Polynomial approximation method for tomographic reconstruction of three-dimensional refractive index fields with limited data

We propose a polynomial approximation method (PAM) for reconstruction of three-dimensional refractive index fields by interferometric tomography using limited data. Based on the assumption that the fields to be reconstructed are usually smooth and can be decomposed into a finite order of (orthogonal) polynomials, a set of linear equations can be constructed using both the measured projection data and the Radon transform of the basis functions. By solving these equations, the least-squares solutions of expansion coefficients can be obtained and then substituted back to yield the desired fields. Numerical results have demonstrated that the proposed method is fast, robust to noise and can achieve satisfactory results for refractive index fields with limited projection views and large opaque objects.     

Measurement of the three-dimensional velocity distribution of Stark-decelerated Rydberg atoms

The full three-dimensional velocity distributions of decelerated and accelerated particles in a Stark decelerator for Rydberg atoms and molecules have been measured. In the experiment, argon atoms in a supersonic beam are excited to low-field and high-field seeking Stark states with principal quantum number in the range n=15 to 25 and are decelerated in a 3 mm long decelerator consisting of four electrodes on which time-dependent voltages are applied. The time dependence of the resulting inhomogeneous electric field is chosen such that the decelerating force acting on the high-field seeking states is maximized at each point along the trajectories. The three-dimensional velocity distribution of the atoms before and after the deceleration is determined by measuring times of flight and two-dimensional images of the atomic cloud on the detector. Under optimal deceleration conditions, the decrease in kinetic energy in the longitudinal dimension amounts to 1.0×10^-21 J and the increase in mean kinetic energy in the transverse dimensions is only 1.0×10^-23 J. The corresponding temperatures of 100 mK and 300 mK in the two transverse dimensions are sufficiently low that trapping can be envisaged. The possibility of focusing a Rydberg atom beam is demonstrated experimentally.     

A method for the determination of three-dimensional velocity fields from holographic images

A simple general method is reported for particle tracking and velocity field determination from the reconstruction of holographic images. A preliminary experimental application is reported.     

A method for phase reconstruction in the optical three-dimensional shape measurement

In the optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x- and y-axis directions are obtained with a phase-shifting mechanism, the origin of which is analysed. Furthermore, to avoid the phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing the numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

On the reconstruction of the energy distribution of electrons accelerated in solar flares

A technique for reconstructing energy spectra of electrons accelerated in solar flares is suggested that is based on the rigorous solution of the inverse problem considering their X-ray bremsstrahlung. Model calculations are made for various spectra, and it is proved that this technique makes it possible to find the electron energy distribution in real flare events. The energy distribution of high-energy electrons accelerated in the solar flare observed on July 26, 2002, is reconstructed. It is shown that the hard X-ray spectrum of the flare may result from the bremsstrahlung of three groups of high-energy electrons.     

A method for phase reconstruction in optical three-dimensional shape measurement

In optical three-dimensional shape measurement, a method of improving the measurement precision for phase reconstruction without phase unwrapping is analyzed in detail. Intensities of any five consecutive pixels that lie in the x-axis direction of the phase domain are given. Partial derivatives of the phase function in the x-and y-axis directions are obtained with a phaseshifting mechanism, the origin of which is analysed. Furthermore, to avoid phase unwrapping in the phase reconstruction, we derive the gradient of the phase function and perform a two-dimensional integral along the x- and y-axis directions. The reconstructed phase can be obtained directly by performing numerical integration, and thus it is of great convenience for phase reconstruction. Finally, the results of numerical simulations and practical experiments verify the correctness of the proposed method.     

测量电子气体的速度分布函数

利用夫兰克-赫兹实验仪测量了电子气体的速度分布函数,并分析了电子与氩原子碰撞的动力学过程.     

Optimization and testing of the tomographic method of velocity measurement in the flow volume

The optic noncontact method of velocity field measurement in the flow volume is considered in this paper for the purposes of hydroaerodynamic experiment. The essence of this method is measurement of particles motion in the flow during short periods between laser pulses. This study offers and implements several algorithmic optimizations, allowing data processing time reduction. It is shown that application of threshold background filtering on the recorded projections (particle images) and fast estimation of initial intensity distribution in the volume allows increasing the speed of tomographic reconstruction algorithm two or three times. Reconstruction accuracy and errors in determination of particle shift were studied in this work using artificial images. The described tomographic method for the velocity field estimation in the flow volume was used for diagnostics of a turbulent submerged jet flowing into a narrow channel. The application of developed approaches in experiment allowed us to obtain spatial distribution of the average velocity field and instantaneous velocity fields in the measurement area.     

Runout error correction in tomographic reconstruction by intensity summation method

An alignment method for correction of the axial and radial runout errors of the rotation stage in X‐ray phase‐contrast computed tomography has been developed. Only intensity information was used, without extra hardware or complicated calculation. Notably, the method, as demonstrated herein, can utilize the halo artifact to determine displacement.     

Spatiotemporal evolution of the distribution function of electrons in sign-changing electric field

A numerical model for solving the Boltzmann unsteady non-local kinetic equation for the distribution function of electrons over energy is constructed. The Boltzmann equation for isotropic part of the distribution function written in natural variables the kinetic energy — the coordinate was solved by the pseudo-unsteady method. The model was applied for describing the spatiotemporal evolution of the distribution function of electrons in a uniform electric field. For a model distribution of the electric field with the “negative” value in the Faraday dark space and the “positive” value in the positive column of the glow discharge, the main macroscopic parameters of electrons are obtained, the diffusion mechanism of the electron current transfer in the negative electric field region is confirmed. The work was financially supported by the Russian Foundation for Basic Research (Grant No. 07-02-00781-a) and by State Contract No. 02.513.11.3242.     

Quasiclassical distribution function of electrons in a homogeneous magnetic field

Vlasov's equation is used to find the classical nonrelativistic and relativistic distribution functions that describe an electron beam of bounded radius in a homogeneous magnetic field. In the quasiclassical approximation, by means of the exact wave functions of an electron in a homogeneous magnetic field, the quantum relativistic distribution function with allowance for the electron spin is found. The mean physical quantities that characterize the radially bounded electron beam are found as functions of the temperature and electron spin.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 50–56, July, 1976.It is a pleasant duty to thank Professor V. G. Bagrov for discussing the results.     

A tomographic approach to Wigner's function

We propose a new derivation of Wigner's function based on the property of positivity of its integrals along straight lines in phase space. Identifying the values of these marginalizations with densities pertaining to invariant observables, we are able to reconstruct Wigner's pseudo-distribution from its slices.     

Superiority of Bessel function over Zernicke polynomial as base function for radial expansion in tomographic reconstruction

Here we describe the superiority of Bessel function as base function for radial expansion over Zernicke polynomial in the tomographic reconstruction technique. The causes for the superiority have been described in detail. The superiority has been shown both with simulated data for Kadomtsev’s model for saw-tooth oscillation and real experimental x-ray data from W7-AS Stellarator.     

Model of the stabilized distribution function for oscillating electrons in a hollow cathode

The form of the velocity distribution function of oscillating electrons in a low-pressure discharge with a hollow cathode is determined using the simple model of mathematical billiards. The distribution function is nonequilibrium and permits the development of instability of the plasma beam type.     

Wavelength-scanning digital interference holography for tomographic three-dimensional imaging by use of the angular spectrum method

A tomographic imaging system based on wavelength-scanning digital interference holography is developed by applying the angular spectrum method. Compared to the well-known Fresnel diffraction formula, which is subject to a minimum distance requirement in reconstruction, the angular spectrum method can reconstruct the wave field at any distance from the hologram plane. The new system allows three-dimensional tomographic images to be extracted with an improved signal-to-noise ratio, a more flexible scanning range, and an easier specimen size selection. Experiments are performed to demonstrate the effectiveness of the method.     

An analytical approach to the distribution function of electrons in the molecular oxygen discharge

Analytical expressions for the electron distribution function and the kinetic coefficients in the molecular oxygen glow discharge are given. The relative importance of the various collisional processes in evaluation of some experimentally measured quantities is discussed as well as the validity of the present results.     

The flow velocity distribution from the doppler information on a plane in three-dimensional flow

In order to observe and estimate the flow of fluid in three-dimensional space, the pulsed Doppler method has been used widely. However, the velocity information acquired is only the velocity component in the beam direction of the wave even if an observation plane is formed by beam scanning. Accordingly, it is difficult to know the velocity distribution in the observation plane in tree-dimensional flow. In this paper, the new idea for processing the velocity distribution in the beam direction on an observation plane for transposing to flux distribution (flow function method) has been introduced. Further, the flow in an observation domain is divided into two kinds of flows, viz., the base flow which indicates the directivity of the flow in the observation domain and the vortex which is considered a two-dimensional flow. By applying the theory of a stream function to the two-dimensional flow, and by using the physical feature of a streamline to the base flow, the velocity component v which intersects perpendicularly to the beam direction is estimated. The flow velocity distribution in a scanning plane (observation plane) can be known from these two components of velocity, viz., beam direction componentu and perpendicular component to the beam directionv. The principle was explained by an example of the blood flow measurement in normal and abnormal heart chamber, by the ultrasonic Doppler method.