Diffuse Correlation Spectroscopy Beyond the Water Peak Enabled by Cross-Correlation of the Signals From InGaAs/InP Single Photon Detectors

Abstract

Objective: Diffuse correlation spectroscopy (DCS) is an optical technique that allows for the non-invasive measurement of blood flow. Recent work has shown that utilizing longer wavelengths beyond the traditional NIR range provides a significant improvement to signal-to-noise ratio (SNR). However, current detectors both sensitive to longer wavelengths and suitable for clinical applications (InGaAs/InP SPADs) suffer from suboptimal afterpulsing and dark noise characteristics. To overcome these barriers, we introduce a cross correlation method to more accurately recover blood flow information using InGaAs/InP SPADs.

Methods: Two InGaAs/InP SPAD detectors were used for during in vitro and in vivo DCS measurements. Cross correlation of the photon streams from each detector was performed to calculate the correlation function. Detector operating parameters were varied to determine parameters which maximized measurement SNR.State-space modeling was performed to determine the detector characteristics at each operating point.

Results: Evaluation of detector characteristics was performed across the range of operating conditions. Modeling the effects of the detector noise on the correlation function provided a method to correct the distortion of the correlation curve, yielding accurate recovery of flow information as confirmed by a reference detector.

Conclusion: Through a combination of cross-correlation of the signals from two detectors, model-based characterization of detector response, and optimization of detector operating parameters, the method allows for the accurate estimation of the true blood flow index.

Significance: This work presents a method by which DCS can be performed at longer NIR wavelengths with existing detector technology, taking advantage of the increased SNR.

Fig. 1.

State space model used to represent a detector module. Detector states are labeled with respect to their position relative to the detection state S₁, with the same numbering given for their state transition probabilities, which are labeled near the arrow indicating the state transition.

Fig. 2.

(a) Pictorial model description for the synthetic data model. The photon counts collected by the simulated detectors are shown with different types of counts color coded to their descriptions. (b) An example of the probabilities for the detection of each type of count is shown color coded in the same way as in (a). Inputs to the model, including the count rate of the back scattered light, DCR of the detector, and afterpulsing probabilities (P=10 kcps, AP₀=140 kcps, and α=1.37), are used to determine the probabilities.

Fig. 3.

(a) Comparison of the g₂(τ) calculated with autocorrelation of the combined counts of both detectors and the cross-correlation between the counts of each detector. The large artifacts due to afterpulsing are present in the autocorrelation calculation, though cross-correlation can be seen to remove the artifacts and extend the g₂ to times below the hold-off time. (b) The comparison between the SNSPD autocorrelation, InGaAs/InP autocorrelation, and InGaAs/InP cross correlation shows that the cross-correlation is not completely without distortion, showing a slower decay. Quantification of this decay is shown in (c), where BF_i is fit from g₂(τ)’s calculated from measurements at different operating conditions. The consistently lower BF_i is likely due to the “extension” of correlation by afterpulsing counts.

Fig. 4.

(a) Comparison of the autocorrelation calculated from the individual detector counts and their respective estimated autocorrelations fit using the detector model for a single set of detector operating parameters (Excess bias = 2.5 V, Hold off time = 10 μs, Temperature = 229 K). (b) Using the fitted properties, the BFi derived from the cross-correlation is corrected to account for the slowing of the correlation decay caused by the afterpulsing, and can be seen to match the BFi derived from the reference measurement. Fitting the correlation curves with the state space model allows for estimation of the afterpulsing probability at hold off time, shown in (c) and (f), measured count rate, shown in (d) and (g), and afterpulsing decay rate, shown in (e) and (h). The plots in (c), (d), and (e) are shown for a fixed temperature of 225K, and for the plots in (f), (g), and (h), the excess bias voltage is fixed at 2.0 V. The fit values for these parameters generally follow the intuition surrounding how altering the operating parameters (excess bias voltage, hold off time, and temperature) should affect the detector characteristics (P, AP₀, and α). Based on the count rate estimation shown in (d), at extremely high afterpulsing rates/detector non-linearity conditions like those for the shorter hold off time condition, the estimation of count rate might be inaccurate, as shown in the difference between the 10 and 20 μs hold off time vs. the rest of the measurements.

Fig. 5.

The comparisons of the SNR of the g₂(τ) curves as a function of the three operating parameters (excess bias voltage, hold off time, and temperature) are shown in (a) for the CW operation and (b) for the gated operation. To increase readability, the results present in (a) and (b) are averaged by the temperature, and presented in (c) and (d), respectively. It can be seen that for CW operation, a high bias voltage does not improve SNR, indicating that the noise counts grow faster than the increase in signal counts mediated by an increase in detection efficiency. For gated operation, the lower duty cycle allows for a reduction in dark counts, and the increase in detection efficiency is better realized, as indicated by the increased SNR at higher bias voltage. In general, across these measurements, increases in the hold off time are detrimental to SNR as they reduce the duty cycle of the detector and limit the number of back scattered photons that can be detected.

Fig. 6.

(a) Comparison of the time course of fitted BF_i during the probe compression protocol. The effect of the afterpulsing on the BF_i is seen in the lower BF_i fitted for the uncorrected data, but following correction, the InGaAs/InP detector cross-correlation gives very similar results to that of the SNSPD. (b) Comparison of the BF_i fitted from the SNSPD and InGaAs/InP measurements with and without the correction by the model. Large systematic errors can be seen in the estimate of BF_i without correction, but the model allows the extraction of accurate BF_i values. Due to the compression of the dynamic range of the autocorrelation decay at higher BF_i values, the variability of the BF_i estimates after correction can be seen to increase with the degree of the discrepancy between the true BF_i and the naively fit BF_i.

Fig. 7:

(a) Comparison of the recovered BF_i from g₂(τ) curves generated by the synthetic data model. The detector characteristics for each detector used for these simulations were AP₀ = [180, 140] kcps, DCR = [0.25, 0.25] kcps, and α = [1.37, 1.54], as fit from the measurements made at the operating conditions used for the in vivo experiments. At low count rates, the BF_i recovered from the curves shows more severe underestimation, seen in both (a) and (b), though with a higher photon count rate, the degree of underestimation is improved. The relationship shown provides a rationale for the relative BF_i matching well between the InGaAs/InP measurement and the reference measurement, as these measurements were made over a relatively small range of BF_i values. With an increase in the range of BF_i made during a particular measurement, this accuracy would likely be degraded, as the relationship between InGaAs/InP derived BF_i and true BF_i is nonlinear.