Abstract
Diffusing wave spectroscopy (DWS) is a well-known set of methods to measure the temporal dynamics of dynamic samples. In DWS, dynamic samples scatter the incident coherent light, and the information of the temporal dynamics is encoded in the scattered light. To record and analyze the light signal, there exist two types of methods—temporal sampling methods and speckle ensemble methods. Temporal sampling methods, including diffuse correlation spectroscopy, use one or multiple large bandwidth detectors to sample well and analyze the temporal light signal to infer the sample temporal dynamics. Speckle ensemble methods, including speckle visibility spectroscopy, use a high-pixel-count camera sensor to capture a speckle pattern and use the speckle contrast to infer sample temporal dynamics. In this paper, we theoretically and experimentally demonstrate that the decorrelation time (τ) measurement accuracy or signal-to-noise ratio (SNR) of the two types of methods has a unified and similar fundamental expression based on the number of independent observables (NIO) and the photon flux. Given a time measurement duration, the NIO in temporal sampling methods is constrained by the measurement duration, while speckle ensemble methods can outperform by using simultaneous sampling channels to scale up the NIO significantly. In the case of optical brain monitoring, the interplay of these factors favors speckle ensemble methods. We illustrate that this important engineering consideration is consistent with the previous research on blood pulsatile flow measurements, where a speckle ensemble method operating at 100-fold lower photon flux than a conventional temporal sampling system can achieve a comparable SNR.
Highlights
Diffusing wave spectroscopy (DWS)1,2 is a well-established approach that is used to measure the temporal dynamical properties of dynamic samples, such as in vivo blood flow monitoring,3 air turbulence quantification,4 and particle diffusion in liquid solution.5 A common experimental setting of DWS is to use a coherent laser source to illuminate the dynamic sample and measure the scattered light
Given a time measurement duration, the number of independent observables (NIO) in temporal sampling methods is constrained by the measurement duration, while speckle ensemble methods can outperform by using simultaneous sampling channels to scale up the NIO significantly
Researchers typically utilize red or near-infrared light to illuminate the brain through skin, probe the dynamic scattering light that interacts with the brain, and analyze the recorded light signal to infer the information of cerebral blood flow (CBF)
Summary
Diffusing wave spectroscopy (DWS) is a well-established approach that is used to measure the temporal dynamical properties of dynamic samples, such as in vivo blood flow monitoring, air turbulence quantification, and particle diffusion in liquid solution. A common experimental setting of DWS is to use a coherent laser source to illuminate the dynamic sample and measure the scattered light. 100-fold lower photon flux than a conventional temporal sampling method can still achieve a comparable SNR, which is consistent with the results in our previous work.20 This is because camera sensors used in speckle ensemble methods typically have very large pixel counts and thereby allow us to achieve a large NIO within the limited measurement time. ΔT needs to be on the order of microseconds or smaller (one order of magnitude smaller than the decorrelation time) This implies that temporal sampling methods require substantially fast detectors. For temporal sampling methods that use a single detector, the SNR of the measured decorrelation time τ, which is defined as the expected decorrelation time τ divided by error(τ) (error of τ in the measurement), has the form of [see Eq (A36) in the Appendix]
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