Depth of correlation

It is also possible to calculate ihe out-of-plane velocity component tv from the two in-plane components w and v by using the continuity equation. Equation (4.5), for incompressible flow, as shown in [5] for a turbulent flow around a surface-mounted obstacle. 

Integration of Equation (4.5) in the z-direction (out-of-plane) yields the expression to gain the w component  

The measurement error of j,-PIV measurements due to detectability Ej is given by the ratio of the uncertainty of the correlation peaklocation dj to the particle displacement Ax 

For a commonly used objective lens 20x/0.5 and a particle diameter dp = 0.5 im, the uncertainty of the correlation peak location 8x is given by 

The/number for the most common infinity-corrected microscope objective lens is given by 

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Future developments will improve singlecamera techniques for 3D imaging. Since particle tracking methods do not suffer from depth-of-correlation errors nor spatial averaging over interrogation windows, they will be applied more often in the future [3]. 

Rossi M, Segura R, Cierpka C, Kahler CJ (2010) On the effect of particle image intensity and image preprocessing on depth of correlation in micro-PIV. Exp Huids 52 1063-1075. doi 10.1007/s00348-011-1194-z... 

The depth of the field for a volume-illuminated p-PIV setup does not define precisely the thickness of the measurement plane because only the sharply focused particles contribute to the correlation function. The depth of the field is defined as twice the distance from the object plane to the plane in which the object is regarded as unfocused. The depth of correlation depends on the axial distance from the object plane in which a particle becomes sufficiently out of focus so that it no longer contributes significantly to the peak in the particle-image correlation function and can be calculated according to... 

It thus becomes clear that the depth of correlation is strongly dependent on the numerical aperture NA, the particle diameter dp and to a lesser extent the magnification M. As an example for a 20 x /0.5 objective and a particle size dp = 0.50 pm, the depth of correlation is 2 Zcorr = 7 pm. An overview of the thickness of the measurement planes for commonly used objectives is presented in [3]. 

Bourdon CJ, Olsen MG, Gorby AD (2004) Power-filter technique for modifying depth of correlation in microPIV experiments, Exp. in Fluids 37 263-271... 

The other effect of Brownian motion is its influence on the depth of correlation. Depth of correlation defines the depth over which particles significantly contribute to the correlation function. Olsen and Adrian (2000) derived an expression of correlation depth as... 

The last term in the right-hand side of the above expression represents the contribution of Brownian motion The depth of correlation increases due to the presence of the Brownian motion. 

Fig. 4a shows a characteristic narrow banded signal (860 kHz center frequency) from a flat steel surface (reference signal). A steel block was milled in a way that the distance of the upper and graved surface varied from 0 to about 1300 microns (Fig. 5). Moving the probe along the edge (see Fig. 5) about 30 signals have been acquired equidistantly (all 4 mm). Fig. 4b and 4c show two characteristic signals (position 6 and 12). The 30 measured signals have been preprocessed and deconvolved. Fig. 6 shows the evident correlation between measured TOF difference and signal position (depth of milled grave).

Both the Pb disc test and the steel dent test are of particular significance to stab detonators. As a matter of illustration, the steel dent test (Ref 10) consists of firing a detonator in direct end-on contact with a steel block. The depth of the dent produced is a measure of output. The depth, or better, the volume of the dent correlates well with initiation effectiveness. The low-rate detonation, which crushes nearly as much sand as high-order detonation, makes no dent in a steel plate. It has been demonstrated that the depth of the dent is proportionate to the excess of pressure over the yield strength of the steel of the dent block, integrated over the volume of the detonation head. It has been found that a detonator of 0.190-inch diameter or larger, which produces a dent 0.010 of an inch deep in a mild steel block, will initiate a lead of Tetryl or RDX under favorable conditions. Specification requirements for detonators to be used in fuses are usually at least 0.015 to 0.020 inch in depth, and many produce dents up to 0.060 inch deep... 

The error of this approximation is less than 0.01% for relevant global mean temperatures (see the Appendix). The thickness of the atmospheric layers, which is increasing with the altitude, is correlated to the optical depth of the... 

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