Cross-Correlation Method

In order to obtain the time lag between two sets of reflected light signals of known distance apart, points a and b, for particles in random movement, the cross-correlation function method is generally used in treating the signals. The cross-correlation function of two sets of random signals a t) and b(t) express the independence of the two sets of sampled data, i.e., 

Legends Same fiber for bulb lacldcat and reflected light  

FIGURE 4-24 Different types of fiber optic probes for particle velocity measurement. 

When T —v oo, the mean product would tend to a correct cross-correlation function. In addition, when a and b are interchanged, Ra(t) in the diagram of cross-correlation is symmetric, i.e., 

Sometimes the cross-correlation coefficient is used to express the maximum time lag, C (tJ, i.e., 

---

Application of the modified cross-correlation method was successfully demonstrated by comparing four independently recorded spectra with a library of spectra from 25 different strains of E. coli.22 These four strains were chosen arbitrarily without prior knowledge of the results. Three of the spectra of these strains used to compare to the library were obtained from cultures other than those used to generate their corresponding library spectra. The... 

Cross correlation methods are more complicated, both to conduct and interpret, than the three methods previously described. In essence, a random tracer signal is allowed to disturb a system and the response is recorded. If... 

A further improvement in transmitted intensity can be achieved in the time-of-flight method by chopping the product beam in a pseudorandom modulation sequence. In this cross-correlation method, the detected signals are then decoded to yield the time-of-flight spectrum and thence the velocity distribution [112]. 

Urban, C., and Schurtenberger, P. (1998). Characterization of turbid colloidal suspensions using light scattering techniques combined with cross-correlation methods. J. Colloid Interf. Sci. 207, 150-158. 

Particle velocity measurement in multiphase systems can be approximately categorized as invasive (probes, impaction devices) and noninvasive (rings, coils, optical beams). Yan (1996) has further detailed particle velocity measurement according to (1) Doppler methods laser and microwave (2) Cross-correlations methods capacitance, electrodynamic, acoustic or... 

Little has been discussed on error about measurement of particle velocity with the cross-correlation method. Usually, the data presented are the average velocity profiles of each measuring point. It is hard to know the exact sampling time at any position, the time interval of data processing, and at... 

Solid/liquid flows are commonly found in industrial processes to avoid flow obstruction, nonintrusive flowmeters are generally preferred. Flowmeters based on ultrasonic techniques are ideal nonintrusive instruments because, in most applications, the ultrasonic transducers are simply clamped on the outside pipe wall. In this section, we describe two ultrasonic flowmeters based on the Doppler and cross-correlation methods. Both require an inherent flow tag thus both are directly applicable to solid/liquid flows because of the presence of solid particles. Both flowmeters measure mainly particle velocity liquid-phase velocity, if different from the particle velocity, is not determined. 

Particle Velocity. Cross-Correlation Methods. The cross-correlation methods involve at least two sensors a known distance apart. These sensors may detect changes in electrical conductivity, capacitance, and... 

What is the advantage of the cross-correlation method in fluorescence lifetime measurements Fluorescence lifetimes are in the order of the ns or / and ps. Thus, high frequencies from the MHz to the GHz are needed to perform fluorescence lifetimes measurements. Still, the accuracy of the measured values is not reached at high frequencies. Therefore, one can translate the high frequency and phase modulation information to lower frequency carrier signal, Aw. In this case, the measured fluorescence lifetimes are highly accurate. 

The mathematical treatment of the cross correlation method is as follows ... 

Alternatively, the phase change can also be calculated by the cross-correlation method [8] ... 

G. Blanc, C. Gabrielli, and N. Keddam [1975] Measurement of the Electrochemical Noise by a Cross Correlation Method, Electrochim. Acta 20, 687. 

T. NOMURA, S. GOTOH, and K. YAMAKI, Reactivity Measurements by the Two-Detector Cross-Correlation Method and Siqpercritical Reactor-Noise Analysis, Neutron Noise, Waves and Pulse Propagation, ABC Symp. Ser. 9, CONF-660206 (May 1967). 

A laser sheet having a width of 10 mm was used for the illumination of the flow field to make the movements of tracer particles visible. After confirming the particles dispersed in the still salt water layer and silicone oil layer did not move, the vessel was declined 10 or 20° to the horizontal at a rotation velocity of 0.070 or 0.327 rad/s, using an air cylinder. A CCD camera mounted on the frame of the vessel was used for recording the movements of the particles at 30 frames/s. A velocity difference for the onset of shear flow instability was measured with PIV. The cross-correlation method was used to process the video images. 

Sobocinski et al. [185] developed a novel reflective type fiber-optic sensor for assessing the sizes of certain type of clusters (strands), as well as strand velocity and solids hold-up in gas-solids downward flowing suspensions. In order to calculate average strand velocity, the cross-correlation method was employed. The signals from the fiber-optic sensors were analyzed statistically to produce a characteristic time delay t between the signal spectrum from adjacent probes. This characteristic time delay corresponds to the maxima of the normalized cross-correlation function [82, 152, 218, 232] ... 

Hazra B, Roffel AJ, Narasimhan S, Pandey MD (2010) Modified cross-correlation method for the blind identification of structures. J Eng Mech 136(7) 889-897... 

Application of seismic noise cross-correlation methods for studies of volcanoes is a rapidly growing field. However, these methods have some important limitations that are mainly related to the properties of the seismic noise recorded at the Earth surface. So far, the basic theoretical foundation of the cross-correlation method assumes a random and homogeneous... 

One of the advantages of the cross-correlation method is that the correlation is less sensitive to background fluctuations because the change may not affect all of the component peaks and will be attenuated accordingly. The correlation scales the noise in proportion to the information, tending to force a constant optimal signal-to-noise ratio over the entire frequency range [147]. 

---