Analyzing effects of temperature on tissue equivalent phantoms using fiber Bragg gratings and optical coherence tomography

The use of optical coherence tomography envelope statistics to quantify local temperature changes in tissue-mimicking phantoms

“…Multiplex several sensors in an array (on a single fiber) [31] 4. Environmentally sturdy [29] The FBG reflects a specific wavelength of light, via periodically varying the refractive index within the optical fiber core [32]. A broadband light source is connected to the optical fiber and at each grating a small reflection of a particular wavelength propagates back, which constructively interferes to form a single, large reflection.…”

“…where, n ef f is the effective refractive index and Λ is the grating period. The effective refractive index (n ef f ) defines the velocity of the propagating light in comparison to its velocity in a vacuum [30][31][32][33]. The Bragg wavelength is susceptible to either increase or decrease with respect to changes in temperature or strain applied on the grating.…”

“…where, ∆λ b is the shift in wavelength, p e is the strain-optic coefficient, is the strain, α Λ is the thermal expansion coefficient, α Π is the thermo-optic coefficient and ∆T is the change in temperature [30][31][32][33]. For a single mode fiber that contains a silica core doped in GeO2, the thermal [31,35].…”

“…The OCT speckle histogram was comparatively fitted to four different types of probability distribution functions (PDF), which were: Normal distribution, Rayleigh distribution, Generalized Gamma distribution and Rician distribution. The Normal distribution, also referred to as the Gaussian distribution, is a distribution function where the highest probability value is positioned at the median value of the sample data set [32]. The probability of the pixel intensities (x) in a Normal distribution function are defined by the mean (µ) and the standard deviation (σ) of the data set and is represented in the following form [32]:…”

“…In order to determine the goodness of fit between the empirical data and the distribution functions of interest, the Kolmogorov-Smirnov (KS) test was applied. The KS test is a non-parametric test that compares a single dimensional probability distribution to a reference PDF, or compares two sample distributions to one another to determine if they originate from the same distribution family [32]. The test relies on the notion that the empirical distribution is asymptotic, in other words, the distribution must verge to zero as it approaches infinity.…”