The form of the wavefunction psi for a semiclassical regular quantum state (associated with classical motion on an N-dimensional torus in the 2N-dimensional phase space) is very different from the form of psi for an irregular state (associated with stochastic classical motion on all or part of the (2N-1)-dimensional energy surface in phase space). For regular states the local average probability density Pi rises to large values on caustics at the boundaries of the classically allowed region in coordinate space, and psi exhibits strong anisotropic interference oscillations. For irregular states Pi falls to zero (or in two dimensions stays constant) on 'anticaustics' at the boundary of the classically allowed region, and psi appears to be a Gaussian random function exhibiting more moderate interference oscillations which for ergodic classical motion are statistically isotropic with the autocorrelation of psi given by a Bessel function.

https://iopscience.iop.org/article/10.1088/0305-4470/10/12/016/pdf

Regular and irregular semiclassical wavefunctions

A mathematical model for non-Rayleigh microwave sea echo is developed which describes explicitly the dependence of statistical properties of the radar cross section on the area of sea surface illuminated by the radar. In addition to the first probability distribution of the scattered radiation, its temporal and spatial correlation functions are also considered. It is shown that, in general, these correlation functions decay on at least two scales, the second, non-Rayleigh, contributions being strongly dependent on the properties of a "single scatterer." Predictions of the model are found to be in qualitative agreement with existing experimental data. A new class of probability distributions, the " K -distributions," is introduced, which may prove useful for fitting such data.

A model for non-Rayleigh sea echo

Laser-speckles show displacement accompanied by structure change when diffuse objects generating them undergo displacement and/or deformation. This behaviour is theoretically investigated by calculating the cross-correlation functions of speckle intensities before and after the deformation. The dependences of speckle displacement on geometries of object illumination and speckle observation as well as on deformation parameters are clarified. The relations derived are interpreted physically by introducing the shift in diffraction rays due to displacement and deformation of a grating. Distributions of speckle displacement are calculated numerically and shown graphically.

Speckle Displacement and Decorrelation in the Diffraction and Image Fields for Small Object Deformation

In connection with the parameters of the optical configuration used to produce speckles and under illumination of a Gaussian beam over a moving diffuse object, this paper discusses the statistical properties of dynamic speckles produced in the diffraction and image fields by the diffuse object moving in a plane with constant velocity. Especially, the space-time correlation function of the dynamic speckle intensity is examined in detail. Two typical speckle motions of translation and boiling are interpreted for various optical configurations in the diffraction and image fields. As one of the interesting applications of dynamic speckles to metrology, various methods for velocity measurements of the diffuse object are introduced.

Dynamic Laser Speckles and their Application to Velocity Measurements of the Diffuse Object

Dynamic laser speckles and their application to velocity measurements of the diffuse object

The statistical, spatial and temporal coherence properties of electromagnetic radiation scattered into the far field by a deep random phase screen are investigated. It is shown that significant departures from Gaussian behaviour can occur even when the phase correlation length is much smaller than the dimensions of the scattering region-a situation in which the central limit theorem might be expected to apply. Formulae are derived relating these departures to elementary properties of the scattering structure, which may therefore be determined by measurement of the fluctuations in the scattered radiation. Application of the results to scattering from very rough surfaces is discussed.

https://iopscience.iop.org/article/10.1088/0305-4470/8/3/010/pdf

E Jakeman

Papers

Non-Gaussian fluctuations in electromagnetic radiation scattered by random phase screen. I. Theory