the equatorial conductive ionospheric plasma, considering the external magnetic field, inhomogeneities of electron density in-homogeneities, as well as non-stationary.

Comparison of geometric optics and «aperture» methods for calculation of the electromagnetic radiation caused by charged particles flying by dielectric objects

Calculation of the electromagnetic field exited by a charged particle flying close to dielectric object is one of the important problems of charged particle radiation theory. In some cases, geometric optics area is preferable for calculations. In the article, two methods of solution of such problem with dielectric prism possessing large size (in comparison with the wavelength under consideration) are considered. One of them is based on geometric optics method, another one is based on asymptotics of «aperture» integrals. It is shown that, in geometric optics area, the first method has a series of advantages. For example, ray tube cross-section expression obtained within geometric optics method allows one to find caustics or to show their abscence, which is demonstrated in the article for three objects of various shapes.

Single-scattering properties of ellipsoidal dust aerosols constrained by measured dust shape distributions

Abstract. Most global aerosol models approximate dust as spherical particles, whereas most remote sensing retrieval algorithms approximate dust as spheroidal particles with a shape distribution that conflicts with measurements. These inconsistent and inaccurate shape assumptions generate biases in dust single-scattering properties. Here, we obtain dust single-scattering properties by approximating dust as triaxial ellipsoidal particles with observationally constrained shape distributions. We find that, relative to the ellipsoidal dust optics obtained here, the spherical dust optics used in most aerosol models underestimate dust single-scattering albedo, mass extinction efficiency, and asymmetry parameter for almost all dust sizes in both the shortwave and longwave spectra. We further find that the ellipsoidal dust optics are in substantially better agreement with observations of the scattering matrix and linear depolarization ratio than the spheroidal dust optics used in most retrieval algorithms. However, relative to observations, the ellipsoidal dust optics overestimate the lidar ratio by underestimating the backscattering intensity by a factor of ∼2. This occurs largely because the computational method used to simulate ellipsoidal dust optics (i.e., the improved geometric optics method) underestimates the backscattering intensity by a factor of ∼2 relative to other computational methods (e.g., the physical geometric optics method). We conclude that the ellipsoidal dust optics with observationally constrained shape distributions can help improve global aerosol models and possibly remote sensing retrieval algorithms that do not use the backscattering signal.

Augmented reality system based on full-color holographic optical elements lens

Holographic optical element (HOE) lens is an imaging element fabricated through recording wavefront by interference. Because of its advantages of small form factor and wavelength, angle selectivity and arbitrary wavefront formation, it has a good application prospect in augmented reality display. To make the system more compact, the HOE lens is adopted as an off-axis optical element. At the same time, according to diffraction principle, its wavelength response is more sensitive than those of traditional refractive and reflective optical elements. Thus the fabrication and design of a full-color HOE lens is a challenge to optimizing the free-space head-up display system. To systematically analyze the HOE imaging system, the conjugate relation between the object and image is derived by scalar diffraction theory. Then the Gaussian conjugate imaging equation is obtained and the off-axis aberration of distortion and astigmatism in the HOE imaging system are analyzed. In addition, A head-up display with field of view (FOV) of 18° and eyebox of 10 mm is simulated and its imaging process is visualized through the geometric optics method of <i> <b>k</b> </i>-vector diagram and ray-tracing. A full-color HOE lens with high diffraction efficiency is fabricated by interference. Its average peak diffraction efficiency is 56.7%, reaching a high level in the world. A prototype of augmented reality system is established by integrating laser pico-projectior with HOE lens. The experimental results of distortion effect and astigmatism effect of the system are obtained, which are consistent with the simulation results. The modulation transfer function (MTF) parameter of the system is measured, and its definition basically meets the requirements of the human eyes for resolution. The aberration of the system is analyzed and the optimization method is proposed. To optimize the monochromatic image quality, an extra cylindrical lens is added to ensure the same optical power of meridian and sagittal plane to eliminate the astigmatism. Besides, a freeform wavefront is designed by the geometric construction method and forms a freeform HOE to deal with the distortion problem. The local recording freeform wavefront can be calculated by the imaging equation. When full-color HOE is applied to the display system, the images of three channels may separate in the space because of their different reconstruction wavelengths and angles. We propose a pre-compensation method of recording process to solve this problem. If these above-mentioned problems can be solved, due to its good image uniformity, sufficient field angle and eyebox area, the head-up display based on HOE lens with extra optical power will have a better application in augmented reality technology.

Six-degree-of-freedom geometrical errors measurement system with compensation of laser beam drifts and installation errors for linear stage

In this paper, an optical measurement system is proposed to measure the six-degree-of-freedom (6DOF) geometrical errors of a linear stage, and the errors are analyzed by the interferometric method and the geometrical optics method. Among them, the interferometric method is mainly used for the position error analysis. This method can solve the problem that geometrical optics is limited by the size of the sensor in our previous system, and improve the measurement accuracy of the position error. The geometrical optics method is used for the error analysis of the remaining 5DOF geometrical errors to simplify the data acquisition time and calculation amount. In addition, this paper also proposes a methodology to compensate for laser beam drifts and installation errors of optical components. We use two sensors to measure the 4DOF laser beam drifts and add them into the proposed mathematical model to solve these errors. We also use sensitivity analysis to analyze the influence of each installation error of optical components and find out the installation errors that need to be considered. Then we bring them into the mathematical model and solved them with least square methods. Finally, we verify the feasibility of the proposed measurement system through repeated experiments and comparisons with a commercial interferometer and an electronic level.