Spatially offset optical coherence tomography: Leveraging multiple scattering for high-contrast imaging at depth in turbid media.

The penetration depth of optical coherence tomography (OCT) reaches well beyond conventional microscopy; however, signal reduction with depth leads to rapid degradation of the signal below the noise level. The pursuit of imaging at depth has been largely approached by extinguishing multiple scattering. However, in OCT, multiple scattering substantially contributes to image formation at depth.

Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions.

Methods for simulation of two-dimensional signals with arbitrary power spectral densities and signal amplitude probability density functions are disclosed. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In most cases the method provides satisfactory results and can thus be considered an engineering approach.

Speckle and fringe dynamics in imaging-speckle-pattern interferometry for spatial-filtering velocimetry.

This paper analyzes the dynamics of laser speckles and fringes, formed in an imaging-speckle-pattern interferometer with the purpose of sensing linear three-dimensional motion and out-of-plane components of rotation in real time, using optical spatial-filtering-velocimetry techniques. The ensemble-average definition of the cross-correlation function is applied to the intensity distributions, obtained in the observation plane at two positions of the object. The theoretical analysis provides a description for the dynamics of both the speckles and the fringes.

Low Earth orbit satellite-to-ground optical scintillation: comparison of experimental observations and theoretical predictions.

Scintillation measurements of a 1064 nm laser at a 5 kHz sampling rate were made by an optical ground station at the European Space Agency observatory in Tenerife, Spain while tracking a low Earth orbit satellite during the spring and summer of 2010. The scintillation index (SI), the variance of irradiance normalized to the square of the mean, and power spectra measurements were compared to theoretical predictions based on the Kolmogorov spectrum, the Maui3 nighttime turbulence profile, weak scintillation finite-beam wave theory, included receiver, and source aperture averaging with no free-fitting parameters. Good agreement was obtained, not only for the magnitude of the observed fluctuations, but also for the corresponding elevation angle dependence and shape of the power spectra.

Level crossing statistics for optical beam wander in a turbulent atmosphere with applications to ground-to-space laser communications.

Level crossing statistics is applied to the complex problem of atmospheric turbulence-induced beam wander for laser propagation from ground to space. A comprehensive estimate of the single-axis wander angle temporal autocorrelation function and the corresponding power spectrum is used to develop, for the first time to our knowledge, analytic expressions for the mean angular level crossing rate and the mean duration of such crossings. These results are based on an extension and generalization of a previous seminal analysis of the beam wander variance by Klyatskin and Kon.

Digital simulation of an arbitrary stationary stochastic process by spectral representation.

In this paper we present a straightforward, efficient, and computationally fast method for creating a large number of discrete samples with an arbitrary given probability density function and a specified spectral content. The method relies on initially transforming a white noise sample set of random Gaussian distributed numbers into a corresponding set with the desired spectral distribution, after which this colored Gaussian probability distribution is transformed via an inverse transform into the desired probability distribution. In contrast to previous work, where the analyses were limited to auto regressive and or iterative techniques to obtain satisfactory results, we find that a single application of the inverse transform method yields satisfactory results for a wide class of arbitrary probability distributions.

Mean level signal crossing rate for an arbitrary stochastic process.

The issue of the mean signal level crossing rate for various probability density functions with primary relevance for optics is discussed based on a new analytical method. This method relies on a unique transformation that transforms the probability distribution under investigation into a normal probability distribution, for which the distribution of mean level crossings is known. In general, the analytical results for the mean level crossing rate are supported and confirmed by numerical simulations.

Speckle dynamics for dual-beam optical illumination of a rotating structure.

An out-of-plane rotating object is illuminated with two spatially separated coherent beams, giving rise to fully developed speckles, which will translate and gradually decorrelate in the observation plane, located in the far field. The speckle pattern is a compound structure, consisting of random speckles modulated by a smaller and repetitive structure. Generally, these two components of the compound speckle structure will move as rigid structures with individual velocities determined by the characteristics of the two illuminating beams.

Statistics of spatially integrated speckle intensity difference.

We consider the statistics of the spatially integrated speckle intensity difference obtained from two separated finite collecting apertures. For fully developed speckle, closed-form analytic solutions for both the probability density function and the cumulative distribution function are derived here for both arbitrary values of the mean number of speckles contained within an aperture and the degree of coherence of the optical field. Additionally, closed-form expressions are obtained for the corresponding nth statistical moments.

Speckle dynamics resulting from multiple interfering beams.

The space-time intensity covariance function for illuminating an object giving rise to fully developed speckle is considered in the case where the object is illuminated with two spatially separated beams, or with a multitude of equidistant but spatially separated spots. Specifically, and to the best of our knowledge for the first time, we obtain the result that the larger speckles will be covered by a fine structure that, in general, translates at a different velocity from that of the larger speckles. In particular, closed-form analytical expressions are found for the space- and time-lagged covariance of irradiance as well as the corresponding power spectrum for each of the two spatially separated, N equidistant separated illuminating beams.

Extraction of optical scattering parameters and attenuation compensation in optical coherence tomography images of multilayered tissue structures.

A recently developed analytical optical coherence tomography (OCT) model [Thrane et al., J. Opt.

Advanced modelling of optical coherence tomography systems.

Analytical and numerical models for describing and understanding the light propagation in samples imaged by optical coherence tomography (OCT) systems are presented. An analytical model for calculating the OCT signal based on the extended Huygens-Fresnel principle valid both for the single and multiple scattering regimes is reviewed. An advanced Monte Carlo model for calculating the OCT signal is also reviewed, and the validity of this model is shown through a mathematical proof based on the extended Huygens-Fresnel principle.

Derivation of a Monte Carlo method for modeling heterodyne detection in optical coherence tomography systems.

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.