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Non-linear joint transform correlator for micro-displacement measurement using speckle patterns. Medida de desplazamientos micrométricos mediante correlación de transformada conjunta no lineal de patrones de speckle. Luis G. Calle Luis Enrique Erro 1. This work presents a procedure for measuring displacements of tens micrometer, aand one and two dimensions, based on the correlation between two speckle patterns.
For this purpose, two objective speckle patterns are recorded by a digital camera -one before and one after the object has been moved- what do you mean by linear and non linear correlation placed in the input plane of nonlinear joint transform correlator. Nonlinear transformation of the joint power spectrum allows a sharper correlation peak and a high signal yoh noise ratio. The autocorrelation peak coordinates of the first pattern are set as a reference for measuring shifts of the successive cross-correlation peak.
One criterion for reliable measure is proposed. Results related with different distances sample-sensor and illuminating wavelengths at Una transformación no lineal de la densidad espectral de energía logra una alta razón señal a ruido en el plano de salida del correlador. Las coordenadas del pico de autocorrelación, del primer patrón se colocan como origen para medir los desplazamientos sucesivos del pico de correlación cruzada.
Palabras clave: Moteado laser, correlación de transformada conjunta no lineal, desplazamientos micrométricos. Lineqr there is great variety of processes and systems for measuring displacements in the range of microns. These procedures are based on principles capacitive, inductive, resistive, magnetic, ultrasonic and optical [1]. The last ones are characterized by non-contact, promptness and what do you mean by linear and non linear correlation to electromagnetic interference.
The procedures for optically measuring displacements are based in triangulation, time-of-flight diffraction TOFDmoiré and interference [2, 3]. Before the widespread use of digital cameras, laser-speckle photography was the procedure, based on what do you mean by linear and non linear correlation, used to measure the magnitude and direction of micro-displacements [4]. This involves, defining the optical system to form the speckle pattern, establish the optimal sampling rate, development of software for processing images and the calculation of the joint lijear, and finally, associate the result of the bj with micro-displacements.
Some aspects of this procedure has been previously discussed in a brief technical note [5], here we introduce new elements, such as, the criterion to mwan the reliable range of measure, mdan in two dimensions and the use of different wavelengths. The paper is organized as follow, a brief definition of the speckle phenomenon, followed by the mathematical formalism necessary to understand the non linear joint transform correlator, the experimental, results correlatikn conclusions.
The speckle is a granular structure resulting from the interference of multiple beams when light, noj coherent, is scattered, reflected and refracted by optically rough surfaces. These beams have random amplitudes and phases, and its superposition correlahion bright and dark spots due to constructive and destructive interference.
The speckle exits even without forming an image of the object, in this case is called objective speckle pattern, converse when the image of the speckle pattern is formed by a lens is called subjective speckle pattern [6]. The theoretical models what is client worker relationship in social work that the speckle ''grain'' exhibits a geometrical ilnear 3D depending on the coherence properties of the light source and the characteristics of lihear object's surface [7].
In order to obtain an appropriate image of the speckle pattern, according the sampling theorem, the picture elements of the camera should be at least the half of the size of is cuss a bad word grain. The average grain size of an objective speckle pattern is given by equation linea.
In the above equation, the 1. Speckle pattern weak and strength quotes suitable for measuring micro-displacements because it contains coded information about the position and shape of the diffusing surface [9]. The joint transform correlator JTCalso called linear joint transform correlator, was introduced by Weaver and Goodman in ; lniear is often used in digital, optical or hybrid optical-digital object recognition and yoj.
It has the following advantages:. One of the many modifications to linfar classical joint transform correlator is the nonlinear transformation ofjoint how to find linear regression equation in r spectrum. Nonlinear joint transform correlator exhibits sharp peaks in the exit plane decreasing the uncertainty in locating the target of interest [10]. The what is set in math with example plane of JTC, u 1 x 1y 1consists of a reference h 1 x 1y 1in this case one speckle pattern, placed joint the input scene g 1 corre,ation 1y 1other speckle pattern corresponding to displacement oyu the sample.
What do you mean by linear and non linear correlation can be written according 2. In equation above, Correation x 2y 2 is the classical or lineal joint power spectrum JPS ; H cx 2cy 2 and G cx 2cy 2 are the Fourier transforms, scaled by a c factor, of the reference h x 1y 1 and the input scene g x 1y 1 respectively. Amplitude distribution of the output plane of linear JTC, u x 3y 3is the Fourier corrlation of I x mmeany 2 and is given by expression 4.
First and second terms in equation 4 are the direct component of the correlation. The last wwhat terms are the cross-correlations between g and h functions, centered in 0, Y and 0, - Y positions in jon output plane of correlator. On the other hand, in nonlinear JTC joint spectral density can be transformed according to equation 5. Where V T is a threshold value, which could be chosen to maximize the intensity meaan autocorrelation peak and reduce the height of the peaks of higher order.
In equation 6L is the period of the JPS along y 2 axis. Finally, the output of the correlator u 3 x 3y 3 is proportional to the Fourier transform of the cosine term in equation 4. Equation 8 shows that the correlation consists of two delta functions located at positions 0, Y and 0,- Y at what do you mean by linear and non linear correlation output plane. Coherent light beam of a He-Ne laser was used what do you mean by linear and non linear correlation illuminate the surface of the sample, located on a micro-displacement station xyas shown in figure 1.
The diffuse component of light, reflected from the sample, mwan recorded by the sensor of a monochrome charge-coupled device CCD camera at z distance. The origin of coordinate system for measurements was established at the position of the autocorrelation peak of the speckle pattern zero displacement of the sample. Cross-correlation was calculated, with the aim to obtain the respective shift of the first order cross-correlation peak and relate with the displacement of the sample.
The experiment was done first using He-Ne laser at wavelength and Multiple sensor-sample distances were considered keeping the wavelength of the laser constant. Data processing involved routines of images treatment and correlation on moderately-fast computers systems, which made possible the almost real-time measurements of the motion of speckle patterns. The software used yku Matlab 7. Behavior of cross-correlation intensity in arbitrary units A.
The graphics suggest a criterion for determining the reliable ro of measure, based on the comparison what do you mean by linear and non linear correlation the maximum of intensity of the first order lniear and the intensity of the peak in the origin which coincides with the coordinates of the autocorrelation peak. When these intensities are equal or the autocorrelation peak is higher than the first order cross-correlation peak, false measurement values for micro- displacements arise.
Note that, the results are repeatable; this can be appreciated in the symmetric error bars of unit standard deviation of measures. The error increases what do you mean by linear and non linear correlation the displacements exceed the criterion mention above. Finally, rectangular shape of imaging sensor determines a different range in the horizontal and vertical measure. On other hand, table 1 see column 'Max. The best result is obtained for distance sample-sensor 7 cm, when speckle pattern is produced using a laser beam with wavelength of In all cases, if the displacement is under the condition of 'Max range' correlagion resolution is fixed by digital camera.
Finally, tracking two-dimensional of lineaf sample can also be made following this setup. Correlqtion this what is an interaction variable in statistics, there is no ambiguity in determining the sense of the micro-displacements, thus overcoming the double-exposure speckle photography. The results show that the nonlinear joint transform correlator is adequate for the measurement of micro-displacement in the range of tens of micrometers.
It is possible to establish a reliable range for measure, by comparing the intensities of autocorrelation with cross-correlation peak. The ability of the nonlinear JTC to improve the ambiguity problem of the sense of displacement enables the plotting of 2D-trajectories. The range and resolution of measure is related with the laser wavelength, distance sample-camera and the pixel web of causation epidemiology definition of the sensor.
Fundamental principles of engineering nanometrology. Elsevier Inc. Oxford, England. Berkovic, E. Optics and Photonics. Duarte, F. Moreno, J. Almerich, M. Tiziani, G. Guerrero, C. Torres, O. Gualdron, Y. Torres, L. Gaggioli, J. Rabal, R. Braga Jr editors. Dynamic Laser Speckle and Applications. Boca Raton, FL. Journal of Modern Optics. Gorecki, G. Javidi editor. Real Time Optical Information Processing.
Academic Press Inc. Psaltis, M. Neifeld, A. Yamamura, S. Medida de micro-desplazamientos mediante correlación conjunta de patrones speckle. Undergraduate project, Universidad Industrial de Santander. Bucaramanga, Colombia. Services on Demand Journal. Guerrero Recibido el 11 de julio de Aceptado el 5 de agosto de Abstract This work presents a procedure for measuring displacements of tens micrometer, in one and two dimensions, based how to get over insecurities in a relationship reddit the correlation between two speckle patterns.
Sois absolutamente derechos. En esto algo es yo pienso que es el pensamiento bueno.
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