3D positioning of micro-spherical particles by using ... - IEEE Xplore

MP6 18.00 - 19.30

3D positioning of micro-spherical particles by using genetic algorithms D. Moreno-Hernández1, V. Ayala-Ramirez1,2, J. A. Guerrero-Viramontes 1 1

Centro de Investigaciones en Óptica A. C. Loma del Bosque 115, Lomas del Campestre, León, Gto., México, 37150 2 Universidad de Guanajuato FIMEE Campus Salamanca Carr. Salamanca-Valle Km. 3.5+1.8, Salamanca, Gto., Mexico, 36700 Abstract-We propose to use an automatic method for detecting and measuring the Central Spot Size (CSS) of a particle image to determine particle defocus position by using a genetic algorithm (GA) optimization process.

I. INTRODUCTION Three-dimensional (3D) positioning of micro spherical particles in 3D velocimetry applications has become an invaluable tool in diverse scientific disciplines such as microbiology, colloidal science and fluid mechanics. As a result, many imaging techniques such as stereoscopic imaging [1], holography [2], and quantitative defocusing methods have been developed for particle positioning determination [3-5].

Fig. 1. Central spot size determination of a calculated particle image diffraction pattern. III. TESTS AND RESULTS

Several methods based on defocusing have been developed to determine the out of plane position (or defocus position) of spherical particles embedded in a fluid flow. Some of them rely on intensity measurements from an experimental particle image and compare them to numerical calculations of the particle light scattering model using the classical Lorenz-Mie theory [3], however non-uniformities in the incident light are present in experimental particle images and make the defocus particle extraction difficult. More-advanced theoretical and experimental techniques depend on the ability to handle a more-general problem in which the scatter center is illuminated by a laser beam and have led to the so called Generalized Lorenz–Mie Theory (GLMT). The GLMT was used in [4,5], however, the procedure to extract defocus position is based on an optimization matching algorithm among the experimental and calculated intensity particle image which does the procedure a time consuming and error-prone task.

The experimental set-up devised allows recording of forward scattering, as in [4,5] (see Figure 2). The experimental set-up included a 35mW He-Ne laser used to illuminate micro-spherical particles, a Canon lens used to capture light scattered by the particles and a Lumenera 1280 by 1024 pixels digital camera used to record image diffraction particle patterns.

Fig. 2. Forward scatter set-up for experimental image acquisition.

In this work we propose to use an automatic method for detecting and measuring the Central Spot Size (CSS) of a particle image to determine particle defocus position by using a genetic algorithm (GA) optimization process [6]. II. OUR APPROACH Using the genetic algorithm method, we search for the triad of points that define the circle in the particle image having the minimal intensity average, a property exhibited by the CSS. When a spherical particle is imaged it is well known that its diffraction pattern CSS presents diameter variations due to two parameters: particle size variations and particle defocusing away from its focal plane position. Therefore, we proposed method based on the measurement of the CSS of a spherical particle image and searching for its nearest value in a CSS calibration curve determined by using a GA-based method on known defocus images. The CSS is typically defined as the first ring in the diffraction pattern of a particle image as the one generated theoretically and shown in Figure 1.

Fig. 3. Experimental defocused images for calculation of calibration curve.

978-1-4244-1926-5/08/$25.00 © 2008 IEEE

21

IV.

CONCLUSION

We are presenting an automatic method to determine 3D particle position of micro-spherical particles. The method was applied to position micro-spherical particles immersed in water. Our method attains subpixellic accuracy that results in an improved resolution for particle depth estimation. REFERENCES [1] R. G. Racca and J. M. Dewey, “A method for automatic particle tracking in a three-dimensional flow field”, Exp. Fluids 6, pp. 25, (1988). [2] Y. Pu, X. Song and H. Meng, “Holographic PIV for diagnosing particulate flows”, Exp. Fluids 29, pp. (2000). [3] B. Ovryn, “Three-dimensional forward scattering particle imaging velocimetry applied to a microcopic field-ofview”, Exp. Fluids, N, pp. 175- 84 (2000). [4] D. Moreno, F. Mendoza-Santoyo, J. A. Guerrero and M. Funes-Gallanzi, “Particle positioning from a single CCD image for Application to Velocimetry: theory and comparison to experiment”, Applied Optics, 39 (28), pp. 5117-5124 (2000). [5] J. A. Guerrero, F. Mendoza-Santoyo, D. Moreno, M. Funes-Gallanzi, and S. Fernandez, "Particle positioning from CCD images: experiments and comparison to the Generalized Lorenz-Mie Theory", Meas. Sci. Technol., 11(5), pp. 568-75 (2000). [6] V. Ayala-Ramirez, C. H. Garcia-Capulin, A. PerezGarcia, and R.E. Sanchez-Yanez. “Circle detection on images using genetic algorithms”. Pattern Recognition Letters, 27, pp. 652–657, 2006.

Fig. 4. Calibration curve for particles of size 37.5 µm.

Fig. 5. A test image of micro-spherical polystyrene particles of identical sizes immersed in water. In order to be able to measure out of plane particle position, a calibration curve that characterize the distance “z” under analysis it is needed. Therefore, the first step in our approach was to obtain the calibration curve which it consists of the recording of particle images for different positions along the “z-coordinate”. To fulfil this purpose, a set of images from 37.5 µm diameter polystyrene particles imaged at different defocus distances ranging from 0 to 3.0 mm in 0.1 mm steps (see Figure 3). A graph of the zcoordinate vs. CSS was determined as it is shown in Figure 4. The determination of the CSS for each particle image was determined by using the GA-based algorithm. Once the calibration curve is obtained, the 3D position of a particle can be determined completely; i.e “x” and “y” coordinate are determined by calculating the particle image centroid and the “z” coordinate by determining the particle image CSS and related directly to the calibration curve. We applied our process to the determination of 3D position of particles immersed in water. We have imaged micro-spherical particles of the same size at a given distance (Fig 5). Our method detects the particles with a difference of radius lower than 0.5 pixels.

22