Noncontact measurements of optical inhomogeneity stratified media parameters by location of laser radiation caustics Anastasia V. Vedyashkina *, Bronyus S. Rinkevichyus, Irina L. Raskovskaya V.A. Fabrikant Physics Department, National Research University Moscow Power Engineering Institute, Moscow, Russia * Correspondent author: an.vedyashkina@gmail.com Keywords: stratified medium, caustics, laser refractography, diffusive layer, noncontact measurement of temperature ABSTRACT One method of investigation of optically inhomogeneous media, which is considered in this paper, is the method of 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. Using the structured laser radiation when its high intensity and direction allows to observe and record the beam path and caustic surfaces in the amount of medium that offers additional opportunities for quantitative diagnostic of the refractive index in cross sections of inhomogeneities. Quantitative data on the localization of the caustic surfaces and their projections are informative characteristics, allowing in some cases to carry out reconstruction of the values of the refractive index, as well as related physical parameters of the medium. The paper is dedicated to development of new method for noncontact determination of physical parameters of optical inhomogeneities in transparent stratified media by location of caustics of probing structured laser radiation. It is considered conditions of caustic occurrence by the longitudinal probing of inhomogeneous media by structured laser beams, which are visualized in the cross-section as a family of geometric shapes. Recorded parameters of the caustic are used to solve the inverse problem of refraction for reconstruction of the physical characteristics of media, causing non-uniformity of the refractive index. Two types of optical inhomogeneities are researched in this work: a diffusion layer of liquids and temperature fields near heated or cooled objects. Experimental setup for determination the parameters of diffusion layer of liquid is shown. The paper shows the results of experimental probing diffusive layer of liquid by plane laser beam and occurring caustic surface. Their temporal dynamic is considered. 1. Introduction Investigation of optically inhomogeneous media represents practical and scientific interest, it is often important to know how properties of a medium change by heating or cooling to optimize the operation of heating or cooling elements of power plants. In turn, the process of diffusion plays has important role in many phenomena studied in hydrophysics and oceanography. For detection and visualization of gradient optical inhomogeneities in transparent media, generally used methods such as schlieren and shadowgraph techniques (Settles 2001) allow to obtain the whole idea of shape and dynamics of the observed object. However, for quantitative diagnostic
parameters of medium shadow images of inhomogeneities in a wide collimated laser beam is only suitable in the case of weak refraction when the spatial variation of image intensity is linearly related to gradient of the refractive index. In the case of strong refraction, especially in presence of probing radiation s caustic, quantitative diagnosis of this method is difficult. For quantitative diagnostic of concentration and temperature stratification in liquids causing inhomogeneity of the refractive index there are well-proven laser methods in which informative parameter is a linear or angular displacement of a refractive thin beam or structured elements of the beam (Rinkevichyus 2011). 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 in optically inhomogeneous media and registration of its form deviations with the digital camera (Raskovskaya 2011). This work is a continuation of researches which are represented in (Rinkevicyus 2012). Using the structured laser radiation when its high intensity and direction allows to observe and record the beam path and caustic surfaces in the amount of medium that offers additional opportunities for quantitative diagnostic of the refractive index in cross sections of inhomogeneities. Quantitative data of localization of the caustic surfaces and their projections are informative characteristics, allowing in some cases to carry out reconstruction of the values of the refractive index, as well as related physical parameters of the medium (Raskovskaya 2015). Other optical methods of caustics are widely used in solving of various problems such as (Pazis 2011, Gao 2014). Theory of caustics is directly related with one of mathematical section the theory of catastrophes (Arnold 2012). 2. Diffusive layer of liquid Diffusive layer of liquid is a special type of inhomogeneity, which appears near interface of two liquid media with various physical characteristics (Vedyashkina 2013). In this work liquids with different refraction indexes are researched. It is considered the variation in time of thickness of the diffusion layer formed in contact NaCl water solution (denser liquid with refractive index n1) and distilled water (less dense liquid with refractive index n2). To create the diffusion layer of liquid it is required in a glass cuvette with denser liquid to pour less dense liquid. To avoid mixing process special devices and methods of pouring are used. With this technique at the boundary between two media the diffusion layer appears whose refractive index depends on the coordinate x. Distribution of the refraction index in diffusive layer can be described by different function such as linear or hyperbolic tangent, in this paper exponential model is used (Vedyashkina 2015):
nx n n = + 1 + exp s 1 2 ( ) n2, (( x x ) h) (1) where h is characteristic half-width of layer, xs is middle of layer. Layer s boundaries x1 and x2 are determined by the level of the refractive index deviation from zero to the value of 10 1/m. -5 This type of optical inhomogeneity can be probed by structure laser radiation of various forms: line, matrix of dots, set of conical rings, cross lines and etc. Computer and experimental 3Dvisualization of the plane and cylindrical laser beams refraction and dynamics of the caustics formation when changing laser plane s elevation angle and the refractive index gradient are described in (Vedyashkina 2015). Diffusive layer can be regarded as a set of thin parallel layers of homogeneous liquids with different refractive indices. From this, we can conclude that for visualization of the laser beam in the diffusion layer it is possible to use relation (2), which 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), α0 is the angle under which the ray enters the medium, n0 is refraction index in entry point of the ray in medium: x n0sinα0dx ( ) = z0 +. 2 2 2 0 ± n ( x) n0 sin α0 zx (2) Using this expression it is possible to simulate propagation of the plane laser beam in diffusion layer of liquid by approximating it with a set of infinitely thin rays. Fig. 1 shows formation and confluence of two caustic surfaces and the refractive index distribution. 1 2 Fig. 1. Modeling of caustics (1) formation and point of their confluence (2) in the propagation of plane laser beam in diffusive layer
With the help of this refractogram modeling and determination the location shape of caustics and the point of confluence it will be possible to solve the inverse task of finding properties of the medium in comparison with the experimental results. In order to observe and register refractogram of plane laser beam propagation in inhomogeneous media it is possible to use setup, which is presented in Fig. 2. By laser 1 and built-in optical system 2 it is formed plane laser beam, which probes cuvette 3 with created in it diffusive layer 4. 2D-refractogram 7 is registered by digital camera 5 and processed using special algorithm on personal computer 6. Fig. 2. Setup for experiment with the diffusive layer of liquid and probing plane laser beam: 1 laser, 2 optical system, 3 transparent cuvette, 4 diffusive layer, 5 digital camera, 6 PC, 7 2D-refractogram Experimentally obtained refractograms, which were made at different times from the inception of the diffusive layer, are shown in Fig. 3 (a-d). This refractogram storing was made by recording the scattered radiation on special particles added in water. Parameters of medium: refractive indexes of saline water n1 = 1.3453 and distilled water n2 = 1.3305.
18th International Symposium on the Application of Laser and Imaging Techniques to Fluid Mechanics LISBON PORTUGAL JULY 4 7, 2016 a) b) c) d) Fig. 3. Experimentally obtained refractograms of the plane laser beam propagation in the diffusive layer of liquid at different times: a) 0, b) 20 min, c) 40 min, d) 60 min Using a specially devised algorithm for refractogram processing it is possible to separate caustic surfaces. Comparing their position and coordinate of their confluence with the calculated ones we can get distribution of the refractive index or the value h. Registering refractograms at variable moments of time allows to determine the dependence of the refractive index distribution on time, that gives an indication on how liquids diffuse each other. 3. Spherically inhomogeneous media In order to investigate of convective processes near the surface of the heated or cooled body in liquid it is possible to use correlation processing of refractive images of structure beams, it allows to restore the temperature distribution in the boundary layer. However, a number of practical problems is required to determine temperature of the body surface. In this case for noncontact monitoring of thermal characteristics of the process it is advisable to use empirical dependences the position of the singular points of observed caustics on the surface temperature (Raskovskaya 2014). In the case of sensing the boundary layer near the cooled ball while moving the observation screen plane laser beam in a section where there is a "beak" of the caustic, there is a particular point (beak) on refractograms (Fig. 4).
a) b) Fig. 4. View of the refractogram characterizing the position of the "beak" of the caustic a) computer modeling; b) experimentally obtained refractogram Fig. 5 shows the dependence of distance z (relative to the center of the ball), which is fixed on a singular point, on the surface temperature of the ball. In fact, the position of the singular point is determined by the difference between surface temperature and liquid. Empirical curves for three different water temperatures T0 were plotted. Fig. 5. Empirical dependence of the position of the singular point of the caustic on surface temperature of the body at different temperatures of water T0 Using this dependences it is possible to determine the serface temperature of the ball. For example, at the temperature of water T0 = 60 C and at the distance z = 500 mm of the beak of the caustic position relatively to the ball center temperature of the ball serface is T = 37.5 C.
4. Conclusion This article describes a new method for noncontact determination of the inhomogeneity parameters of the investigated medium. This method is based on the detection of singular points of caustics position of the structured laser radiation generated in inhomogeneous media. Two examples of the method application are considered: determination of the diffusive layer parameters formed as the result of contact between two liquids and measuring temperature of the cooling body surface placed in transparent liquid. 5. Acknowledgements This work was supported by Russian Foundation for Basic Research (grant No 16-32-00530-mol_a and grant No 14-08-00948-а). 6. References o Arnold V, Gusein-Zade S, Varchenko A (2012) Singularities of Differentiable Maps. Volume I., Springer, New York o Gao G, Li Z, Negehban M (2014) Dynamic fracture analysis of polycarbonate by the optical method of caustics. Procedia materials science:165 176 o Pazis D, Agioutantis Z, Kourkoulis S (2011) The optical method of reflected caustics applied for a plate with a central hole: critical points and limitations. An international journal for experimental mechanics 47(6):489 498 o Raskovskaya I (2014) Refractometry of optical inhomogeneous media by registration of caustics position with used of structured laser radiation. Avtometriya 50(5):92 98 o Raskovskaya I (2015) Specific Imaging of Caustics upon Refraction of Structured Laser Radiation in Stratified Media. Technical Physics 60(6):911 916 o Raskovskaya I, Rinkevichyus B, Tolkachev A (2011) Structured Beams in Laser Refractography Applications. In books: Laser Beams Theory, Properties and Applications. Nova Science Publishers. Inc., New York, pp.399 414 o Rinkevichyus B, Evtikhieva O, Raskovskaya I (2011) Laser Refractography. Springer, New York
o Rinkevichyus B, Skornyakova N, Tolkachev A, Raskovskaya I (2012) Diagnostics of Boundary Effects in Fluids using Structured Laser Radiation. Processings of 16th Int. Symp. on Applications of Laser Techniques to Fluid Mechanics. Lisbon, Portugal o Settles G (2001) Schlieren and Shadowgraph Techniques, Visualizing Phenomena in Transparent Media. Springer, New York o Vedyashkina A (2013) Computer modeling of optical rays refraction in inhomogeneous mediums. Journal of Beijing Institute of Technology 22 (1):71 76 o Vedyashkina A, Raskovskaya I, Pavlov I (2015) Formation of Caustics by Refraction of Structured Laser Radiation in the Diffusive Layer of Liquid. PIERS Proceedings, Prague, Czech Republic:884 887 o Vedyashkina A, Rinkevichyus B (2015) 3D-visualization of Caustics Formation in Laser Refractography Problems. Physics Procedia 73:205 210