Application of Zernike polynomials to atmospheric propagation problems

Hu, P. H.; Stone, Jon R.; Stanley, T.

doi:10.1364/josaa.6.001595

Cited by 39 publications

(18 citation statements)

References 8 publications

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“…This approach allows for the exclusion of insignificant modes from the analysis. Expressions for the correlation functions of Zernike coefficients for the Kolmogorov model [3] of turbulence are given in Hu et al [4]. More complex models consider inner [5] and outer [6] scales of turbulence.…”

Section: Introductionmentioning

confidence: 99%

Method of estimation of turbulence characteristic scales

et al. 2012

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We propose an optical method that uses phase data of a laser beam obtained from a Shack-Hartmann sensor to estimate both the inner and outer scales of turbulence. The method is based on the sequential analysis of normalized correlation functions of Zernike coefficients. It allows the exclusion C(n)(2) from the analysis and reduces the solution of a two-parameter problem to a sequential solution of two single-parameter problems. The method has been applied to estimate the outer and inner scales of turbulence induced in the water cell.

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Section: Introductionmentioning

confidence: 99%

Method of estimation of turbulence characteristic scales

et al. 2012

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“…Submitting it into Eqs. (12) and (14), and utilizing the symmetrical characteristics of the beams, we can obtain:…”

Section: Example 1: Quartic Aberrationmentioning

confidence: 99%

“…Zernike polynomials have been used widely for describing optical wave fronts [9][10][11][12] when the aperture of a laser beam shows a circular symmetry. Mafusire and Forbes found the relationship between M 2 and the first eleven orders of Zernike polynomials [10], but the expressions are unavailable for higherorder Zernike aberrations, as Zernike terms are not orthonormal with respect to Gaussian function.…”

Section: Introductionmentioning

confidence: 99%

Method to evaluate beam quality of Gaussian beams with aberrations

et al. 2012

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Zernike polynomials are commonly used to describe the aberration of light beams, and the beam quality of Gaussian beams with aberrations can be deduced when the order of Zernike polynomials is limited. In this paper, Hermite polynomials are utilized to reconstruct the aberrations of Gaussian beams. The beam quality factor is directly related to the coefficient and terms of Hermite polynomials and has no limit on its index. We analyzed the beam quality of a Gaussian beam with a quartic aberration and other former 11th Zernike aberrations by Hermite polynomial expansion. The result corresponds with the published research work.

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“…These expressions may be found in References 6 through 9. For this work, I have used the greatly simplified ad-hoc expressions given by Equations (9), that were devised from a simulation study and with reference to the more-complex expressions in Reference 7. The quantity "F" in Equation (9) is also used to define α for atmospheric Strehl with tilt anisoplanatism as given in Table 2.…”

Section: Physical Effects and Radiometric Scaling Lawsmentioning

confidence: 99%

“…Experimental and theoretical studies have been conducted to better understand and characterize these dependencies and to provide relations to simplify the design process. [4][5][6][7][8][9][10][11][12] These relations, or scaling laws, generally predict the time-average or space-average influence of the various physical effects in terms of system design parameters.…”

Section: Introductionmentioning

confidence: 99%

Comparison of radiometric scaling laws and detailed wave-optics simulations for designing ground-based laser satellite-illumination and receiver systems

Bush

2002

SPIE Proceedings

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Ground-based optical transmitter and receiver systems designed for active imaging, active tracking and laser ranging of satellites in Earth orbit are very sensitive to physical conditions limiting the radiometric returns for achieving these measurements. The initial design of these systems is often based on simple radiometric scaling laws that provide estimates of average radiometric returns and are derived from experimental data or from more complex theoretical calculations. While these laws are quite useful, it is often easy to lose sight of the initial assumptions made in their formulation, and hence, the limits of their accuracy for designing certain systems. The objective of this paper is to review some of the commonly used radiometric scaling laws for active systems and to establish guidelines for their use based on comparisons of their predictions with results from detailed wave-optics simulations for different system design requirements and physical conditions. The combined effects of laser and transmitter beam parameters, wave-front aberrations, atmospheric turbulence, and satellite optical cross-section are considered.

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Application of Zernike polynomials to atmospheric propagation problems

Cited by 39 publications

References 8 publications

Method of estimation of turbulence characteristic scales

Method of estimation of turbulence characteristic scales

Method to evaluate beam quality of Gaussian beams with aberrations

Comparison of radiometric scaling laws and detailed wave-optics simulations for designing ground-based laser satellite-illumination and receiver systems

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