Caustic Image Research Articles

Mix-and-match holography

Computational caustics and light steering displays offer a wide range of interesting applications, ranging from art works and architectural installations to energy efficient HDR projection. In this work we expand on this concept by encoding several target images into pairs of front and rear phase-distorting surfaces. Different target holograms can be decoded by mixing and matching different front and rear surfaces under specific geometric alignments. Our approach, which we call mix-and-match holography, is made possible by moving from a refractive caustic image formation process to a diffractive, holographic one. This provides the extra bandwidth that is required to multiplex several images into pairing surfaces. We derive a detailed image formation model for the setting of holographic projection displays, as well as a multiplexing method based on a combination of phase retrieval methods and complex matrix factorization. We demonstrate several application scenarios in both simulation and physical prototypes.

Efficient freeform lens optimization for computational caustic displays.

Phase-only light modulation shows great promise for many imaging applications, including future projection displays. While images can be formed efficiently by avoiding per-pixel attenuation of light most projection efforts utilizing phase-only modulators are based on holographic principles which rely on interference of coherent laser light and a Fourier lens. Limitations of this type of an approach include scaling to higher power as well as visible artifacts such as speckle and image noise. We propose an alternative approach: operating the spatial phase modulator with broadband illumination by treating it as a programmable freeform lens. We describe a simple optimization approach for generating phase modulation patterns or freeform lenses that, when illuminated by a collimated, broadband light source, will project a pre-defined caustic image on a designated image plane. The optimization procedure is based on a simple geometric optics image formation model and can be implemented computationally efficient. We perform simulations and show early experimental results that suggest that the implementation on a phase-only modulator can create structured light fields suitable, for example, for efficient illumination of a spatial light modulator (SLM) within a traditional projector. In an alternative application, the algorithm provides a fast way to compute geometries for static, freeform lens manufacturing.

High-contrast computational caustic design

We present a new algorithm for computational caustic design. Our algorithm solves for the shape of a transparent object such that the refracted light paints a desired caustic image on a receiver screen. We introduce an optimal transport formulation to establish a correspondence between the input geometry and the unknown target shape. A subsequent 3D optimization based on an adaptive discretization scheme then finds the target surface from the correspondence map. Our approach supports piecewise smooth surfaces and non-bijective mappings, which eliminates a number of shortcomings of previous methods. This leads to a significantly richer space of caustic images, including smooth transitions, singularities of infinite light density, and completely black areas. We demonstrate the effectiveness of our approach with several simulated and fabricated examples.

Characterizing the geometry of InAs nanowires using mirror electron microscopy

Mirror electron microscopy (MEM) imaging of InAs nanowires is a non-destructive electron microscopy technique where the electrons are reflected via an applied electric field before they reach the specimen surface. However strong caustic features are observed that can be non-intuitive and difficult to relate to nanowire geometry and composition. Utilizing caustic imaging theory we can understand and interpret MEM image contrast, relating caustic image features to the properties and parameters of the nanowire. This is applied to obtain quantitative information, including the nanowire width via a through-focus series of MEM images.

112 3次元応力問題に対するコースティック像シミュレーションの適用(OS2-(2)オーガナイズドセッション《材料強度と構造設計》)

The method of the caustics is well known as a technique to measure the stress intensity factor. In this method, numerical simulation of the caustic image is necessary to evaluate the stress intensity factor. Since the plane stress state has been assumed in previous studies, experimental result doesn't coincide with the theoretical one when the caustic image is delivered from the vicinity of the crack tip. In such case, the caustic image becomes smaller than the theory in which plane stress is assumed. Accordingly, we developed a new simulation system of the caustic image for 3D stress field coupled with 3D FEM analysis. Our system could provide the caustic image that met experiment even the caustic image delivered from vicinity of the crack tip. Furthermore, we could obtain the image better agreed with the experiment, when we consider the stress distribution through the thickness direction in detail.

G2000-1-3 生活の中のコースティック像のコンピュータ・シミュレーション(技術と社会部門一般講演,社会変革を技術で廻す機械工学)

Caustic image is one of bright line images created by concentrating light rays. We can see the typical image like a half of a nephroid created at the bottom of a cup by reflected light from the wall. The method of caustics is an engineering application to evaluate stress intensity factors of cracks and contact forces of contact problems. This report deals with a computer program and simulation for caustic images observed in our daily life for easy understanding the principle of caustic. The computer program developed can simulate caustic images for variable conditions, such as the position and type of light source, the size and shape of the cup of object. This computer program is possible to apply to engineering problems as well.

1157 汎用有限要素解析ソフトウェアを用いたコースティック像の簡易シミュレーション(G03-6 材料力学(6)力学挙動2,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

The caustic method is a non-contact measurement method using a laser ray. This method has been applied to evaluate contact forces and stress intensity factors. For the application of the caustic method, numerical simulation is necessary to evaluate the stress state from the caustic image. However, the theoretical simulation is not possible if the stress state is complex. In the paper, we propose to use ANSYS, which is general used FEM software, for the simulation. This method will be applicable for more complicated stress state.

20419 Javaを用いたコースティックス法測定システムの開発 : 応力拡大係数の測定への応用(材料力学(2))

The caustics method is a non-contact measurement method using a laser ray. This method has been applied to stress concentration state such as a crack tip to measure the stress intensity factors. This method has a lot of advantage: for example, it is applicable to a continuous measurement of a dynamic change of stress distribution; it is easy to set up the optical apparatus for measurements. For using the caustics method, the theoretical simulation is necessary to evaluate the stress intensity factors from the caustic images. So, in this paper, simulation program of caustic image based on the theory is developed. "Java" is used as the programming language, thus this program can be used through the following web site without limitation of time and area.

4049 Javaを用いたコースティックス法測定システムの開発 : 接触力の測定精度の検証(G03-8 解析・計算技術,G03 材料力学)

The method of caustics, which is one of nondestructive optical measuring methods, is powerful technique to evaluate stress intensity factors (SIFs) and contact forces using caustic images formed from their stress concentrated areas. The shape and size of the caustic images depend on conditions of material, thickness, optical setup, etc. Caustic image simulation is applicable to evaluate the values of SIFs and contact forces. A subject was a fact that the relationships between contact forces and size and shape of the images are widely changed with the conditions, then numerical simulations were necessary before the tests. In this paper, therefore, database of the relationship between the loading conditions and the caustic images is developed, and then the evaluation program of the contact load from the caustic image is developed. Using this program, pre-simulation is no longer necessary to apply the method of caustics to measure the contact load.

1453 ポリカーボネートの環境変化におけるクレーズへの影響(S20-2 材料特性評価(2),S20 実験力学的手法による材料・製品の評価)

The experimented about the craze which it was high molecular matter (plastic materials) polycarbonate (PC) was used, and occurred on the crack tip, and it was analyzed. What is craze, there is a thing growing on a defect part of materials by a phenomenon peculiar of low crystallization nature high molecular matter such as a PC. The experiment method thought that technique of optics was effective than transparency of a PC photoelasticity method and caustics method were used jointly by this study, and they experimented. CT specimen is used for reference by a JSME standard as specimen shape. a quantity of crack development, examination by crack opening displacement (COD) are done by a photoelasticity method. J value by measuring a diameter of a caustic image by caustics method was calculated.

Low Velocity Impact Study of Laminate Composites with Mode I Crack Using Dynamic Optical Caustics

The dynamic evolutions of stress singularities at mode I crack tip in laminate composites are studied by combining optical caustic with high-speed schardin camera. Theoretical caustics and initial curve for two different fiber laminate composites are simulated. Some characteristics of stress singularity at crack tip are analyzed. On the other hand, the generation and the subsequent evolution of dynamic failure around the crack tip are visualized by the optical shadow spots. The characteristic sizes of local stress concentration are extracted and the stress intensity factors at crack tip are determined. The local response and failure evolution mechanism of laminated composite after impact are analyzed by means of a series of optical caustic image and the deformation of composites.

Determining the Optical Properties of PETAL, the 400m2 Parabolic Dish at Sede Boqer

PETAL (Parabolic Energy Transformation and Astrophysics Laboratory) is a large multipurpose dish-shaped concentrator, located at Sede Boqer. Its 2-axis tracking paraboloidal surface, with aperture area in excess of 400m2, is constructed from 216 adjustable mirror panels. The very large aperture and high concentration ratio of PETAL render the direct characterization of its optical performance a nontrivial task. We have applied a variety of methods in order to assess PETAL’s optical quality. These include imaging the full moon and Jupiter at night, and analysis of the 3-D caustic image produced by the scattering of focused sunlight off particles in the air. The main results of these studies, together with the preliminary results of measurements on 36 individual panels, are presented here. Among the three measurements that look at objects of the same angular size (i.e. the sun and moon), the average image size (i.e. radius of circle containing 90% of the intensity) is 0.247±0.012m, demonstrating a 5% spread about the mean for three different methods. This result is in agreement with 0.22 m for the Jupiter image. Successful application of these methods for characterization of PETAL proves their applicability to more commonly used solar dishes of smaller sizes but with similar or better concentration ratios.

コースティックス法のWEBプログラムの開発 : 円板/円板接触への適用(G03-6 実験計測(2),G03 材料力学)

The method of caustics, which is one of nondestructive optical measuring methods, is powerful technique to evaluate stress intensity factors (SIFs) and contact forces using caustic images formed from their stress concentrated areas. The shape and size of the caustic images depends on conditions of material, thickness, optical setup, etc. Caustic image simulation is applicable to evaluate the values of SIFs and contact forces, and also to set the experimental conditions before tests. To widely use the method and simulation of caustics, in this paper, a Java program has been developed for online simulations via web. The site opened is http://www.kouku-k.ac.jp/〜t-tamiya/index.html.

Application of the Method of Caustics to Rolling Contact Fatigue and Simulation of the Caustic Images.

As a series of studies to clarity the mechanism of crack initiation and propagation in rolling contact fatigue, the experimental method of caustics has been applied to disk-to-disk rolling contact fatigue tests. The cusp-like and round type caustic images were generated from the rolling contact point and the crack tip, respectively. Although the shape and size of the cusp-like image depending on the magnitude of applied load was constant, that of the round image was markedly changed with the relative position between the crack and the rolling contact point. The experimental caustic images have been simulated using a computer program developed by combining the theory of caustics with the theory of boundary element method. By comparing experimental caustic images with simulated ones, it is shown that the round type caustic image obtained in rolling contact is strongly affected by shear deformation of the crack.

A Direct Caustics Simulation Method Based on FEM.

In this paper, for the sake of prediction of caustic experiments, explanation and verification of experimental results, a new numerical method based on the finite element method, which can directly simulate the caustic patterns, is presented. Based on this new idea, the program for directly determining the gradient solution from the 2 dimensional displacement solution is presented. It is also proven to be necessary for only 8 or 12 node isoparametric element to apply this new method to the 2 dimensional problem. For verifying the accuracy of this method, the simulations of 4 point bending problem and concentrated load problem are performed. The simulated results have good agreement with the theoretical values. As the applied examples, the simulation is carried out for the plate specimen with a single edge crack, or double edge crack, or a short single edge crack under mode I condition. The changes of caustic image under the influence of the interferometry between cracks and the influence of the boundary are given.

Simple calibration method for determining KI using the method of caustics

The uncertainty in selecting the length parameter (the maximum diameter) of a caustic image is investigated. A simple calibration method is used to determine the mode-I stress intensity factor <i>K_I</i> at a crack tip. The accuracy is further improved by using white light. The effect of the pinhole size on the determination of <i>K_I</i> is investigated. The accuracy of the proposed measurement location is demonstrated by comparing experimental results with theory.

Determination of [formula omitted] and [formula omitted] by using a least-squares method with caustics

Current techniques that utilize the method of caustics to determine stress intensity factors at a crack tip use only a limited amount of data from the caustic image. This paper presents a non-linear least-squares technique that has been developed to extract K I , K II and the initial curve radius r 0 from an overdetermined set of data. Since the crack tip is obscured by the caustic, the technique presented treats the crack tip location as an unknown. The tip location is determined numerically during an iteration process. The diffraction effect is considered using a digital image-analysis system, EYECOM III. Thin plexiglas specimens with two parallel edge cracks are loaded in tension and used to illustrate the technique.

Evaluation of Stress Intensity Factor of Silicon Nitride with Bridge Indentation Crack by Caustic Method

The caustic method is an optical technique for determining the dynamic stress intensity factor of metals and plastics. In this study, the application of the caustic method to ceramics was investigated, and a technique is proposed here for determining the static stress intensity factor from a fine caustic image of a ceramic specimen. The degree of deviation of parallelism and surface roughness of a specimen are important factors in obtaining a clear caustic image of ceramics. A reliable method for measuring the diameter of a caustic by image processing was proved to be effective in this experiment. The stress intensity factor of Si3N4 with a BI (bridge indentation) crack was evaluated, and the residual stress intensity factor caused by a Vickers indentation for a starter crack was examined using this method.

Caustic Image Simulation Based On BoundaryElement Method

The experimental method of caustics has been applied to rolling contact fatigue for determining the crack growth mechanism. Caustic images formed from stress fields under rolling contact with a crack are very complicated. Therefore, the theoretical background of the experimental caustic images formation has been studied through caustic image simulations. The simulation has been done by the scheme combining directly caustics method with boundary element method. The size and shape of simulated caustic images, which are formed from the contact region and crack tip in disk-on-disk rolling contact fatigue, was coincident with experimental caustic images. In the present paper, the computer program was extended to simulate not only caustic images but also their initial curves that are loci of points in the disk through where the light rays passed. This program is utilized to discuss the mechanism of damage formation in rolling contact fatigue and to examine experimental results.