Limits of small angle scattering theory

McLean, J.; Crawford, Donald R.; Hindman, C. L.

doi:10.1364/ao.26.002053

Cited by 20 publications

(7 citation statements)

References 5 publications

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“…As the beam passes through water, the transmitted optical beam will spread due to scattering and its power will reduce due to absorption. Therefore, the analytical formulation of the BSF requires the solution of a complex radiative transfer equation [38], [39]. However, by considering small angle approximation (SAA), [40], [41], researchers have come up with an integral form of BSF [22]- [24], [42], given by:…”

Section: Bsf Prelimnariesmentioning

confidence: 99%

A Simplified Form of Beam Spread Function in Underwater Wireless Optical Communication and its Applications

Saxena

Bhatnagar

2019

IEEE Access

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Underwater wireless optical communication (UWOC) refers to the transmission of data in unguided water medium through optical carriers. Beam spread function (BSF) characterizes the amount of light irradiance received at the receiver as a function of receiver's distance from main beam axis for a particular link length. The existing form of BSF includes multiple integrals which are burdensome to use for mathematical analysis. Because of this, it gets very difficult to employ the existing form of BSF to derive non-integral expressions for bit error rate (BER), capacity, and outage probability of UWOC systems. Moreover, it is very difficult to find any insight into the UWOC systems based on this integral form of BSF. In this paper, we derive a simplified power series expression of BSF by solving the existing integral form. Closed-form expressions of BSF with some approximations, which simplify the derived power series expression, are also provided as special cases. Important insights regarding the behavior of BSF are also obtained from the derived simplified forms. Furthermore, closed-form expressions of BER, capacity, and outage probability of the UWOC system, taking the effect of scattering, absorption, and misalignment in consideration, are also derived. INDEX TERMS Beam spread function, bit error rate, capacity, log-normal distribution, outage probability, scattering phase function, underwater optical communication, volume scattering function. I. INTRODUCTION Since earth's surface is mainly water, we need technologies that can help with communications inside water. Underwater wireless communication (UWC) systems are very useful for study of the environment inside the ocean [1]. Further, UWC systems are very helpful in vehicle-to-vehicle communication inside water. Many technologies such as radio frequency (RF) communication [2], [3] and underwater acoustic communication (UWAC) [4], [5] are widely being used for wireless communication inside water. Despite strong attenuation, acoustic waves can travel a distance of about 10-90 km inside water [6], [7]; the attenuation gets stronger The associate editor coordinating the review of this manuscript and approving it for publication was Miaowen Wen.

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Section: Bsf Prelimnariesmentioning

confidence: 99%

A Simplified Form of Beam Spread Function in Underwater Wireless Optical Communication and its Applications

Saxena

Bhatnagar

2019

IEEE Access

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“…(1) is equivalent to the expression 5+N(Q, xr) =S(x,r), (4) Here the surface area element ds' points into the integration volume at the surface. Equation (6) G(x, r; x', r') = exp[ a(r r') ]e-(r -r-') Xfi (x -x' Q(r r-')) .…”

Section: The Integral Equation and Its Approximate Solutionmentioning

confidence: 99%

“…A third class of schemes for carrying out practical calculations involves Monte Carlo simulation [4]. The primary advantage here is simplicity and the fact that one is not required to oversimplify the physics (or the geometry) in order to achieve mathematical tractability.…”

Section: Introductionmentioning

confidence: 99%

Transport of light in a scattering medium through multiple small-angle scattering

Wilcox¹

1991

Phys. Rev. A

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Scattering of light by relatively large and numerous particles suspended in a liquid with a nearly matched index of refraction results in deflection through very small angles. The cumulative effect of many scatterings can, however, be substantial. Taking advantage of this small-angle-scattering property, we derive a simple asymptotic expression for the Xth-order multiple-scattering term based on steepestdescents evaluation of the 1Vth-order multiple integrals. When the dominant contribution to the scattering is high order (large Ã), the path followed by photons can be described by analogy with a deformed elastic rod, for which a constrained variational principle or principle of least action is specified. EulerLagrange equations are obtained for this constrained-end-point problem.

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“…Wells suggested an algebraic form for the VSF, which has been widely used because the PSF solution can then be obtained analytically. [3][4][5] The resulting PSF is used to predict the amount of blur in an image based on water quality.…”

Section: Introductionmentioning

confidence: 99%

Application of the small-angle approximation to ocean water types

Swanson¹,

Billard²,

Gehman³

et al. 2001

Appl. Opt.

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The small-angle approximation to the radiative transport equation is applied to particle suspensions that emulate ocean water. A particle size distribution is constructed from polystyrene and glass spheres with the best available data for particle size distributions in the ocean. A volume scattering function is calculated from the Mie theory for the particles in water and in oil. The refractive-index ratios of particles in water and particles in oil are 1.19 and 1.01, respectively. The ratio 1.19 is comparable to minerals and nonliving diatoms in ocean water, and the ratio 1.01 is comparable to the lower limit for microbes in water. The point-spread functions are measured as a function of optical thickness for both water and oil mixtures and compared with the point-spread functions generated from the small-angle approximation. Our results show that, under conditions that emulate ocean water, the small-angle approximation is valid only for small optical thicknesses. Specifically, the approximation is valid only for optical thicknesses less than 3.

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Limits of small angle scattering theory

Cited by 20 publications

References 5 publications

A Simplified Form of Beam Spread Function in Underwater Wireless Optical Communication and its Applications

A Simplified Form of Beam Spread Function in Underwater Wireless Optical Communication and its Applications

Transport of light in a scattering medium through multiple small-angle scattering

Application of the small-angle approximation to ocean water types

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