Application of a Taylor series approximation to the Debye-Wolf integral in time-domain numerical electromagnetic simulations.

Finite-difference time-domain (FDTD) and pseudospectral time-domain (PSTD) methods are numerical electromagnetic simulation techniques that have been employed to perform rigorous simulations of broadband illuminations in several contexts. However, the computational cost of calculating the incident source fields introduced into the FDTD/PSTD grid can be considerable. In some cases, this can exceed the computational cost of what might be considered the principal part of the FDTD/PSTD algorithm, which calculates the spatial derivative of fields throughout the computational grid. In this paper, we analyze an existing method that has been used to approximate broadband illumination, which uses knowledge of the field only at a central frequency of the spectrum. We then present a new, to the best of our knowledge, approximation of the broadband illumination, which is more accurate, while remaining computationally tractable. Finally, we present some examples to verify the accuracy and efficiency of the new method and compare these results with the existing method.

Designing phantoms to accurately replicate circular depolarization in biological scattering media.

We introduce an iterative method for designing optical phantoms that are able to replicate the depolarization profiles of various target media, including colloidal suspensions of Intralipid, bovine milk, and ex vivo samples of ovine kidney cortex tissue. The designed phantoms comprise spherical scattering particles with fine-tuned size distributions and are capable of simultaneously reproducing spatially resolved intensity measurements and depolarization measurements of target media when illuminated with circularly polarized light.

Characterizing the depolarization of circularly polarized light in turbid scattering media.

We investigate the effectiveness of various bulk optical parameters in characterizing the degree of circular polarization (DOCP) of light diffusely reflected from scattering media. It is demonstrated that the traditional set of bulk optical parameters (namely, the scattering and absorption coefficients and the scattering asymmetry parameter) fail to characterize the observed depolarization. However, we find that there exists an additional parameter connected to the circular polarization memory phenomenon that consistently relates to observations, even in media with widely varying refractive indices and particle size distributions. This relationship is demonstrated using both Monte Carlo simulations and a new method for designing microsphere-based phantom media, which contain carefully controlled particle size distributions and depolarization characteristics.

Optimized diffusion approximation.

We show that the diffusion approximation (DA) to the radiative transport equation, which is commonly used in biomedical optics to describe propagation of light in tissues, contains a previously unexplored adjustable parameter. This parameter is related to the rate of exponential decay of the reduced intensity. In conventional theories, there are two distinct choices for this parameter. However, neither of these choices is optimal. When the optimal value for the parameter is used, the resulting DA becomes much more accurate near the medium boundaries, e.g., at the depth of up to a few ℓ*, where ℓ* is the transport mean free path (typically, about 1 mm in tissues). We refer to the new adjustable parameter as the reduced extinction coefficient. The proposed technique can reduce the relative error of the predicted diffuse density of the optical energy from about 30% to less than 1%. The optimized DA can still be inaccurate very close to an interface or in some other physical situations. Still, the proposed development extends the applicability range of the DA significantly. This result can be useful, for instance, in tomographic imaging of relatively shallow (up to a few ℓ* deep) layers of tissues in the reflection geometry.

Reciprocity relation for the vector radiative transport equation and its application to diffuse optical tomography with polarized light.

We derive a reciprocity relation for the 3D vector radiative transport equation that describes propagation of polarized light in multiple-scattering media. We then show how this result, together with translational invariance of a plane-parallel sample, can be used to efficiently compute the sensitivity kernel of diffuse optical tomography by Monte Carlo simulations. Numerical examples of polarization-selective sensitivity kernels are given.

Numerical investigation of polarization filtering for direct optical imaging within scattering media.

We investigate the ability of polarization filtering to improve direct imaging of absorbing objects which are buried within scattering environments. We extend on previous empirical investigations by exploiting an efficient perturbation-based formalism, which is applicable to arbitrarily arranged sources and detectors with arbitrary polarizations. From this approach, we are able in some cases to find certain non-trivial linear combinations of polarization measurement channels that maximize the object resolution and visibility.

On the inverse problem in optical coherence tomography.

We examine the inverse problem of retrieving sample refractive index information in the context of optical coherence tomography. Using two separate approaches, we discuss the limitations of the inverse problem which lead to it being ill-posed, primarily as a consequence of the limited viewing angles available in the reflection geometry. This is first considered from the theoretical point of view of diffraction tomography under a weak scattering approximation. We then investigate the full non-linear inverse problem using a variational approach. This presents another illustration of the non-uniqueness of the solution, and shows that even the non-linear (strongly scattering) scenario suffers a similar fate as the linear problem, with the observable spatial Fourier components of the sample occupying a limited support. Through examples we demonstrate how the solutions to the inverse problem compare when using the variational and diffraction-tomography approaches.

Approximate image synthesis in optical coherence tomography.

Full-wave models of OCT image formation, which are based on Maxwell's equations, are highly realistic. However, such models incur a high computational cost, particularly when modelling sample volumes consistent with those encountered in practice. Here, we present an approximate means of synthesizing volumetric image formation to reduce this computational burden. Instead of performing a full-wave scattered light calculation for each A-scan, we perform a full-wave scattered light calculation for a normally incident plane wave only. We use the angular spectrum field representation to implement beam focussing and scanning, making use of an assumption similar to the tilt optical memory effect, to approximately synthesize volumetric data sets. Our approach leads to an order of magnitude reduction in the computation time required to simulate typical B-scans. We evaluate this method by comparing rigorously and approximately evaluated point spread functions and images of highly scattering structured samples for a typical OCT system. Our approach also reveals new insights into image formation in OCT.

Controlling the optical pathlength in continuous-wave reflectance spectroscopy using polarization.

We investigate potential improvements of continuous-wave diffuse reflectance spectroscopy within highly scattering media by employing polarization gating. Simulations are used to show the extent at which the effective optical pathlength varies in a typical scattering medium as a function of the optical wavelength, the total level of absorption, and the selected polarization channels, including elliptical and circular polarization channels. Experiments then demonstrate that a wavelength dependent polarization gating scheme may reduce the prior knowledge required to solve the problem of chromophore quantification. This is achieved by finding combinations of polarization channels which have similar effective optical pathlengths through the medium at each wavelength.

Diffuse correlation tomography in the transport regime: A theoretical study of the sensitivity to Brownian motion.

Diffuse correlation tomography (DCT) uses the electric-field temporal autocorrelation function to measure the mean-square displacement of light-scattering particles in a turbid medium over a given exposure time. The movement of blood particles is here estimated through a Brownian-motion-like model in contrast to ordered motion as in blood flow. The sensitivity kernel relating the measurable field correlation function to the mean-square displacement of the particles can be derived by applying a perturbative analysis to the correlation transport equation (CTE). We derive an analytical expression for the CTE sensitivity kernel in terms of the Green's function of the radiative transport equation, which describes the propagation of the intensity. We then evaluate the kernel numerically. The simulations demonstrate that, in the transport regime, the sensitivity kernel provides sharper spatial information about the medium as compared with the correlation diffusion approximation. Also, the use of the CTE allows one to explore some additional degrees of freedom in the data such as the collimation direction of sources and detectors. Our results can be used to improve the spatial resolution of DCT, in particular, with applications to blood flow imaging in regions where the Brownian motion is dominant.