M De Billy
email: mdebilly@univ-paris-diderot.fr

Crossing of acoustic envelope solitary waves in homogeneous elastic rods: Experiments

In this letter we focused on the problem in which two shear envelope solitary waves traveling in 1-D homogeneous system (elastic PMMA rod of constant cross-section) and incoming in opposite directions, meet one another and head-on collide. The properties of incident acoustic waves after collision are investigated. Two cases are experimentally examined: incoming waves with close amplitudes and quite large difference in magnitude. No phase shift and no variation of polarization are experimentally detected after the collision.

Introduction

Since many years the research on solitary waves was one of the most field developed in various area such as nonlinear dynamics, optics, biophysics and atomic physics. The property commonly admitted for presenting this wave is the following: it is a wave spatially localized within a finite region and which arises from a balance between nonlinearity and dispersive effects. This wave propagates with a permanent form and a constant velocity. Two types of waves were mainly analyzed as solution of the Korteweg-de Vries (KdV) or the nonlinear Schrödinger (NLS) equations. The NLS equation gives rise to envelope solitary waves exhibiting both a carrier and a modulation [START_REF] Samsonov | Strain Solitons in Solids and How to Construct Them[END_REF][START_REF] Peyrard | Physique des solitons[END_REF][START_REF] Remoissenet | Waves Called Solitons: Concepts and Experiments[END_REF][START_REF] Cadet | Transverse envelope solitons in an atomic chain[END_REF][START_REF] Wu | Observation of envelope solitons in solids[END_REF][START_REF] Maugin | Nonlinear surface waves and solitons[END_REF][START_REF] Yagi | Strongly nonlinear envelope soliton in a lattice model for periodic structure[END_REF][START_REF] De Billy | On the formation of envelope solitons with tube ended by spherical beads[END_REF][START_REF] Porubov | Long nonlinear strain waves in layered elastic half-space[END_REF]. Many theoretical works and few experimental studies have been devoted to the collision of these types of non-linear waves. Such head-on collisions were studied in water [START_REF] Yuen | Nonlinear deep water waves: theory and experiment[END_REF][START_REF] Hammack | Solitary wave collisions[END_REF][START_REF] Maxworthy | Experiments on collisions between solitary waves[END_REF][START_REF] Baecklund | Analytical and numerical study of soliton collisions[END_REF][START_REF] Chen | Laboratory experiments on counter-propagating collisions of solitary waves. Part 1. Wave interactions[END_REF][START_REF] Slunyaev | Simulations and experiments of short intense envelope solitons of surface water waves[END_REF][START_REF] Craig | Solitary water wave interactions[END_REF][START_REF] Slunyaev | The laboratory investigation of surface envelope solitons: reflection from a vertical wall and collisions of solitons[END_REF], in nonlinear dusty plasma [START_REF] Zabusky | Interaction of ''solitons" in a collisionless plasma and the recurrence of initial states[END_REF][START_REF] Zhang | Head-on collision and overtaking collision between an envelope solitary wave and a KdV solitary wave in a dusty plasma[END_REF][START_REF] Jaiswal | Theoretical study of head-on collision of dust acoustic solitary waves in a strongly coupled complex plasma[END_REF][START_REF] Qi | Particle in cell simulation of head-on collision between two ion acoustic solitary waves in plasmas[END_REF][START_REF] Zhang | Envelope solitary waves exist and collide head-on without phase shift in a dusty plasma[END_REF], in rods [START_REF] Samsonov | Solitary longitudinal waves in an inhomogeneous non-linearly elastic rod[END_REF][START_REF] Clarkson | Solitary wave interactions in elastic rods[END_REF][START_REF] Porubov | Cubic non-linearity and longitudinal surface solitary waves[END_REF][START_REF] Dai | Head-on collision between two solitary waves in a compressible Mooney-Rivlin elastic rod[END_REF][START_REF] Soerensen | Solitary waves on nonlinear elastic rods. I[END_REF] and in superimposed elastic thin films [START_REF] Hadouaj | Surface solitons on elastic surfaces: numerics[END_REF]. The objective of this letter is to experimentally investigate the collision of two transversally polarized envelope solitary waves propagating in opposite directions in polymethylmetacrylate (PMMA) rods and compare the experimental observations with those available for other laboratory conditions.

Experiments and results

The experimental set-up (sketched in Fig. 1) is fundamentally the same than the one described in Ref. [START_REF] De Billy | On the formation of envelope solitons with tube ended by spherical beads[END_REF]. It is well known that the generation of solitary waves is based on the balance between the non-linearity and dispersion. In the present laboratory work, the rod is ended with small glass bead of 8 mm in diameter and the whole sample (rod + beads) is clamped with two shear contact transmitters driven by the same acoustic impulse and submitted to a static compression. At the contact points between the spherical beads and the front face of the emitters a structural nonlinearity is caused and is described by the nonlinear Hertz' law. So it is natural to consider (and it is experimentally verified) that the transmitted waves are affected by the non-linearity. In addition the propagation in bars of small diameter (with comparison to the wavelength) is dispersive. As the displacement of these wave trains is at the surface, it is possible, as they propagate, to record it with a third shear transmitter (receiver) in contact with the surface of the bar and acting over a linear distance equal to the diameter of the transmitter. The spatial localization of this PZT transducer may vary along the rod and its direction of polarization has to be maintained parallel to the common direction of the polarization of the two emitters. This simple experimental set-up was used to investigate the colliding problem of two envelope solitary waves propagating in the same bar and traveling in opposite directions (bidirectional collision). The waveguides used for experiments are cylindrical PMMA bars whose length (l) is less than 66 cm. The diameter of the rods (d) is 10 mm. The choice of glass beads is justified by the fact that with this material short acoustic signals are transmitted.

In The two groups of wave trains with close amplitudes income from opposite directions (see top of Fig. 2) and interact at the head-on collision point (d = 0) where a single group of wave trains is formed during the collision. Then the process of reconstruction of the original wave trains is observed: two groups of wave trains appear and, as the distance d increases, move away (see bottom of Fig. 2).

What happens when one of the train waves has a lower amplitude than the other? Experimental records, reproduced in Fig. 3, illustrate this case. They are obtained with the sample above described; on the surface and from the right end of the bar glue was continuously put over 6 cm in length. One clearly verified that the incident acoustic wave train of low amplitude (coming from the right) crosses the other wave train (with higher amplitude and coming from the left) and propagates towards the left direction with low magnitude after collision.

Discussion

Before making comments on the results above presented we have to ask an important question: how the nonlinearity can be relevant for collisions of the wave trains in the rod when they have moved from the beads into the rods?

To answer this question we suggest to experimentally observe the joint amplitude of the interacting wave trains whose maxima coincide in time domain (see Fig. 4). The two first plots represent the signals detected by the receiver located at the middle of the bar one of the two emitter being off. The receiver is very slightly moved (one or two mm) to avoid phase shift between the two extremum of the two signals. Then as the experimental conditions (length of propagation, attenuation, dispersion, frequency response) are the same, the shapes are very similar and the measured amplitude are 5.7 ± 0.1 and 6.0 ± 0.1 mV respectively. The sum of these magnitudes may be compared to the amplitude of the third signal (9.8 mV ± 0.1 mV) observed when the two emitters are on. We notice that this amplitude is smaller than the linear sum of the two incoming signals This is in contradiction with to what would happen if the two waves overlapped linearly and the principle of linear superposition is not fulfilled which indicates that the head-on collisions of the pulse trains are affected by nonlinearity. However we have to underline again that we have to be careful because effects as dispersion, attenuation and limitation in accuracy measurement may perhaps contribute to a phase shift. This is the reason why we have chosen the position of the receiver for which the maximum of the two signals are collapsing in the time domain.

Another argument for justifying the fact that nonlinearity exists in the collision of the acoustic wave trains may be related to the frequency analysis of the detected signal. In the top of Fig. 5 is represented the wave train resulting from the interaction of two colliding incident waves propagating in a PMMA rod of 65.3 cm in length. The associated frequency power is reported in the bottom of Fig. 5. This spectrum clearly points out peaks at 30 and 58 kHz. A more careful analysis allows us to identify maximum around 14 and 44 kHz. An analysis of this series of values confirm the existence of two fundamental modes generated by the glass beads (f 1 = 30 and f 2 = 44 kHz) acting as a low frequency filter. In the presence of non linearity, the power spectra should include combinations of the fundamental frequencies f 1 and f 2 (frequencies transmitted by the beads) such as f 2 ± f 1 , and the higher harmonics 2f 1 ,2 f 2 , ... [START_REF] Korobov | Nonlinear elastic properties of a model one-dimensional granular unconsolidated structure[END_REF]. Then the first value (14 kHz) may be identified as the combination f 2 À f 1 and the last one (58 kHz) may represent the second harmonic of the first fundamental frequency 2f 1 . Usually the frequency combinations 2f 2 and f 1 + f 2 are not observed in the spectra. This missing is probably due to the low response of the transmitter in the frequency region which corresponds to the values higher than 80 kHz. We also experimentally noticed that the shape of the power spectrum slightly depends on the position of the receiver on the rod. In our opinion, these frequency responses clearly demonstrate that non linearity plays a role in the collision process even for large propagating distances.

From these important considerations we may conclude that the collisions of the incident wave trains support non linearity. In fact once the non linear waves are formed they propagate through the rod whose spatially small structure yields dispersion and change the non linear waves to envelope solitons. Then as the shape of the time signals exhibit both a carrier (high frequency) and a modulation (low frequency) it should be consistent to claim that the experimentally transmitted short pulse trains may be identified as envelope solitary waves (ESW) or NL solitons.

From an analysis of the experimental records we notice that after collision the pulse shape survives (cf. Figs. 2 and3). Also we verified that the velocity of propagation does not depend on the pulse height [START_REF] Duan | The cubic nonlinear Schrödinger equation in a fluid-filled elastic tube[END_REF] and is constant. We noticed that no post collision phase shift is observed (or too small to measure) as it is observed in the plots of Fig. 6 which represent the variations of the time distance of the echoes as a function of the distance d (l = 64.5 cm). Mention that for compressional solutions of the NLS equation (envelope solitary waves), no phase shift is theoretically observed in plasma dusty [START_REF] Zhang | Envelope solitary waves exist and collide head-on without phase shift in a dusty plasma[END_REF]. Besides it was noted a variation of the amplitude of the signals as the distance d varies; this is consistent with the presence of dissipative process particularly sensitive in PMMA material [START_REF] Tran | Ion acoustic solitons in a plasma: a review of their experimental properties and related theories[END_REF][START_REF] Samsonov | Do the bulk solitary strain waves decay?[END_REF]. We also focused on the polarization of the solitary waves and it was experimentally verified that the direction of polarization of the incident waves is not affected by the collision.

Another question may be formulated: how the contact non linearity at the beads can affect pulse collisions in the center of the rod? In spite of the large amount of theoretical works on the subject of understanding the dynamics of several systems, the problem of dynamics of the alignment of beads and rod was not studied yet in our knowledge and looks to be difficult for theoretically modeling: the specimen is neither a pure linear arrangement of identical spheres nor a rode alone. The space between the transmitter and the rod can be described by three contacts: plane/bead (of 8 mm in dia.), bead/tube (of 5 mm in height) and tube/rod. Then the dynamic of the generation and propagation of the physical non linearity due to Hertz contact (first contact) should be considered with care.

At an intuitive level the dynamics of the specimen could be solved by considering a single bead and then -after move -by modeling the rod (and the tube) as a chain of beads immersed in a medium whose the physical properties are the same that in the rod. In other words and intuitively the dynamics of the small tube and the rod could be solved by modeling the both as a chain of beads whose the diameters of the beads and rod should be equal. The first Hertzian contact (transmitter/bead) behaves as a nonlinear system initially pre-compressed to insure the propagation of the short signal which is transmitted trough the tube and the rod under non-linear surface acoustic wave. In the present experimental work, short non linear pulses suffer dispersion due to the geometry of the rod. When non-linearity is balanced by dispersion these waves become envelope soliton and the dynamics of the whole problem can be governed by a usual nonlinear Schrödinger equation at the surface of the rod. This situation was solved for longitudinal excitation in a rod. In the present theoretical model it should be necessary to consider a shear excitation. The difference of the material between the beads and the rod could be neglected in a first approximation.

In the laboratory work above described (head-on collision) two short nonlinear pulses propagates in the rod in opposite directions. Then we are in presence of two almost monochromatic envelope solitary waves and the whole problem should be modalize as the sum of the two analytic equations of the two opposite solitary waves, solutions of the two NLS equations, propagating with opposite velocities and overlapping at the middle of the rod.

Conclusion

In the present letter we considered an experimental device devoted to the analysis of the head-on collision of two incoming transversally polarized wave trains simultaneously excited and propagating in opposite directions in PMMA rods. We have verified that during collision envelope solitary waves exist. Our study clearly shows that the two incident envelope solitary waves emerge after collision, maintain their shape, propagate at a constant velocity and does not modify their direction of polarization. We have noticed that the principle of linear superposition is not fulfilled and that frequency combinations of two initial frequencies are observed as predicted in the case of non linear interaction. It was also confirmed that no phase shift is observed after collision which a characteristic of the solution of the NLS equation. We suggest, in a very first approximation, to solve the dynamics problem by considering the whole specimen as a chain of beads and by modelling the collision as the sum of the two non linear dispersive solitary waves each of them being described by a usual NLSE propagating with opposite direction.

Fig. 2

 2 are reproduced experimental data of temporal wave signal profiles, as a function of the spatial location (d) of the receiver. The distances (d) are measured by the middle of the rod taken as the origin and the vertical axis describes the displacement of the surface of the rod in arbitrary unit. Systematic records on ''offcenter" positions have been registered from d = À25 cm (top of the figure) to 25 cm (bottom of the figure) by step of 5 cm. The length value of the PMMA bar is 64.5 cm.

Fig. 1 .

 1 Fig. 1. Schematic diagram of the experimental set-up.

Fig. 2 .

 2 Fig. 2. Time evolution of the recorded signal as a function of the position (d) of the receiver; case of two incident acoustic signals of close amplitude. d varies from À25 cm to 25 cm by step of 5 cm from the top to the bottom of the figure. The values of the length and diameter of the PMMA rod are respectively 65.3 cm and 10 mm.

Fig. 3 .

 3 Fig. 3. Time evolution of the recorded signal as a function of the position (d) of the receiver; case of two incident acoustic signals of different amplitude. d varies from À20 cm to 20 cm by step of 5 cm from the top to the bottom of the figure. The values of the length and diameter of the PMMA rod are respectively 63.8 cm and 10 mm.

Fig. 4 .

 4 Fig. 4. Wave trains detected by the receiver: top: the emitter at the left end of the rod is out; middle: the emitter at the right end of the rod is out; bottom: the both emitters are working.

Fig. 5 .

 5 Fig. 5. Frequency analysis: case of a PMMA rod (10 mm in diameter and 65.3 cm in length). The top of the figure represents the wave train in the middle of the rod; the bottom shows the associated frequency power spectrum. The peaks are observed for values of the frequency: 14, 30, 44 and 58 kHz.

Fig. 6 .

 6 Fig. 6. Arrival time of the two colliding envelope solitary waves as a function of the displacement (d).

Acknowledgments

The author thanks the reviewers for their help and the many suggestions and comments for improving the manuscript.


Kert Pjatkin

Morteza Daneshmand

Pejman Rasti

Gholamreza Anbarjafari

Probability Distribution Function based Iris Recognition Boosted by The Mean Rule

Keywords: Probability distribution function, Kullback-Leibler divergence, Iris recognition, Classification, Mean rule

In this work, a new iris recognition algorithm based on tonal distribution of iris images is introduced. During the process of identification probability distribution functions of colored irises are generated in HSI and YCbCr color spaces. The discrimination between classes is obtained by using Kullback-Leibler divergence. In order to obtain the final decision on recognition, the multi decision on various color channels has been combined by employing mean rule. The decisions of H, S, Y, Cb and Cr color channels have been combined. The proposed technique overcome the conventional principle component analysis technique and achieved a recognition rate of 100% using the UPOL database. The major advantage is the fact that it is computationally less complex than the Daugman's algorithm and it is suitable for using visible light camera as opposed to the one proposed by Daugman where NIR cameras are used for obtaining the irises.

I. INTRODUCTION

Several ophthalmologists notice during clinical research that the patterns on the iris are clearly distinctive and have unique texture potentially used successfully as a mean of biometric identification and it doesn't change during the lifespan of a person [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF][START_REF] Chen | A robust segmentation approach to iris recognition based on video[END_REF]. J. G. Daugman took advantage of the previous ideas and introduced the first and still the most widely used algorithm for iris recognition in 1993 [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF].

Daugman explains that the human iris has at least several hundred degrees of freedom [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF]. Being more precise, in a later research in cooperation with C. Downing, they discovered by examining 2.3 million iris pairs that an iris has 244 independent degrees of freedom [START_REF] Daugman | Epigenetic randomness, complexity and singularity of human iris patterns[END_REF]. Therefore, iris recognition is considered to be one of the most foolproof biometric person recognition methods nowadays and it is regarded as the most reliable mean of biometric identification out of the seven most popular ones [START_REF] Mansfield | Biometric Product Testing[END_REF].

The morphogenesis of an iris is random and the physical appearance depends heavily on the conditions during the fetus. Even identical twins do not have the same patterns and color. What is more, iris is counted as the only internal organ visible outside and hence, it is practically impossible to shape the pattern of it [START_REF] Muroň | The Human Iris Structure And Its Usages[END_REF].

The current algorithm dominating the market is the one created and patented by Daugman. The method uses an integrodifferential operator that is described by eqn. [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF]. Eqn.

(1) is used twice during the first iteration looking for the outer boundaries of an iris and during the second run removing the pupil from the previously found iris. After obtaining the real iris, the next step is to transfer the pixels from traditional Cartesian coordinate space to the polar coordinate system in order to maintain the reference to the same iris points independent on the angel under which the photo was. During the pattern analysis the upper part and 45 degree slice of the lower part of the iris are excluded, because these are the regions where most probably a disturbing noise, like eyelids or reflections, exists [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF].

𝑚𝑎𝑥 (𝑟,𝑥 0, 𝑦 0 ) = |𝐺 0 (𝑟) * 𝜕 𝜕𝑟 ∮ 𝐼(𝑥, 𝑦) 2𝜋𝑟 𝑑𝑠 𝑟,𝑥 0 ,𝑦 0 | (1)
𝐺 0 (𝑟) is Gaussian blur, * is convolution, 𝐼(𝑥, 𝑦) is location to apply the circle, and 𝑟 is circle radius. The algorithm used Gabor filter to generate numerical comparable data out of the filtered images and used the Hamming window to compare two irises [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF].

The most significant difference of our proposed algorithm to the one that Daugman created is that the proposed method is taking advantage of the color information of the irises, whereas Daugman uses just the patterns to detect irises and all the images have to be taken with IR cameras. The latter are mostly used because the image reveals usually more of the texture of an iris than using a visible light camera [START_REF] Chou | Non-Orthogonal View Iris Recognition System[END_REF], but the traditional color cameras are more widespread today and therefore a suitable algorithm using color information would make the recognition process more robust [START_REF] Melgani | Incremental Learning based Color Iris Recognition[END_REF].

Anbarjafari and Demirel have proposed a similar statistical algorithm for iris recognition that uses tonality information of the irises. In their method they have represented an iris image by sets of its histogram in HSI color space. Then they have used cross correlation in order to obtain the recognition in each class. Furthermore majority voting has been employed to combine the decisions in different color channels [START_REF] Demirel | Iris recognition system using combined histogram statistics[END_REF].

Another widespread method is Principal Component Analysis (PCA) that has been run on the grayscale images of same database that we are using and hence we are using it as a tool to compare the performance of the proposed algorithm by us [START_REF] Shi | The comparison of iris recognition using principal component analysis, independent component analysis and Gabor wavelets[END_REF][START_REF] Shlens | A Tutorial On Principal Component Analysis[END_REF]. There has been various works conducted on iris recognition dealing with iris images in different light spectrum [START_REF] Cui | An iris image synthesis method based on PCA and super-resolution[END_REF].

This paper is organized as follows: in the next section the process of iris segmentation is explained. Afterwards, the proposed algorithm is explained in details followed by a section on experimental results. In the end conclusion is represented.

II. IRIS SEGMENTATION

The first major step of the recognition workflow is to get only the iris out of the image of an eye. It is vital to leave as much of the patterns of the iris as possible, but on the other hand remove all the disturbing noise, which affects the decision like parts of pupil, eyelids, eyelashes, and reflections of light.

Besides the algorithm introduced by Daugman that is described by eqn. [START_REF] Daugman | High confidence visual recognition of persons by a test of statistical independence[END_REF] there is also Hough transform, which is very popular in the area [START_REF] Shen | A New Iris Locating Algorithm[END_REF].

However, as we are presenting an iris recognition algorithm in the current paper and not dealing with filtering itself, we have developed manually a suitable mask that takes into account all the irises in the database. It has to be noted that the mask can't be used on any other database and other mean of filtering has to be used when trying to implement the algorithm with some other irises.

In order to obtain noise free irises that we can start to use in the recognition process, we apply Boolean AND operator between the mask and the filter.

III. PROPOSED IRIS RECOGNITION TECHNIQUE

One of the main questions of iris recognition using texture and color information is what channels to use as a trustworthy source of information and how to combine the data so that we would enhance the recognition rate as much as possible [START_REF] Melgani | Incremental Learning based Color Iris Recognition[END_REF].

In order to generate histograms of the filtered images, we need to convert the irises from traditional RGB color space to HSI and YCbCr color space. RGB color space is not being used because it includes both chrominance and luminance information into the three channels and therefore the color space itself is very sensitive to any kind of changes in lightning conditions and might affect the recognition rate significantly. Instead, both HSI and YCbCr are used for the identification process. These color spaces are suitable for us as they separate the tonality and illumination information. Additionally channel I has been excluded, because it includes theoretically the same information as Y and thus we need to remove one of them not to emphasize the influence of the illumination. The number of independent channels and decisions can be increased but in that case we would increase also computational complexity and that is always the unwanted result.

In order to reliably compare the irises, we need to have probability distribution functions (PDF) of all the channels of all the irises. The first step to obtain the PDFs is to generate the corresponding histograms.

A histogram represents the tonal distribution of an image. In simpler terms, it means that we collect and plot the number of specific pixel values and is defined by eqn. ( 2 2)-( 4), we will use the bin size of 256, but this can be altered in a way that seems the most convenient. It is important to note that reducing the number of bins means that we will lose precision and this might result in false matches, because in case of less bins different pixel values are considered as being in the same categories. Hence, it could be compared with down sampling an image.

Kullback-Leibler Divergence is a tool to measure the similarity of two irises that we will use in this paper. It is described by eqn. [START_REF] Muroň | The Human Iris Structure And Its Usages[END_REF].

𝐷 𝐾𝐿 (𝑃||𝑄) = ∑ 𝑙𝑛 ( 𝑃(𝑖) 𝑄(𝑖) ) 255 𝑖=0 * 𝑃(𝑖) (5)
P(i) in eqn. ( 5) notes the PDF of an iris in the database and Q(i) the input iris. Vidyasagar [START_REF] Vidyasagar | Divergence, Variational Kullback-Leibler[END_REF] defines it as relative entropy between two probability density functions 𝑃 and 𝑄.

The more similar the two PDF vectors are to each other, the smaller the value of KLD is, reaching zero for identical vectors and theoretically infinity for vectors that are totally different from each other [START_REF] Vidyasagar | Divergence, Variational Kullback-Leibler[END_REF]. All in all, KLD is an ideal tool to compare similarity between two irises as the irises of the same eye should have very similar histograms with minor fluctuation caused by different conditions while taking the image.

In order to compare two irises, we need to calculate the corresponding KLD values of H, S, Y, Cb and Cr channel by using the PDFs obtained in the previous section. Finally, the similarity of two irises in the context of this paper is found by adding all the KLD values and then dividing the sum by 5 i.e. finding the mean of the calculations.

The method does not use the RGB color space because it encodes both luminance and chrominance information into 3 channels and hence, due to its sensitivity on slight illumination changes affects also the recognition rate.

Combining channel statistics in the mentioned way means that an error in one of the channels will be probably cancelled out by the others. Table 1 shows clearly that recognition rate by using one specific channel is really low and in order to get more precise identification, we need to use the combination of different channels and leave out the ones that will duplicate each other.

The decision making process is described by eqn. ( 6) where 𝑎 𝑖 is the average KLD value for both left and right irises for channels H, S, Y, Cb and Cr. 𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛 = min (𝑎 0 … 𝑎 𝑛 )

IV. EXPERIMENTAL RESULTS

The UPOL database [START_REF] Dobeš | Iris Database[END_REF] is used for obtaining experimental results. It consists of 64 pair of irises classes (left and right) and each class has 3 samples of every iris. Table I is showing the recognition rate of each color channel for the left and right irises separately. The training and test irises have been randomly assigned for each class. In order to have an unbiased performance, the process of recognition with given number of training set has been repeated 100 times and the reported recognition rate is average of the performances. As can be seen from Table II, applying mean rule to H,S, Y, Cb, and Cr color channels on just left or right iris for recognition enhances the performance significantly. In order to improve the recognition rate the decision of right and left irises is also combined by using mean rule. This means that instead of 5 channels we will use 10 channels and the probability recognition will be increased. Table III describes this result using the mean rule with both left and right irises. As it can be seen, the algorithm performs significantly better than PCA applied to the grayscale iris images. Also Table III shows the comparison of the proposed technique with a state-of-the-art technique proposed in [START_REF] Demirel | Iris recognition system using combined histogram statistics[END_REF]. Although our proposed technique in case of existence of only 1 sample per class in training set is not over performing, the proposed technique has less computational complexity than [START_REF] Demirel | Iris recognition system using combined histogram statistics[END_REF], as in [START_REF] Demirel | Iris recognition system using combined histogram statistics[END_REF] cross correlation coefficient is used which is a well-known expensive operation. The proposed technique is exclusively suitable for visible light data due to the fact that PDF of color channels in visible light spectrum is being used.

  Figures 1, 2 and 3 illustrate the process.

Fig. 1 .

 1 Fig. 1. Original iris with noise

  ) and eqn. (3). 𝐻 = [𝜀 0 , 𝜀 2 , 𝜀 3 , … , 𝜀 255 ] eqn. (2) N represents the total number of pixels in the image. Probability distribution function (PDF) is a normalized histogram, where the sum of all the elements is always 1. This means that in order to convert a traditional histogram into PDF, we need to divide all the values in eqn. (2) by N from eqn. (3). Hence, eqn. (3) will take the form described by eqn. (4). 𝐻 = [𝜀 0 /𝑁, 𝜀 2 /𝑁, 𝜀 3 /𝑁, … , 𝜀 255 /𝑁] (4) As it can be noticed from eqn. (

TABLE I

 I

	.	RECOGNITION RATES OF THE PROPOSED PDF BASED BY
		CHANNELS (%)
	Direction	Channel\Number of training	Recognition rate (%) 1 2
		H	64.06	78.13
	LEFT	S I Y	75 46.88 46.88	87.5 65.63 65.63
		Cb	62.5	78.13
		Cr	60.16	75
		H	78.13	84.38
	RIGHT	S I Y	78.13 60.94 60.94	85.94 73.44 73.44
		Cb	65.63	78.13
		Cr	69.53	81.25

TABLE II .

 II RESULTS USING THE MEAN RULE.BY SEPARATING LEFT AND

		RIGHT IRISES
			Proposed mean rule
	# of training	PCA (%)	based technique (%)
			Left iris	Right iris
	1	60	88.3	93.8
	2	70	92.2	98.4

TABLE III .

 III RESULTS USING THE MEAN RULE AND BOTH LEFT AND RIGHTThis research work has proposed a new iris recognition technique based probability distribution function of iris images. During the process of identification probability distribution functions of colored irises were generated in HSI and YCbCr color spaces. KLD was used for discrimination between classes and final decision on recognition was achieved by combination of decision obtained in H, S, Y, Cb, and Cr color channels by employing mean rule. The experimental results showed that the proposed technique overcame the conventional PCA technique.

			IRISES
			Histogram based	Proposed mean
	# of training	PCA (%)	technique [8]	rule based
			(%)	technique (%)
	1	60	98.91	94.5
	2	70	100	100
		V. CONCLUSION

ACKNOWLEDGMENT This work is partially supported by ERDF program "Estonian higher education information and communications technology and research and development activities state program 2011-2015 (ICT program)" and the European Union through the European Social Fund (MTT76).


Pejman Rasti

Arko Kesküla

Henry Haus

Helmut F Schlaak

Gholamreza Anbarjafari

Alvo Aabloo

Rudolf Kiefer
email: rudolf.kiefer@ut.ee

A Passive Autofocus System by Using Standard Deviation Of the Image on a Liquid lens

Keywords: Sharpness Measurement, Liquid lens, Dielectric Elastomer Actuator, Standard deviation

Today most of applications have a small camera such as cell phones, tablets and medical devices. A micro lens is required in order to reduce the size of the devices. In this paper an auto focus system is used in order to find the best positon of a liquid lens without any active components such as ultrasonic or infrared. In fact a passive auto focus system by using standard deviation of the images on a liquid lens which consist of a Dielectric Elastomer Actuator (DEA) membrane between oil and water is proposed.

INTRODUCTION

Cell phones or small cameras do not have enough free space to let users move rigid lenses in focal lengths ranges. In order to overcome the latter issue, [START_REF] Kuiper | Variablefocus liquid lens for portable applications[END_REF] suggests using adaptive liquid lenses in small cameras, enabling them to focus without requiring extra room. On the other hand, classical methods using electric current for changing the shape of liquids consume lots of power. Auto-focus liquid lenses are of two sorts [START_REF] Kuiper | Variable-focus liquid lens for miniature cameras[END_REF] [START_REF] Hsieh | Thin autofocus camera module by a large-stroke micromachined deformable mirror[END_REF]. The reflective type, being used as variable mirror, can be implemented in deigning reflector telescopes, where the transmissive type is based on convex-concave lens shape over immiscible fluids, with different refractive indices.

Using one or more fluids, unmoving, infinitely-variable liquid lenses can be produced for controlling the meniscus shape, which can be of liquid/liquid or liquid/air interface sorts. This way, the fluids could manipulate mechanically and electrically, and exploit the virtue of surface tension of the liquid [START_REF] Wippermann | Bifocal liquid lens zoom objective for mobile phone applications[END_REF]. When it comes to the mechanical method, the surfaced is displaced so as to adjust the lens' shape [START_REF] Gorman | Control of the Shape of Liquid Lenses on a Modified Gold Surface Using an Applied Electrical Potential across a Self-Assembled Monolayer[END_REF] [START_REF] Pelrine | Dielectric elastomer artificial muscle actuators: toward biomimetic motion[END_REF], where in the case of electric method, ellectrowetting [7] [8] is the means by which the surface tension is adjusted. For some purposes, such as endoscopic medical imaging [START_REF] Subbarao | The Optimal Focus Measure for Passive Autofocusing and Depth-from-Focus[END_REF], fiber-optic telecommunication systems or micro cameras, liquid lenses can be used efficiently, which is based on the boundary between the two fluids, constructing a regular and smooth surface [START_REF] Kuiper | Variable-focus liquid lens for miniature cameras[END_REF]. In this study, a Dielectric Elastomer Actuator (DEA) liquid lens with passive autofocus system is developed.

Autofocus systems can be either active or passive. In active ones, a couple of active components, such as ultrasonic components or infrared rays are embedded so as to assist the lens in reaching the desired position. In the sense of designing low-cost, thin and low-consumption applications, active systems entail some drawbacks. Passive systems, on the other hand, try to find the best focused lens position while obviating the need to incorporate active components [START_REF] Subbarao | The Optimal Focus Measure for Passive Autofocusing and Depth-from-Focus[END_REF]. A couple of image processing techniques, such as sharpness measurement can be utilized in the foregoing type of systems. A sharpness curve with respect to the lens position is shown in fig. 1, where the lens is in the best focused position, leading to the highest sharpness possible.

DESIGN AND FABRICATION

Two insoluble liquids and a membrane actuator are needed to fabricate the lens. In this case, an aqueous electrolyte and oil is used which separated with a membrane actuator, which had a hole with a diameter of 4 mm in the middle. A meniscus is formed by the liquids in correspondence of the central hole of the actuator as shown in Figure 2 [START_REF] Kiveste | Autofocus liquid lens device with implementation of dielectric elastomer actuators[END_REF]. The diameter and the shape of the meniscus is changeable by field-induced actuator deformation. The meniscus will work as a lens, if light passes through the hole. Focal length of the lens is adjustable by applying the different potential to membrane actuator which modifies the meniscus shape. Polyoxymethylene (POM) material is used to construct the liquid lens due to its resistance to all used chemicals and solvents [START_REF] Kiveste | Liquid lens Device Construction And Actuator Performance Based On Electroactive Polymers[END_REF]. A rectangular shape is considered for all parts of the initial device. The device is assembled easily in flexible design with actuator membranes of various sizes [START_REF] Kiveste | Autofocus liquid lens device with implementation of dielectric elastomer actuators[END_REF]. Figure 3 shows the prototype device First, spin coated substrate is used to keep a thin elastomeric film (P7670 -Wacker) fixed. The thickness of the film is dependent on the rotation speed, and could range from 5 and 100 μm accordingly. Next, thermal heating is used in order to cure the elastomer. Afterward, using spraying, the compliant electrode (graphite powder) is deposited onto the dielectric. The foregoing process is iterated 100 times in order to stacked DEA membrane. A PDMS layer covers the l th cycle of the DEA membrane so as to make sure it will be encapsulated. Single-layermembrane prototypes are also built in order to compare their performance with the DESA.

RESULTS AND DISCUSSION

Mathematical behavior of the DEA liquid lens

The shape of the meniscus will change by changing in diameter of the hole. In fact, the diameter of the hole will contract by stretching the DEA due to pressure in dielectric elastomer (p) which obtained by the following equation. AsV m ), r ε is defined as dielectric constant of the polymer, U is applied voltage and T is the thickness of the elastomer film.

According to [START_REF] Kiveste | Liquid lens device modification with implementation of dielectric elastomer actuators[END_REF], the maximal applied voltage is varied from 1150V to 2250V depending on the layer thickness of DEA from 45 µm to 100 µm respectively. Also, depending on the applying voltage, the contraction of the hole is changed from 0 to 8%. Despite of the range of voltage between 0 to 2250 for DEA, changing in the size of the membranes, initial curvature of meniscus, device configuration, hole diameter and focal length starting from 50V to 600V. Figure 4 shows the contraction of the hole by increasing the applied voltage

Where ℜ is a region with N pixels. In fact a s is an estimate of a σ (Σ) of the underlying brightness probability distribution.

The proposed system is divided to some phases. In the first phase, a photo is captured by the image acquisition device equipped with a DEA liquid lens. Then sharpness of the captured image is computed to find the amount of edge information. In the second phase the amount of applied voltage to the membrane actuator is increased in order to change in the shape of the meniscus. The number of edges of the second photo which taken afte r deformation of the meniscus is calculated and compared with the earlier one. In the third phase, according to the result of sharpness comparing of taking images, the applied voltage is increased or decreased to take the next photo. The process is iterated till the number of the edges in the photo decreases regardless of the variations of the applied voltage. Figure 5 shows the scheme of the proposed method.

Conclusions

In this work a passive autofocus system for a liquid lens with Dielectric Elastomer Actuator (DEA) was presented which can easily achieve the function of auto focus without any active component such as ultrasonic or infrared in comparison with the conventional active focus system. To implement the technique we used a liquid lens with DEA membrane and a system to measure the sharpness of the image. The proposed method found the best position of the lens by controlling the voltage which is applied to the membrane.

Fig. 1 :

 1 Fig. 1: The curve C of sharpness values versus lens position.

Figure 2 :

 2 Figure 2: The working principle of an autofocus liquid lens based on mechanical lens change in applying membrane actuators [12].

Figure 3 :

 3 Figure 3: The prototype device 2.1 Fabrication of DEA membranes DEA transform electric energy into mechanical work which consists of an elastic dielectric sandwiched between two compliant electrodes. Maxwell stresses are produced as a result of compression of the dielectric material sandwiched between the electrodes when a potential difference is applied to them. In this work a stack of DEA is used which fabricated by an automated fabrication process [12] [13].First, spin coated substrate is used to keep a thin elastomeric film (P7670 -Wacker) fixed. The thickness of the film is dependent on the rotation speed, and could range from 5 and 100 μm accordingly. Next, thermal heating is used in order to cure the elastomer. Afterward, using spraying, the compliant electrode (graphite powder) is deposited onto the dielectric. The foregoing process is iterated 100 times in order to stacked DEA membrane. A PDMS layer covers the l th cycle of the DEA membrane so as to make sure it will be encapsulated. Single-layermembrane prototypes are also built in order to compare their performance with the DESA.

ε

  is the vacuum permittivity (8.85*10 -12 /

Figure 4 :

 4 Figure 4: The contraction of the hole3.2 Sharpness MeasurementIn this work we need to recognize focus and out of focus images in order to find a proper voltage to apply to the membrane. One of the approaches to find focus image obtain by computing the standard deviation of the image. In this way a sample standard deviation of an image is computed by:

Figure 5 :

 5 Figure 5: The scheme of the proposed method

Fig. 6 :

 6 Fig. 6 : The changing of the focal length

Scientific Network for Artificial Muscles (ESNAM, ECOST-STSM-MP1003), partly supported by ERDF program "Estonian higher education information and communications technology and research and development activities state program 2011-2015 (ICT program)" and Estonian Research Council grant PUT (PUT638).

ACKNOWLEDGEMENTS

The research was supported by the European Union through the European Social Fund (MTT76) the European