In this article we present a new method for reconstructing three-dimensional (3D) images with cylindrical symmetry from their two-dimensional projections. The method is based on expanding the projection in a basis set of functions that are analytical projections of known well-behaved functions. The original 3D image can then be reconstructed as a linear combination of these well-behaved functions, which have a Gaussian-like shape, with the same expansion coefficients as the projection. In the process of finding the expansion coefficients, regularization is used to achieve a more reliable reconstruction of noisy projections. The method is efficient and computationally cheap and is particularly well suited for transforming projections obtained in photoion and photoelectron imaging experiments. It can be used for any image with cylindrical symmetry, requires minimal user’s input, and provides a reliable reconstruction in certain cases when the commonly used Fourier–Hankel Abel transform method fails.

Reconstruction of Abel-transformable images: The Gaussian basis-set expansion Abel transform method

Development of micro power generators – A review

The kINPen—a review on physics and chemistry of the atmospheric pressure plasma jet and its applications

We present an iterative method for the extraction of velocity and angular distributions from two-dimensional (2D) ion/photoelectron imaging experiments. This method is based on the close relationship which exists between the initial 3D angular and velocity distribution and the measured 2D angular and radial distributions, and gives significantly better results than other inversion procedures which are commonly used today. Particularly, the procedure gets rid of the center-line noise which is one of the main artifacts in many current ion/photoelectron imaging experiments.

An iterative procedure for the inversion of two-dimensional ion/photoelectron imaging experiments

A new method for the reconstruction of velocity maps from ion images is presented, which is based on the maximum entropy concept. In contrast to other methods used for Abel inversion the new method never applies an inversion or smoothing to the data. Instead, it iteratively finds the map which is the most likely cause for the observed data, using the correct likelihood criterion for data sampled from a Poissonian distribution. The entropy criterion minimizes the information content in this map, which hence contains no information for which there is no evidence in the data. Two implementations are proposed, and their performance is demonstrated with simulated and experimental data: Maximum Entropy Velocity Image Reconstruction (MEVIR) obtains a two-dimensional slice through the velocity distribution and can be compared directly to Abel inversion. Maximum Entropy Velocity Legendre Reconstruction (MEVELER) finds one-dimensional distribution functions Ql(v) in an expansion of the velocity distribution in Legendre polynomials l(cos θ) for the angular dependence. Both MEVIR and MEVELER can be used for the analysis of ion images with intensities as low as 0.01 counts per pixel, with MEVELER performing significantly better than MEVIR for images with low intensity. Both methods perform better than pBASEX, in particular for images with less than one average count per pixel.

Inverting ion images without Abel inversion: maximum entropy reconstruction of velocity maps.

A method is presented for calculating the reconstruction of a circularly symmetric, two-dimensional function from its projection, a relation known as the Abel inversion. This technique differs from earlier methods by using integral transforms for its implementation. The frequency-domain analysis allows for experimentally obtained data, which are often noisy and off-center, to be processed in a systematic manner. The formulation of the Abel inversion in terms of transforms, filtering of the noise, and estimate of the off-center shift are discussed. Sample calculations of simulated noisy data and the application of the method to an image of a laser-sustained plasma are presented.

Abel inversion using transform techniques

An experiment was performed to determine the temperature distribution within a stationary plasma in atmospheric air produced by a continuously operating CO2 laser A peak temperature of 17000 °K (±5%) was found to exist at a point 11 cm ahead of the focal point The radiation surrounding the hot plasma core was found to consist primarily of the first negative system of nitrogen

Experimental study of a stationary laser−sustained air plasma

A theoretical model has been developed for laser‐sustained argon plasmas in a forced convective axisymmetric pipe flow. The two‐dimensional model based on Navier–Stokes equations was solved using a finite difference algorithm, and included geometric optics, temperature‐dependent thermodynamic, transport, and optical properties, as well as radiation‐induced thermal conductivity. The results showed good agreement with existing experimental data on temperature distribution, shape, and size of the plasma. The calculated velocity distribution revealed the complexity of the flow field and indicated that the constant axial mass flux (product of axial velocity and density) assumption adopted by existing one‐dimensional and semi‐two‐dimensional models is not adequate. The radiation transfer was found to have a significant influence on the predicted temperature distribution and peak temperature of laser‐sustained plasmas.

Theoretical investigation of laser-sustained argon plasmas

In this experimental investigation, stable and axisymmetric laser-sustained plasmas were produced in flowing argon. Energy was provided by the focused beam from a carbon dioxide laser; two different focusing geometries were used. Spatial distributions of absolute radiance from the plasmas, in a narrow-wavelength band, were measured. The assumption of axial symmetry, along with the assumption of local thermodynamic equilibrium, was used to deduce the radial profiles of temperature in the plasmas. From this and a geometric raytrace, the detailed spatial distribution of power absorption was calculated, as well as the radiation lost from the plasmas. In addition to the focusing geometry, the flow velocity, pressure, and incident laser power were systematically varied in the experiments. The quantitative results indicate clearly that a perceptive analysis of such laser-sustained plasmas must take into consideration the two-dimensionality of both the flowfield and the laser energy distribution in the focused beam.

Power absorption in laser-sustained argon plasmas

Charge exchange collisons between beam ions and neutral propellant gas can result in erosion of the accelerator grid surfaces of an ion engine. A particle in cell (PIC) is developed along with a Monte Carlo method to simulate the ion dynamics and charge exchange processes in the grid region of an ion thruster. The simulation is two-dimensional axisymmetric and uses three velocity components (2d3v) to investigate the influence of charge exchange collisions on the ion sputtering of the accelerator grid surfaces. An example calculation has been performed for an ion thruster operated on xenon propellant. The simulation shows that the greatest sputtering occurs on the downstream surface of the grid, but some sputtering can also occur on the upstream surface as well as on the interior of the grid aperture.

Dennis Keefer

Papers

Abel inversion using transform techniques

Experimental study of a stationary laser−sustained air plasma

Theoretical investigation of laser-sustained argon plasmas

Power absorption in laser-sustained argon plasmas

Plasma particle simulation of electrostatic ion thrusters