Correlation of signals of thermal acoustic radiation

The spatial correlation function is measured for the pressure of thermal acoustic radiation from a source (a narrow plasticine plate) whose temperature is made both higher and lower than the temperature of the receiver. The spatial correlation function of the pressure of thermal acoustic radiation is found to be oscillatory in character. The oscillation amplitude is determined not by the absolute temperature of the source but by the temperature difference between the source and the receiver. The correlation function changes its sign when a source heated with respect to the receiver is replaced by a cooled one.     

Measurement of the space-time correlation function of thermal acoustic radiation

The space-time correlation function of thermal acoustic radiation pressure is measured for a stationary heated source (a narrow plasticine plate). The correlation dependence is obtained by the multiplication of two signals shifted in time with respect to each other and measured by two receivers. The dependence exhibits an oscillating behavior and changes sign when the source is displaced by half the spatial period of the correlation function.     

Experimental studies of passive correlation tomography of incoherent acoustic sources in the megahertz frequency band

Correlation properties of thermal acoustic radiation in the megahertz frequency band are studied experimentally. The amplitudes of correlation peaks measured at the sum of the delays that correspond to the direct signal propagation between the piezoelectric transducers are found to depend on the relative transducer positions. This effect is explained by a possible difference between the receive patterns of the transducers and the patterns of their intrinsic thermal radiation. The correlation of signals received from a spatial region heated above the ambient medium is measured. The correlation between the received signals is found to depend on the time of heating of the emitter’s working medium. Numerical calculation of temperature distributions and the allowance for the decorrelation effect due to the spatial extent of the source provide a quantitative agreement between the theoretical and experimental results. Estimates of the spatial resolution achievable with the given experimental configuration show that it is close to the coherence length of the received radiation.     

Three-dimensional diffuser and three-dimensional speckles

The well-known model of a diffusely scattering surface as a set of randomly distributed point scatterers is generalized to the case of a volume diffuser. Assuming that the coordinates of the coherent radiation source, the observer, and also the diffuser shape are arbitrary, a formula is obtained for the spatial correlation function of the scattered radiation intensity in a free field. Expressions to determine the transverse and longitudinal dimensions of the speckles are obtained for diffusers in the form of a rectangular parallelepiped and a cylinder. Zh. Tekh. Fiz. 68, 59–63 (December 1998)     

Lens ghost imaging with thermal light: From the far field to the near field

For a fixed 2-f reference path, we demonstrate both theoretically and experimentally that based on the spatial correlation between two light fields, ghost imaging in spatial domain (GI) and Fourier-transform ghost interference (FRT) can be obtained by only increasing the transverse size of the thermal source D. Both explanation of the transformation from GI to FRT and their potential applications are also discussed.     

Lifetime of the superconductive state in short and long Josephson junctions

We study the transient statistical properties of short and long Josephson junctions under the influence of thermal and correlated fluctuations. In particular, we investigate the lifetime of the superconductive metastable state finding the presence of noise induced phenomena. For short Josephson junctions we investigate the lifetime as a function both of the frequency of the current driving signal and the noise intensity and we find how these noise-induced effects are modified by the presence of a correlated noise source. For long Josephson junctions we integrate numerically the sine-Gordon equation calculating the lifetime as a function of the length of the junction both for inhomogeneous and homogeneous bias current distributions. We obtain a non-monotonic behavior of the lifetime as a function of the frequency of the current driving signal and the correlation time of the noise. Moreover we find two maxima in the non-monotonic behaviour of the mean escape time as a function of the correlated noise intensity.     

Extension of the doubling method to inhomogeneous sources

This paper gives a general theory for applying the doubling method to spatially inhomogeneous radiation sources whose angular and spatial variations separate. In particular, inhomogeneous sources of thermal radiation may be efficiently treated by the methods herein, as well as direct and specularly-reflected beams of radiation which do not lie along a quadrature direction for the intensity. Doubling rules for a linear-in-optical-depth source (which may approximate a source of thermal radiation) and for an exponential-in-optical-depth source are derived as special cases.     

Transport of strongly comptonized radiation

For strongly Comptonized radiation in a nonrelativistic plasma, we calculate the bremsstrahlung source of Comptonized photons with an accurate allowance for free-free absorption and nonlinear stimulated Compton emission. We formulate radiation hydrodynamics equations that are valid in the limit of strong Compton energy exchange between plasma and radiation. We derive a formula for the energy dissipation rate under these conditions. For an optically thick region, we have found an equation that describes the spatial variation in the exponential fall-off factor of the radiation spectrum.     

Stochastic distribution of the fibrils that yielded the Shroud of Turin body image

The fibrils that yielded the Shroud body image show a stochastic distribution on the Linen of Turin. In fact, the probability of a fibril yellowing is a function of the energy, while this is not the case for the optical density value. This means that the above image is a latent image. We suggest thermal radiation or low-temperature chemical processes as possible natural energy sources to explain, by stochastic effects, the Shroud body image formation. Unfortunately, due to the nature of the phenomenon, we are not able to extract the energy source.     

Optimal dense coding with thermal entangled states

We study optimal dense coding with thermal entangled states of a two-qubit Heisenberg XX chain and a two-qutrit system. For a two-qubit Heisenberg XX chain, the dense coding capacity is a function of temperature and external magnetic field. Only in the case of an external magnetic field being less than the coupling constant, the optimal dense coding can be realized with thermal entangled states. For a two-qutrit system, we consider the dense coding capacity taking into account of nonlinear coupling constant and an external magnetic field. We find that the nonlinear coupling constant must be less than 0 for dense coding. For the two models, we give the conditions that the parameters of the models have to satisfy a valid dense coding.     

Tagged Particle Diffusion in One-Dimensional Gas with Hamiltonian Dynamics

We consider a one-dimensional gas of hard point particles in a finite box that are in thermal equilibrium and evolving under Hamiltonian dynamics. Tagged particle correlation functions of the middle particle are studied. For the special case where all particles have the same mass, we obtain analytic results for the velocity auto-correlation function in the short time diffusive regime and the long time approach to the saturation value when finite-size effects become relevant. In the case where the masses are unequal, numerical simulations indicate sub-diffusive behaviour with mean square displacement of the tagged particle growing as t/ln(t) with time t. Also various correlation functions, involving the velocity and position of the tagged particle, show damped oscillations at long times that are absent for the equal mass case.     

Determination of the size of a radiation source by the method of calculation of diffraction patterns

In traditional X-ray radiography, which has been used for various purposes since the discovery of X-ray radiation, the shadow image of an object under study is constructed based on the difference in the absorption of the X-ray radiation by different parts of the object. The main method that ensures a high spatial resolution is the method of point projection X-ray radiography, i.e., radiography from a point and bright radiation source. For projection radiography, the small size of the source is the most important characteristic of the source, which mainly determines the spatial resolution of the method. In this work, as a point source of soft X-ray radiation for radiography with a high spatial and temporal resolution, radiation from a hot spot of X-pinches is used. The size of the radiation source in different setups and configurations can be different. For four different high-current generators, we have calculated the sizes of sources of soft X-ray radiation from X-ray patterns of corresponding objects using Fresnel-Kirchhoff integrals. Our calculations show that the size of the source is in the range 0.7–2.8 μm. The method of the determination of the size of a radiation source from calculations of Fresnel-Kirchhoff integrals makes it possible to determine the size with an accuracy that exceeds the diffraction limit, which frequently restricts the resolution of standard methods.     

Spatial resolution limits for the reconstruction of acoustic source strength by inverse methods

One method for deducing the strength of an acoustic source distribution from measurement of the radiated field involves the inversion of the matrix of frequency response functions relating the field measurement points to the strengths of a number of point sources used to represent the source distribution. In practice, the frequency response function matrix to be inverted may very often be ill-conditioned. This ill-conditioning will also often result in an ill-posed problem and thus regularization algorithms are used to produce reasonable solutions. For this purpose, Tikhonov regularization has been applied, and generalized cross-validation (GCV) has been introduced as an effective method for determining the proper amount of regularization without prior knowledge of either the source distribution or the contaminating errors. In the present work, the emphasis is placed on the relationship between the spatial resolution of the reconstructed source distribution and the small singular values of the frequency response function matrix to be inverted. However, the use of Tikhonov regularization often suppresses the effect of small singular values and these are in turn often associated with high spatial frequencies of the source distribution. Thus, the process of regularization produces a useful estimate of the acoustic source strength distribution but with a limited spatial resolution. Furthermore, in the field of Fourier acoustics, the spatial resolution of the reconstructed source distribution is usually limited by the wavelength of the radiation. This paper expresses the relationship between estimation accuracy, spatial resolution, noise-level and source/sensor geometry, when a range of inverse sound radiation problems are regularised using Tikhonov regularization with GCV. The results presented form the basis of guidelines that enable the reconstruction of acoustic source strength with a resolution that is finer than the intrinsic half-wavelength limit.     

Temperature analysis of laser heated polymers on microsecond time scales

To investigate the temperature profiles on laser heated polymer films, we track the thermal radiation with 1 μs time and 1 μm spatial resolution. The resulting two-dimensional temperature graphs are compared to finite element simulations in order to understand the heat conversion and flow. The temperature measurement setup consists of a NIR laser and an optical detection system, which includes high performance optics and a microsecond gated camera, equipped with several interference filters. In this way the thermal radiation is detected in the visible range with spectral resolution. Fitting the spectrum with Planck’s law, two-dimensional micrographs of the temperature distribution are obtained. For polystyrene surfaces we were able to analyze the heating and the ablation behavior. Good agreement was found between experimental results and finite element simulations, when ablation is limited to a few tens of nanometers of the film thickness. Ablation of polystyrene starts at 150°C, 50 K above the glass transition temperature. We suggest a photomechanical ablation mechanism at that threshold fluence. For ablation at higher fluence and peak temperature, experiments indicate a thermal decomposition reaction. The temperature range of spinodal decomposition is not reached and can in our case be ruled out as ablation mechanism.     

Polymers in a vacuum

In a variety of situations, isolated polymer molecules are found in a vacuum, and here we examine their properties. Angular momentum conservation is shown to significantly alter the average size of a chain and its conservation is only broken slowly by thermal radiation. For an ideal chain, the time autocorrelation for monomer position oscillates with a period proportional to chain length. The oscillations and damping are analyzed in detail. Short-range repulsive interactions suppress oscillations and speed up relaxation, but stretched chains still show damped oscillatory correlations.     

Application of focusing arrays to the problems of acoustic brightness thermometry

Theoretical and experimental studies on the localization of heated objects by the methods of acoustic brightness thermometry are carried out. It is demonstrated that, in the case of using a single focusing array, the spatial localization of heated objects depends on the size of the source. One-and two-dimensional tomography of a real heated source is performed by an acoustic thermal tomograph with a focusing array. The results agree well with the data calculated according to the suggested model. The applicability of correlation focusing acoustic brightness thermometry to the localization of a heated source is investigated both theoretically and experimentally. It is demonstrated that a considerable increase in the spatial resolution of the method leads to a significant loss in sensitivity.     

Spatial nonlocal pair correlations in a repulsive 1D Bose gas

We analytically calculate the spatial nonlocal pair correlation function for an interacting uniform 1D Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects.     

Two-dimensional isotropic scattering in a semi-infinite medium

Exact results are presented for the source function, radiative flux, and intensity at the boundary of a two-dimensional, isotropically scattering, semi-infinite medium subjected to collimated or diffuse radiation. The spatial distributions of incident radiation considered are (1) cosine-varying, (2) semi-infinite step, (3) step at the origin and (4) finite strip. Two-dimensional effects are most pronounced at large albedos.     

Characterizing nonclassicality and entanglement

In Quantum Optics, the widely accepted definition of nonclassicality is based on the P function of Glauber and Sudarshan. When it fails to be interpreted as a classical probability density, the corresponding quantum state is said to be a nonclassical one. Here we present the first reconstruction of a nonclassical P function of a single-photon added thermal state. We also consider the nonclassical properties of general spacegtime dependent correlation functions of radiation fields. For the detection of these correlation functions, a balanced homodyne correlation technique was proposed. It is shown that the measurable correlation functions also allow one to completely characterize bipartite entangled quantum states with a negative partial transposition. Finally, we present a method for identifying general bipartite entanglement for continuous variables.     

Two-dimensional isotropic scattering in a semi-infinite cylindrical medium

Beginning with the integral equation for the source function, the solutions for the source function, flux and intensity at the boundary of a two-dimensional, isotropically scattering cylindrical medium are found. The incident radiation is collimated and normal to the surface of the medium and depends only on the radial coordinate. For a Bessel function boundary condition, separation of variables is used to reduce the source function integral equation to a one-dimensional equation. The resulting integral equation is shown to be the same as that for the two-dimensional planar case. Solutions for other boundary conditions are then shown to be superpositions of the Bessel function solution. Numerical results are presented for a Gaussian distribution of incident radiation which closely models a laser beam. These multiple scattering results are compared to the single scattering approximation. Also, the solution for a strongly anisotropic phase function which is made up of a spike in the forward direction superimposed on an otherwise isotropic phase function is expressed in terms of the isotropic results.