K−distribution plays a significant role in describing the statistics of the electromagnetic scattering. The influence of shape factor on the K−distribution is very significant because different shape factors in K-distributed sea clutter represent different actual scenarios. In this paper, we investigate the impact of different shape factors in the K−distributed sea clutter and provide the statistics of the Stokes parameters in electromagnetic scattering of the K−distribution under different shape factors.
In some applications, including but not limited to synthetic-aperture radar (SAR) imagery and wireless communication, the Weibull distribution is more flexible than the exponential distribution for these purposes, because it fits particularly well at the heavy tail of the sea clutter. In this paper, we conduct a statistical analysis of Stokes parameters based on random polarization phasor sums. We provide a comprehensive analysis for the statistical properties of the Stokes parameters in stochastic electric field with a Weibull-distribution intensity. The presented statistics of the Weibull-distribution optical field will be useful to optical scattering from random birefringent medium and polarization speckle imaging, which can also be extended to deal with the characterization of the scattering matrix in radar polarimetry.
Classical stochastic electromagnetic field assumes that the number of steps is infinite, but in practice, the number of steps for random walk is limited, even though the number of steps is large. Therefore, the statistical properties of finite-step random phasor sums are different from those of classical ones. As an example, the negative exponential probability density function of classical intensity speckles is not suitable for speckles with limited steps. In some applications, including but not limited to synthetic-aperture radar (SAR) imagery, wireless communication and wavelet analysis, when the probability density function of the classical speckle is used to calculate, the acquired result is often biased, and can’t provide appropriate estimation with reasonable accuracy. In this paper, we make the statistical analysis of the Stokes parameters of the random polarization phasor sums with a limited number of steps. The statical properties for the stochastic optical fields generated with a limited number of steps are presented with different applications in optical engineering
In this paper, a three-dimensional representation of the probability density distribution of the Stokes parameters in polarization speckle was developed. Following the electron cloud model used widely to visualize the hydrogen atomic orbitals, we present the density of the dots sculptured in the Hilbert space shows the probability density of finding the Stokes parameters in polarization speckle. Advantages of the electron cloud presentation for the statistics of the Stokes parameters are also discussed.
In many applications using light for practical purposes, the accuracy of optical experiment is limited most fundamentally by the finite amount of light utilized in the measurements. Special emphasis should be put on interferometry aimed at measuring the parameters of simple fringe patterns due to the following reasons. First, fringe parameter measurement provides a relatively well defined and tractable example of application of the theory. The desired parameters are easily defined, and methods for their measurement are readily devised based on common sense. Second, fringe parameter measurement is central to all problems involving coherence. The fundamental descriptors of light waves utilized in coherence theory are in fact measurable parameters of fringes. By examining the limitations to fringe parameter measurement, we are actually examining the limitations to the measurability of coherence itself. In this paper, fundamental limitations of estimating the amplitudes and phases of polar-interferograms recorded at low light levels are investigated. By modeling the receiver as a spatial array of photon-counting detectors, results are obtained that permit specification of the minimum number of photoevents required for estimation of fringe parameters to a given accuracy. Both a discrete Fourier-transform estimator and an optimum joint maximum-likelihood estimator are considered to specify the limiting performance of all unbiased estimators in terms of the collected light flux.
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