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Physics Procedia 73 ( 2015 ) 205 – 210
4th International Conference Photonics and Infoformation Optics, PhIO 2015, 28-30 January 2015 3D-visualization of caustics’ formation in laser refractography problems
A.V. Vedyashkina*, B.S. Rinkevichyus
Nattional Research University “Moscow Power Engineering Institute”, V.A. Fabricant Physics Department, Krasnokazarmennaya st. 14, Moscow 111250, Russia
Abstract
In an optically homoogeneous medium (a medium in which the refractive index is the same in any point) light spreads rectilinearly without being refracted. However, the refractive index can be changed, its gradient can be created as a result of making inhomogeneity. Such inhomogeneity can be made by diffusion of liquids or their heating, cooling, and so on. One actual and promising method of researching optically inhomogeneous media is the method of the laser refractography. It is based on the phenomenon of refraction of structured laser radiation in optically inhomogeneous media and registration of its form deviations with the digital camera. Two types of optical inhomogeneitiees are researched in this work: a diffusion llayer of liquids and temperature fields near heated or cooled objects. It was considered conditions for the occurrence of caustics in longitudinal probing of optical sttratified inhomogeneous media by plane and cylindrical laser beams in this paper. Experimental setup for 3D- visualization of laser beams’ refraction was shown. © 20152015 The The Authors. Author s.Published Published by bElseviery Elsevier B.V. B.V. This is an open access article under the CC BY-NC-ND license (Peerhttp://creativecommons.org/licenses/by-nc-nd/4.0/-review under responsibility of the National). Research Nuclear University MEPhI (Moscow Engineering PPhysics Institute). Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) Keywords: caustics; structured laser radiation; laser refractography; refraction’s dynamics; 3D-visualization; optical inhomogeneous medium; diffusive layer.
1. Introduction
Currently research of optically inhomogeneous media represents great scientific interest. IIn such media the refractive index is not the same in any point and light spreads due to refraction not rectilinearly. Itt is often important to know what occurs when two or more mediums with diffferent physical characteristics contact eaach other, how the
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1875-3892 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the National Research Nuclear University MEPhI (Moscow Engineering Physics Institute) doi: 10.1016/j.phpro.2015.09.158 206 A.V. Vedyashkina and B.S. Rinkevichyus / Physics Procedia 73 ( 2015 ) 205 – 210
refractive index of liquid changes by heating or cooling objects inside it. Methods for optically inhomogeneity exploration can be significant in researches of the diffusion process, optimization of heating or cooling elements’ work. One method of investigation optically inhomogeneous media is the method of laser refractography. It is based on the phenomenon of refraction of structured laser radiation (SLR) in optically inhomogeneous media and registration of its form deviations with the digital camera [Rinkevichyus, Evtikhieva, Raskovskaya (2011), Raskovskaya, Rinkevichyus, Tolkachev (2011)]. This method is in essence different from the previously known methods for researching of optically inhomogeneity such as schlieren and shadowgraph techniques [Settles (2001)]. Application of laser techniques for the reconstruction of physical characteristics of medium, causing inhomogeneity of the refractive index it is advisable to probe medium by structured laser beams (SLB) formed by diffractive optical elements (DOE). Use of structured laser radiation as opposed to wide light beams allows with high accuracy to estimate changes of the refractive index in the boundary layer. Bright light fanciful curves arise on the lit table, on which a glass of water was put. Similar moving curves can be seen at the bottom of a shallow pond, water surface of which is roughness. This curves are caustics. Caustic is the envelope of light rays reflected or refracted by the curved surface or object [Born, Wolf (1999)]. But in this method, caustics are special lines and special surfaces near which the intensity of the light field increases sharply [Vedyashkina (2013)]. Other optical methods of caustics are widely used in various problems such as [Pazis, Agioutantis, Kourkoulis (2011), Gao, Li, Negehban (2014)]. When probing inhomogeneity by SLB caustics appears, its location can be determined using refractogram processing program with high precision, it is possible to solve the inverse task of finding properties of the inhomogeneous medium. Theory of caustics is directly related with one of mathematical section – the theory of catastrophes [Arnold, Gusein-Zade, Varchenko (2012)]. Computer and experimental 3D-visualization in laser refractography technique helps better understand the structure of inhomogeneity in liquids.
2. Description of the method of shots modelling
Diffusive layer of liquid is a special type of inhomogeneity, which appears near interface of two liquid media with various physical characteristics. In this work liquids with various refraction indexes are considered. The diffusion layer is a stratified medium, the refractive index depends only on the one Cartesian coordinate. Thus, when slowly pouring thin layer of less dense liquid with the refractive index n1 on the surface of optically denser liquid with the refractive index n2 eventually between them the diffusion layer is formed, its refractive index can be described by the following expression of hyperbolic tangent [Raskovskaya (2014)]:
nn12 nn 12§· xx s nx() th¨¸, (1) 22©¹h
where h – characteristic half-width of layer, xs – middle of layer. Layer’s boundaries x1 and x2 are determined by the -5 level of deviation from the refractive index values n1 and n2 at 10 respectively. This type of optical inhomogeneity can be probed by SLR of various forms: line, matrix of dots, set of conical rings, cross lines and etc. Computer and experimental 3D-visualization of the plane laser beam refraction and dynamics of the caustics’ formation when changing laser plane’s elevation angle and the refractive index gradient are described in [Vedyashkina, Pavlov, Raskovskaya, Rinkevichyus (2014)]. Relation (2) is the equation of the ray trajectory in a plane-layered medium, given the refractive index distribution n(x) and the initial conditions z0 = z(0), Į0 – the angle under which the ray enters the medium, n0 – refraction index in entry point of the ray in medium: A.V. Vedyashkina and B.S. Rinkevichyus / Physics Procedia 73 ( 2015 ) 205 – 210 207
x n0 sinĮ0dx zx() z . (2) 0 ³ 2 22 0 r nx( ) n0 sin Į0
Using this exprression it is possible to simulate propagation of a parallel cylindrical laser beam in diffusion layer of liquid. Let layered-inhomogeneous medium in which there is the diffusive layer has the following parameters: n1 = 1.3380, n2 = 1.3320, xs = 50 mm, h = 1.1 mm. For visualization of caustics there are three characteristic main positions: laser beam’s center lies in the planes of the upper, lower booundaries layer and in the plane of middle of layer. Fig. 1 shows this causes, different colors show the different radii of the cylinders (red – 8 mm, green – 16 mm).
a b c
Fig. 1. Modeling of 3D-visualization of cylindrical laser beam’s refraction in diffusive layer of liquid and caustics (1) formation: (a)) beam’s center lies in the plane of middle of layer; (b) beam’s center lies in the plane of upper bounddaary; (c) beam’s center lies in the plane of lower boundary
In order to observe and register refractogram of cylinddrrical laser beam propagation in inhomogeneous media it is possible to use experimental setup, which is presented in Fig. 2. To form cylindrical laser beeam it was created optical system, which consists of laser 1, lens 2 for focusinng beam in registration area, DOE 3 and lens 4 for making beam parallel. In order to receive 3D-refractograms without distortion it was suggested to use two cuvettes [Yesin, Raskovskaya, Rinkevichyus, Tolkachev (2012)]. Creation of diffusive layer is taking place in cuvette 5, registration of refractogram is implementeed in the second cuvette 6. Registration of 3D-refractoram 8 was made by digital camera 7 and processed on personal computer 9. For creation of diffusive layer of liquid we used distilled water and watere -NaCl mixture. Refractogram storing was made by recording the scattered radiation on special particles added in water. Parameters of medium: refractive indexes of salinne water n1 = 1.3410 and distilled water n2 = 1.3320.
Fig. 2. Experimental setup: 1 – laser, 2, 4 – lenses, 3 – DOE, 5 – cuvette with diffusive layer of liquid, 6 – cuvette with sscattering particles in water, 7 – digital camera, 8 – 3D-refractogram, 9 – PC 208 A.V. Vedyashkina and B.S. Rinkevichyus / Physics Procedia 73 ( 2015 ) 205 – 210
3D-refractogram of the laser beam propagating in the inhomogeneous medium is shown in Figg. 3.
1
a b
1 1 c d
Fig. 3. Experimental 3D-refractogram of cylindrical laser beam’s refraction in diffusive layer of liquid and caustics (1) foormation: (a) laser beam propagation in homogeneous medium; (b) beam’s center lies in the plane of middle of layer; (c) beam’s center lies in the plane upper boundary; (d) beam’s center lies in the plane lower boundary
3. Spherically inhomogeneous mediums
Distribution of refraction index in spherically symmetric temperature field near cold ball withh the radius R in hot water can by described by the radial temperature dependence:
2 rR (3) a2 Tr TT0 'e,
where T 0, 'T, a – are the parameters of the temperature field model, the T 0 parameter is determine by temperature of cuvette’s wallls with liquid, and the relation of 'T/a corresponds to the gradient of the temperature field in A.V. Vedyashkina and B.S. Rinkevichyus / Physics Procedia 73 ( 2015 ) 205 – 210 209 boundary layer with thickness ɚ. Then transition to dependence of refraction index on temperature is realized with support of the following approximating dependence [Rinkevichyus, Pavlov, Raskovskay, Tolkachev (2014)]:
2 nT n0 0,000051 Tr ( ) 0,0000011 Tr ( ) . (4)
3D-refractograms of plane laser beam, which in propagated over the cold ball with the radius 8.4 mm are presented in Fig. 4.
1 1
a b
Fig. 4. 3D-refractogram of plane laser beam propagation over the cold ball in hot water and caustics (1) formation: (a) difference between temperatures ǻT = 50°C; (b) difference between temperatures ǻT = 60°C
It is possible to see how 3D-refractograms change. As usually, laser sheet curved in direction of increasing gradient of refractive index. 2D-refractogram in this case looks like a loop, which decreases with decreasing of refractive index gradient (difference between temperatures). This case is much harder to reproduce in experiment because of this medium is very nonstationary and light intensity distribution in it is irregular.
4. Conclusion
3D-visualization of structured refractive laser radiation’s refraction makes possible to see the caustic surfaces in volume, as well as get qualitative notion of the optical inhomogeneity and gradient of the refractive index. 3D computer refractogram modeling allows optimize experiments. To solve the inverse task of reconstruction the properties of the medium in the method of laser refractography it is necessary to make 2D-refractograms registration, surveying the front wall of the cuvette, or side wall with pre-installed on it measurement screen.
Acknowledgements
This work was supported by Russian Foundation for Basic Research (grant ʋ 14-08-00948-ɚ).
210 A.V. Vedyashkina and B.S. Rinkevichyus / Physics Procedia 73 ( 2015 ) 205 – 210
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