The dependence of speckle contrast on velocity: a numerical study

Abstract

We study how the speckle contrast depends on scatterer velocity, with the goal of further developing laser speckle imaging as a quantitative measurement technique. To that end, we perform interferometric computer simulations on a dilute plug flow. The results of our numerical experiment, that we compare with known analytical expressions to confirm their veracity, match well at low velocities with the Gaussian expression. Finally, we address the issue of how velocity depends on speckle decorrelation time, and show that the speckle size is most likely the relevant connecting length scale.

Toward detecting atherosclerosis using dynamic laser speckle contrast imaging: A numerical study

“…When a Gaussian autocovariance of the temporal fluctuations is assumed, an equation for the relation between K and the speckle decorrelation time τ c may be derived 25 that compares reasonably well with our previous simulations. 28 However, there is no agreement in the literature how to convert τ c into velocity v, making the exact relationship elusive. 25,51 Regardless, we have found previously from simulating a sine input signal (which is just a single peak in the frequency spectrum) that the frequency spectrum of the speckle contrast time series has higher-order peaks at multiples of the dominant frequency.…”

“…All settings (as are summarized in Table II) were chosen based on our previous results: the speckle contrast [see Eq. ( 2)] is sensitive to changes in scatterer velocity at our chosen camera integration time, 28 and the number of integration samples is a compromise between computational time and an 1% numerical integration error. 30 Altogether, 400 scattering simulations are performed for each flow period.…”

“…25,51 In ideal situations, the model that assumes Gaussian statistics for the autocovariance of the temporal speckle fluctuations seems to perform well. 25,28 However, in realistic situations K is affected by disturbances, such as the speckle boiling caused by the scatterers entering/leaving the imaging plane (i.e., out-of-plane motion) and entering/leaving the illuminated volume. The speckle contrast is also bound to a minimum value due to the influence of static scatterers 26 and the influence of multiple scattering.…”

“…Therefore, it is also useful to calculate the frequency spectrum of K(t) using the FFT; however, it should be noted that the frequency spectrum of K(t) will not equal the frequency spectrum of the underlying velocity, since K(t) does not scale linearly with velocity. 25,28 Rather, the frequency spectrum of K(t) will have roughly the same major (i.e., first-order and second-order) frequency modes as the frequency spectrum of the velocity, but it will have additional higher-order frequency modes due to the nonlinearity of the relationship. 30…”

“…Although it is now widely accepted in the literature that K scales inversely with velocity, the exact quantitative relationship still remains elusive. [25][26][27][28] Consequently, quantitative measurements still rely on combining multiple measurement techniques. 29 Nevertheless, with our goal of detecting atherosclerosis, we may bypass these challenges and use LSCI to qualitatively describe features of the underlying (blood) flow.…”