STUDY ON THE AXIAL DISTRIBUTION OF THE STORED MICROPARTICLES IN AN ELECTRODYNAMIC TRAP BY USING SOFTWARE IMAGE PROCESSING

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1 STUDY ON THE AXIAL DISTRIBUTION OF THE STORED MICROPARTICLES IN AN ELECTRODYNAMIC TRAP BY USING SOFTWARE IMAGE PROCESSING O.S. STOICAN National Institute for Laser, Plasma and Radiation Physics Atomistilor 409, RO , PO BoxMG36, Măgurele-Bucharest, Romania Received July 16, 2015 A method aimed to study the properties of a solid particles assembly trapped by an electrodynamic trap is reported. Method is based on the digital processing of the trapped microparticles video image obtained by using a web camera. The algorithm used to derive the trapped microparticles axial density distribution from qualitative information embedded in an image is described. Key words: Electrodynamic trap, web camera, digital image processing. PACS: Kf, Hj, Ty, d, t. 1. INTRODUCTION An electrodynamic trap is able, under certain conditions, to maintain the charged solid microparticles in a levitation state for a long time (of the order of hours). Basically, its operating principle is similar to that of a rf trap called Paul trap, used to store ions in ultra high vacuum. As a result the Paul trap general theory is applicable for electrodynamic traps. Extensive reviews on the various types of electrodynamic traps and their applications can be found in [1, 2]. The term of microparticles will be assigned here to the solid grains having the size within the range µm. It becomes necessary to develop methods to determine characteristics and state of the trapped microparticles. One of the important approach consists of the study of the laser radiation scattered by trapped microparticles recorded by a camera (e.g. [3 11]). Based on this principle and using a web camera, we will be described here a method which allows to be analysed simultaneously the variation of the light intensity scattered by the microparticles placed in different regions inside the electrodynamic trap. Some elements of the processing method used here has been also described in [12]. RJP Rom. 61(Nos. Journ. Phys., 3-4), Vol , Nos. 3-4, (2016) P , (c) 2016 Bucharest, - v.1.3a*

2 2 Study on axial distribution of stored microparticles using software image processing EXPERIMENTAL SETUP The experimental setup is shown in Fig. 1 Fig. 1 Experimental setup (not to scale): (a) cross section; (b) axial section. The device used to maintain the microparticles in a levitation state consists of a linear quadrupole electrodynamic trap. The electrodynamic trap mechanical layout and electrical wiring is similar to those already described in [13 15]. The rod electrodes E2 and E3 are connected together to ac sinusoidal high voltage U ac of frequency f 0. The two disk electrodes E5 and E6 are connected together to a dc voltage U z. To compensate the gravity force, another dc voltage U x are applied between the rod electrodes E1 and E4. The electrode E1 is connected to ground and represents the reference electrode. The dc voltages magnitude, frequency and amplitude of the ac voltage needed to be applied to the electrodes depend on the trap geometry, the physical characteristics of the microparticles (size, density and electric charge) and the pressure of the surrounding gas. The conditions necessary to be fulfilled by those parameters in order to achieve the microparticles trapping are well known (e.g. [1, 16]) and will be not recalled here. When these conditions are met, the microparticles are trapped as a filamentary bunch of solid grains floating in a narrow region in the middle of the distance between the rod electrodes. Further, this solid particles aggregation will be abbreviated TMC-Trapped Microparticles Cloud. To view TMC a laser beam has been directed along the longitudinal trap axis. For this purpose a cylindrical hole has been cut through one of the disk electrodes (E5 or E6). The laser beam is provided by a low power laser diode LD (650 nm, 3mW). The trapped microparticles imaging is performed by a web camera W placed on a side of the electrodynamic trap and pointing along a direction passing between the rod electrodes and perpendicular to the laser beam. The position and viewing field of the camera have been properly adjusted to record the whole region containing TMC. The main mechanical and electrical characteristics of the electrodynamic trap used

3 538 O.S. Stoican 3 during experiments are summarized in Table 1. All voltages are measured with the respect of the electrode E1 potential which is connected to ground. Table 1 Electrodynamic trap characteristics Parameter Symbol Value Length L 38 cm Rods E1, E2, E3, E4 diameter d 10 mm Distance between electrodes D 10 mm Disks E5 and E6 diameter e 7 mm AC voltage U ac = 2 kvrms Frequency of AC voltage f 0 60 Hz DC voltage applied to disk electrodes (E5 and E6) U z V DC voltage applied to bottom electrode (E4) U x 130 V 3. IMAGE PROCESSING FLOW The web camera records the image of the TMC, illuminated by the laser beam, for several seconds and stores it in a computer as a file of type *.avi. By software the web camera is adjusted so that the video frames includes the whole visible shading due to TMC and excludes the shading due to other elements (electrodes, for example). The video image is then decomposed into a chain of bitmap (*.bmp) files. Each bitmap file represents an individual frame of the video image. These bitmap files, containing color images, are then converted to bitmap files containing black-andwhite images by applying a so called threshold filter. As a result of the threshold filter the color of a image pixel becomes either withe if its brightness exceeds a predefined level or black otherwise. In this way, it is obtained the footprint of the TMC defined by the set of white pixels (Fig. 2). All the above operations are performed by using a software application for video capture processing called VirtualDubMod licensed under GPL [17]. Finally, a series of images (in a form of bitmap files), representing the instant TMC footprints taken at equal time intervals T is obtained. The trapped microparticles illuminated by the laser beam appear on the bitmap images, after threshold filter is applied, as collections of white points. The time interval T between two succeeding TMC footprint records are given by T = 1/f where f represents the frame rate (fps) of the video image. The frame index is denoted as k, first frame has the index 0 and the last frame considered has the index n. Thus, total frames number is equal to n + 1. By knowing the frame index k the time interval between the beginning of the video record (frame of index 0) and the current frame (frame of index k) can be devised as t = kt = k/f. Let us consider a single frame,

4 4 Study on axial distribution of stored microparticles using software image processing 539 Fig. 2 A video image frame before (left) and after (right) the threshold filter was applied. Threshold level=50%. TMC footprint is defined by white pixels. of index k, in a form of bitmap image (Fig. 3). The parameters w and h represent the width and height, respectively, of the image, expressed in pixels. Fig. 3 A single frame of width w and height h, containing TMC footprint (white pixels). The parameter N k (z) is the number of white pixels, counted within the frame of index k, along a vertical line at the distance z from the origin. Let N k (z) the number of white pixels counted within the frame, along a vertical line, at the distance z, expressed in pixels, from the origin. Thus 0 N k (z) h. The N k (z) has been interpreted as a measure of the TMC density at the point L w z/w, along the longitudinal axis of the electrodynamic trap, at the time t = kt. The parameter L w represents the width of the frame, measured along the longitudinal axis of the electrodynamic trap, captured by the web camera. It is known that trapped microparticles positions, implicitly the TMC bounds as a whole, vary in time. Under the conditions required by the adiabatic approximation, for example, the motion of a single trapped microparticle is the result of the superposition of two oscillations: micromotion at frequency f 0 and a low frequency oscillation called secular motion ([1, 16, 18, 19]). Consequently, in order to determine the axial profile of the TMC density it is need to average N k (z) over time. Thus the quantity N(z) calculated as: N(z) = 1 n + 1 n N k (z) (1) can be interpreted as the average local density of the TMC at the point given by coordinate z. k=0 4. RESULTS AND DISCUSSIONS In Fig. 4 is plotted quantity N(z) calculated for two operating points characterized by dc voltage U z = 0.15 kv (left) and U z = 0.5 kv (right), respectively. The other electrodynamic trap parameters have been kept unchanged being listed in Table 1. Microparticles under study consist of grains of Al 2 O 3, µm in

5 540 O.S. Stoican 5 diameter, trapped at atmospheric pressure, in air. It has been used a web camera LifeCam Studio HD Q2F The web camera settings were controlled by the interface provided by the application VirtualDubMod The frame rate for the video image used as a primary source for the data represented in Fig. 4 was f = 30 fps while the length of the video recording considered, for the two cases, was 150 frames (about 5s). Fig. 4 Axial distribution of the average number of white pixels N(z), calculated according to (1), for U z=0.15kv (left) and U z=0.5kv (right). Frames characteristics: w=248 pixels, h=28 pixels. As expected the width of the TMC footprint, w T MC, decreases with voltage U z (w T MC =183 and 147 pixels, respectively). The U z voltage assures longitudinal stability of the trapped microparticles. If U z is too small the microparticles slide toward the two ends of trap being ultimately lost. Also, TMC axial density does not vary uniform but exhibits a series of peaks. This behavior complies with early experimental observations available in literature that shown that trapped microparticles tend to form ordered structures similar to the crystals [15, 20 22]. According to our interpretation, the highest peaks correspond to the microparticles whose average position are placed at the distance from web camera where image is best focused. As it has been stated above, a trapped microparticle executes a complex motion, so that its position can be changed both parallel and normal to the viewing direction of the web camera. As a result the number of pixels N k (z) can oscillate with time but the averaged quantities must decrease uniform (due to the microparticles lost) or remain approximately constant in time. In Fig. 5 are plotted variation of the area filled by TMC, N w (k) (thin line), simultaneously with average area filled by TMC, N mw (k) (thick line) as a function of frame index k. The quantities N w and N mw are calculated according to the following

6 6 Study on axial distribution of stored microparticles using software image processing 541 formulas: w 1 N w (k) = N k (i) (2) i=0 N mw (k) = 1 k + 1 k N w (j) (3) In other words, N w (k) represents area filled by TMC footprint corresponding to the frame of index k. The quantity N mw (k) represents the average of the area filled by TMC footprint calculated over k + 1 frames, from frame 0 to frame k. As explained above, by knowing any parameter variation as a function of frame index k one can calculate its variation as a function of time, because t = kt. The graphs from Fig. 5 show that, at least during the considered sequence of the video record, the total number of the microparticles remains approximately constant. The variation of the quantity N w with frame index, is due to the motion of the trapped microparticles along the viewing direction of the web camera. j=0 Fig. 5 Variation of the area filled by TMC, N w (thin line) and average area filled by TMC, N mw (thick line) as a function of frame index k for U z=0.15kv (left) and U z=0.5kv (right). N w and N mw are calculated according to (2) and (3), respectively. 5. CONCLUDING REMARKS The main goal of this report was to highlight the principle of a method aimed to study the collective dynamic of the trapped microparticles. A web camera is a cheap, widespread and easily to operate device. It is not mainly aimed to be a scientific instrument. We used it in order to illustrate the method basics. Consequently, results must be deemed taking into account the technical limits of this device. Some common features, as either manually or automatically image correction, or autofocus, could affect the accuracy of the images recorded. Also its frame rate which is

7 542 O.S. Stoican 7 satisfactory for a common movie could be too slow for application like that reported here. Despite these limitations, qualitatively, the results are in accordance with previous theoretical and experimental developments related to the trapped microparticles properties. Replacing the web camera by an instrument able to record bare images, at high frame rate, for example a CCD camera, represents an improvement recommended for the method described here. Acknowledgements. This work is done in the framework of the project funded by ANCSI, PN REFERENCES 1. F. G. Major, V. N. Gheorghe, G. Werth, Charged Particle Traps, Physics and Techniques of Charged Particle Confinement, Springer Verlag, 2005, ISBN G. Werth, V. N. Gheorghe, F. G. Major, Charged Particle Trap II, Applications, Springer Verlag, 2009, ISBN S. Arnold, L. M. Folan, A Korn, J. Appl. Phys. 74, (1993) 4. R. Vehring et al., Rev. Sci Instrum., 68, (1997) 5. F. Zheng, M. L. Laucks, E. J. Davis, J. Aerosol. Sci., 31, (2000) 6. C. Heinisch, J. Petter, N. Damaschke, T. Tschudi, C. Tropea, An electrodynamic trap with an advanced geometry used for evaporation rate measurements of single water droplets, Proc. of the 21th, ILASS-Europe Meeting, A. A. Zardini et al., Atmos. Chem. Phys., 8, (2008) 8. M. Beránek, I. Cermák, Z. Něme cek, J. Šafránková, Trapping Charged Microparticles in the Linear Quadrupole Trap, WDS 10 Proceedings of Contributed Papers, Part II, , W. Guan, S. Joseph, J. H. Park, P. S. Krstić, M. A. Reed, PNAS, 108, (2011) 10. L. Jiang, W. B. Whitten, S. Pau, Optics Express, 19, (2011) 11. E. A. Vinitsky, E. D. Black, K. G. Libbrecht, arxiv: v1, 14 Aug O. S. Stoican, An image processing method for the study of the unicomponent plasma formed in a linear electrodynamic trap, INDLAS 2013, Program, p.29 P1, May 2013, Bran, Romania 13. G. Visan, O. S. Stoican, Rom. Journ. Phys., 58, ( 2013) 14. O. S. Stoican, Studies on the Interaction Between an Acoustic Wave and Levitated Microparticles, pp in Wave in Fluids and Solids, Prof. Ruben Pico Vila (Ed.), ISBN: , InTech, V. N. Gheorghe, L. Giurgiu, O. Stoican, D. Cacicovschi, R. Molnar, B. Mihalcea, Acta Physica Polonica A, 93, (1998) 16. R.E. March, Mass Spectrometry Reviews, 28, (2009) D.J. Berkeland et al., J. Appl. Phys., 83, (1998) 19. J. H. Parks, S. Pollack, W. Hill, J. Chem. Phys., 101, (1994). 20. R. F. Wuerker, H. Shelton, R. V. Langmuir, J. Appl. Phys., 30, (1959). 21. H. Winter, H. W. Ortjohann, Am. J. Phys, 59, (1991) 22. L. M. Vasilyak et al., New Journal of Physics, 15, (2013)