Abstract
Speckle, amplitude fluctuations in optical coherence tomography (OCT) images, contains information on sub-resolution structural properties of the imaged sample. Speckle statistics could therefore be utilized in the characterization of biological tissues. However, a rigorous theoretical framework relating OCT speckle statistics to structural tissue properties has yet to be developed. As a first step, we present a theoretical description of OCT speckle, relating the OCT amplitude variance to size and organization for samples of discrete random media (DRM). Starting the calculations from the size and organization of the scattering particles, we analytically find expressions for the OCT amplitude mean, amplitude variance, the backscattering coefficient and the scattering coefficient. We assume fully developed speckle and verify the validity of this assumption by experiments on controlled samples of silica microspheres suspended in water. We show that the OCT amplitude variance is sensitive to sub-resolution changes in size and organization of the scattering particles. Experimentally determined and theoretically calculated optical properties are compared and in good agreement.
Highlights
Identical scattering particles within the sampling, or coherence volume VC defined below, the backscattered field phases are uniformly and randomly distributed between 0 and 2π13
We study the dependence of the optical coherence tomography (OCT) amplitude and it’s variance on sub-resolution changes in size and concentration of the scattering particles, by probing controlled samples of silica microspheres suspended in water with equal μs, but different scattering particle size
We derive the OCT signal for discrete random media (DRM) containing mono-sized spherical scattering particles that are randomly distributed throughout the sample
Summary
Identical scattering particles within the sampling, or coherence volume VC defined below, the backscattered field phases are uniformly and randomly distributed between 0 and 2π13. Assuming the OCT amplitude to be Rayleigh distributed, we find expressions for the amplitude mean and amplitude variance in terms of sample optical properties These expressions are used to study the relation between retrieved optical properties and particle size and concentration. ∆ r = r2− r1 and an analytical solution can be found In this case the pair correlation function can be interpreted as a probability distribution for distances between particles. The Percus-Yevick solution[19] to the pair correlation function for three volume fractions (fv = ρ.Vparticle) is depicted in the left panel of Fig. 1, in which the horizontal axis is the distance between particles normalized on particle diameter. The structure factor fworhmerseaqF=our4λiπers-ipnair[21] θ; with λ the with the pair correlation function, and serves as a volume-fraction dependent weighting factor on the angular scattering pattern of the individual particles in the sample. Note that the horizontal axis is multiplied with diameter for scaling
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