We have developed a new theoretical description of the optical coherence tomography (OCT) technique for imaging in highly scattering tissue. The description is based on the extended Huygens-Fresnel principle, valid in both the single- and multiple-scattering regimes. The so-called shower curtain effect, which manifests itself in a standard OCT system, is an inherent property of the present theory. We demonstrate that the shower curtain effect leads to a strong increase in the heterodyne signal in a standard OCT system. This is in contrast to previous OCT models, where the shower curtain effect was not taken into account. The theoretical analysis is verified by measurements on samples consisting of aqueous suspensions of microspheres. Finally, we discuss the use of our new theoretical model for optimization of the OCT system.

In order to estimate deleterious effects caused by heating in continuous-wave end-pumped solid-state lasers, the heat equation has been solved for an axially heated cylinder with a thermally conductive boundary at the periphery. Steady-state thermal profiles are developed using both a full numerical solution and an analytic approximation which assumes only radial heat flow. The analytic solution, which is in good agreement with the numerical solution, is utilized to obtain an expression for the thermal focusing due to temperature-induced refractive index changes. For Nd:YAG, 1 W of pump power deposited as heat is predicted to cause a thermal focusing length comparable to the cavity length of a typical diode end-pumped laser.

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The first part of this paper is devoted to extending the Huygens-Fresnel principle to a medium that exhibits a spatial (but not temporal) variation in index of refraction. Utilizing a reciprocity theorem for a monochromatic disturbance in a weakly inhomogeneous medium, it is shown that the secondary wave-front will be determined by the envelope of spherical wavelets from the primary wavefront, as in the vacuum problem, but that each wavelet is now determined by the propagation of a spherical wave in the refractive medium. In the second part, the above development is applied to the case in which the index of refraction is a random variable; a further application of the reciprocity theorem results in a formula for the mean intensity distribution from a finite aperture in terms of the complex disturbance in the aperture and the modulation transfer function (MTF) for a spherical wave in the medium. The results are applicable for an arbitrary complex disturbance in the transmitting aperture in both the Fresnel and Fraunhofer regions of the aperture. Using a Kolmogorov spectrum for the index of refraction fluctuations and a second-order expression for the MTF, the formula is used to calculate the mean intensity distribution for a plane wave diffracting from a circular aperture and to give approximate expressions for the beam spreading at various ranges.

A Monte Carlo (MC) method for modeling optical coherence tomography (OCT) measurements of a diffusely reflecting discontinuity embedded in a scattering medium is presented. For the first time to the authors' knowledge it is shown analytically that the applicability of an MC approach to this optical geometry is firmly justified, because, as we show, in the conjugate image plane the field reflected from the sample is delta-correlated from which it follows that the heterodyne signal is calculated from the intensity distribution only. This is not a trivial result because, in general, the light from the sample will have a finite spatial coherence that cannot be accounted for by MC simulation. To estimate this intensity distribution adequately we have developed a novel method for modeling a focused Gaussian beam in MC simulation. This approach is valid for a softly as well as for a strongly focused beam, and it is shown that in free space the full three-dimensional intensity distribution of a Gaussian beam is obtained. The OCT signal and the intensity distribution in a scattering medium have been obtained for several geometries with the suggested MC method; when this model and a recently published analytical model based on the extended Huygens-Fresnel principle are compared, excellent agreement is found.