H. T. Yura

Mutual coherence function of a finite cross section optical beam propagating in a turbulent medium.

On the basis of the extended Huygens-Fresnel principle, a general expression is derived for the mutual coherence function (MCF) of a finite optical beam propagating in a weakly inhomogeneous medium. The results obtained here for the beam MCF are valid both in the near and far field of the laser transmitting aperture and for an arbitrary complex disturbance in the exit pupil of the aperture. A general expression is also derived for the propagation distance z(B) such that for distances much less (greater) than z(B), the MCF is well approximated by the plane (spherical) wave results. An analytic expression is pre-sented for a Gaussian beam such that a numerical error in previous results is corrected. Finally, some comments regarding higher order statistical moments of the field are given.

Analysis of optical coherence tomography systems based on the extended Huygens–Fresnel principle

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.

Optical scintillation statistics for IR ground-to-space laser communication systems

Statistical estimates of selected scintillation parameters for an infrared laser ground-to-space communication system are presented for a point-receiving aperture. The quantities estimated here are the fraction of time that the signal power is both above and below a given value, the mean number of times per second the signal power crosses a given signal level, and the mean duration of both surges and fades for a given log-irradiance variance.

Short-term average optical-beam spread in a turbulent medium

On the basis of the extended Huygens–Fresnel principle, a general expression is derived for the short-term average optical-beam spread, as measured with respect to the instantaneous center of energy of the beam, of an initially coherent optical-beam wave propagating in a weakly inhomogeneous medium. The present analysis applies to the near field of the effective coherent transmitting aperture, where the beam wanders (dances) as a whole and does not break up into multiple patches or blobs. Central to the analysis is the short-term average mutual coherence function (MCF) of a spherical wave. This quantity is obtained from the corresponding long-term MCF by removing the random tilt of the wave front. Analytic expressions for the short-term beam spread are presented for the case of a Kolmogorov spectrum and the short-term average MCF derived by Fried. As expected, the short-term, turbulence-induced beam spread is always less than the corresponding long-term beam spread. Analytic and numerical results are given for the short-term average irradiance at focal range f, which is always greater than the corresponding long-term average irradiance.

Physical model for strong optical-amplitude fluctuations in a turbulent medium

Tatarskii’s geometrical-optics model of scintillation has been generalized to include both diffraction and the loss of spatial coherence of the wave as it propagates through the turbulent medium. An estimate is obtained of the amplitude fluctuations that agrees with the results of perturbation theory for σϒ2⪡1 and saturates to a constant value of the order unity for σT2⪢1 ( σT2 is the amplitude variance calculated on the basis of perturbation theory). In addition, we have calculated the amplitude correlation function. For σT2⪡1, the amplitude correlation function agrees with the results of perturbation theory and for the Kolmogorov spectrum is characterized by a correlation length of the order (L/k)1/2, where L is the propagation distance and k is the optical wave number. Conversely, for σT2⪢1 the amplitude correlation length decreases with increasing propagation distance and is shown to be equal to the lateral coherence length of the wave ρ0(L). In this regime, a residual correlation tail is obtained in agreement with recent experiments.

Telescope-Performance Reciprocity for Propagation in a Turbulent Medium

Abstract : The authors demonstrate that, with the effects of atmospheric turbulence included, reciprocity exists between the performance of a telescope (i.e., an antenna) when it functions as part of an optical heterodyne receiver and its performance when it functions as part of a laser transmitter. For a given optical antenna operating through atmospheric turbulence to some distant point, the effect of atmospheric turbulence upon antenna gain is the same whether the antenna is used as part of a laser transmitter, of an optical heterodyne receiver, or of an image-forming device. It follows that, if the same antenna is used in two or more ways simultaneously, e.g., as a transmitter and as an imaging device, measurements of the performance in one role may be used to gauge the concurrent performance in the other role. (Author)

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. Soc. Am. A 17, 484 (2000)] allows the extraction of optical scattering parameters from OCT images, thereby permitting attenuation compensation in those images. By expanding this theoretical model, we have developed a new method for extracting optical scattering parameters from multilayered tissue structures in vivo. To verify this, we used a Monte Carlo (MC) OCT model as a numerical phantom to simulate the OCT signal for heterogeneous multilayered tissue. Excellent agreement between the extracted values of the optical scattering properties of the different layers and the corresponding input reference values of the MC simulation was obtained, which demonstrates the feasibility of the method for in vivo applications. This is to our knowledge the first time such verification has been obtained, and the results hold promise for expanding the functional imaging capabilities of OCT.

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. Moreover, for the first time the model is verified experimentally. From the analytical model, an algorithm for enhancing OCT images is developed: the so-called true-reflection algorithm in which the OCT signal may be corrected for the attenuation caused by scattering. For the first time, the algorithm is demonstrated by using the Monte Carlo model as a numerical tissue phantom. Such algorithm holds promise for improving OCT imagery and to extend the possibility for functional imaging.

Second-order Rytov approximation

Abstract : An explicit and useful formulation of the solution for the second- order Rytov approximation is given. From this solution a condition of validity for the Rytov solution is obtained. It is concluded that, in general, both the Born and Rytov approximations have the same domain of validity.

Speckle: statistics and interferometric decorrelation effects in complex ABCD optical systems

The mean, the variance, and the correlation function of the intensity pattern resulting from an incoherent source that has propagated through a complex ABCD optical system are derived. The number of speckle correlation cells (or modes, N) within an effective measurement area is presented and discussed. Optical field decorrelation effects with respect to secondary fringe formation in phase-shifting speckle interferometry are discussed. In particular, the correlation coefficient resulting from load-induced object tilt, in-plane translations, and displacements parallel to the optic axis as a function of the number of modes propagating through the optical system is derived and discussed. In contrast to previous research, in which the calculation of speckle interferometric decorrelation effects was restricted to direct imaging systems and the special case where N → ∞, the correlation coefficients that we derive are valid for arbitrary complex ABCD systems (i.e., nonimaging configurations) and for all finite values of N ≥ 1.