Noise and bias in optical coherence tomography intensity signal decorrelation

Abstract

Functional optical coherence tomography (OCT) imaging based on the decorrelation of the intensity signal has been used extensively in angiography and is finding use in flowmetry and therapy monitoring. In this work, we present a rigorous analysis of the autocorrelation function, introduce the concepts of contrast bias, statistical bias and variability, and identify the optimal definition of the second-order autocorrelation function (ACF) g(2) to improve its estimation from limited data. We benchmark different averaging strategies in reducing statistical bias and variability. We also developed an analytical correction for the noise contributions to the decorrelation of the ACF in OCT that extends the signal-to-noise ratio range in which ACF analysis can be used. We demonstrate the use of all the tools developed in the experimental determination of the lateral speckle size depth dependence in a rotational endoscopic probe with low NA, and we show the ability to more accurately determine the rotational speed of an endoscopic probe to implement NURD detection. We finally present g(2)-based angiography of the finger nailbed, demonstrating the improved results from noise correction and the optimal bias mitigation strategies.

Real-time co-localized OCT surveillance of laser therapy using motion corrected speckle decorrelation

“…where the bracket • • • denotes an ensemble average implemented as klm . Decorrelated speckle patterns will have g (2) → 1 while correlated patterns will have g (2) → 2 for speckle with unity contrast, as is the case of OCT [52]. These theoretical values for g (2) are reached for infinitely large ensembles.…”

“…The second-order autocorrelation function g (2) is defined as the time-delayed correlation of the intensity of an ensemble at a time difference τ. Considering that an OCT system determines the intensity of backscattered light as a function of depth z (first index), lateral position x (second index) and time t (third index), the inter-B-scan autocorrelation function can be written as [51,52] g (2)…”

“…The term {I ens (z, x, t − τ), I ens (z, x, t)} is a concatenation of the two ensembles I ens (z, x, t − τ) and I ens (z, x, t). We ignore any dependency of the calculated value of the autocorrelation function with the ensemble size as we do not compare results among different ensemble sizes [52]. During therapy, we calculate g (2) n for all positions in the OCT tomogram.…”

“…As such, it is crucial to implement noise correction methods that account for these effects. We use a novel analytic correction for the noise-induced decorrelation, as proposed by Uribe-Patarroyo et al [52], which does not suffer from the loss in temporal resolution of previous corrections [53]. Briefly, the shot noise component in the OCT tomogram can be modeled as an additive white-noise contribution to the complex-valued tomogram [54].…”

Forward multiple scattering dominates speckle decorrelation in whole-blood flowmetry using optical coherence tomography

“…This defines the expected relationship in a SS regime between speed in mm/s and the corresponding decorrelation rate in ms −1 for this system. We expect that the main sources of discrepancy between model and experiment in a SS regime to be imperfect knowledge of the exact NA of the system and statistical bias in the calculation of g (1) due to the relatively small correlation window [49]. In a final flow experiment, we wanted to evaluate the dependence of the increased decorrelation due to FMS with the blood layer thickness.…”