Steven H. Izen

Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope

The details of a model used to predict the scattering of a plane polarized wave by a spherical particle as observed with a microscope are presented. The model accounts for the effect of a refractive interface on the outgoing scattered field and determines the image produced by a lens with high numerical aperture. The predictions of the model are verified by direct comparison with the experimentally observed scattering from polystyrene spheres in a fluid.

Advanced Optical Diagnostics for Ice Crystal Cloud Measurements in the NASA Glenn Propulsion Systems Laboratory

A light extinction tomography technique has been developed to monitor ice water clouds upstream of a direct connected engine in the Propulsion Systems Laboratory (PSL) at NASA Glenn Research Center (GRC). The system consists of 60 laser diodes with sheet generating optics and 120 detectors mounted around a 36-inch diameter ring. The sources are pulsed sequentially while the detectors acquire line-of-sight extinction data for each laser pulse. Using computed tomography algorithms, the extinction data are analyzed to produce a plot of the relative water content in the measurement plane. To target the low-spatial-frequency nature of ice water clouds, unique tomography algorithms were developed using filtered backprojection methods and direct inversion methods that use Gaussian basis functions. With the availability of a priori knowledge of the mean droplet size and the total water content at some point in the measurement plane, the tomography system can provide near real-time in-situ quantitative full-field total water content data at a measurement plane approximately 5 feet upstream of the engine inlet. Results from ice crystal clouds in the PSL are presented. In addition to the optical tomography technique, laser sheet imaging has also been applied in the PSL to provide planar ice cloud uniformity and relative water content data during facility calibration before the tomography system was available and also as validation data for the tomography system. A comparison between the laser sheet system and light extinction tomography resulting data are also presented. Very good agreement of imaged intensity and water content is demonstrated for both techniques. Also, comparative studies between the two techniques show excellent agreement in calculation of bulk total water content averaged over the center of the pipe.

Exploiting Symmetry in Fan Beam CT: Overcoming Third Generation Undersampling

A new reconstruction algorithm is presented for tomographic reconstruction from fan beam data acquired with a quarter detector shift. This algorithm exploits the reflection property of the divergent beam transform by representing the sample and reflected points as a discrete, multichannel sample set. A doubling of the reconstruction resolution is achieved by increasing the number of source locations without changing the detector sample density. The algorithm can be used to reconstruct images from a third generation CT scanner at the maximum resolution consistent with the frequency characteristics of the detector.

Generalized sampling expansion on lattices

The Papoulis Generalized Sampling Expansion (GSE) can be combined with Petersen-Middleton lattice sampling to obtain a GSE for n-dimensional bandlimited functions. Such expansions will be discussed for nonperiodic/periodic hybrids. The periodic and nonperiodic cases are incorporated as special cases. For a restrictive special case, a Parseval-like formula is proved for n-dimensional bandlimited functions sampled on periodic, nonuniform sample sets.

Three-dimensional computed tomography from interferometric measurements within a narrow cone of views

A theory is presented and tested for recovering a fluid property from measurements of its projections. Viewing comes as small as 10 degrees are evaluated, and the only assumption is that the property is space limited. The results of applying the theory to numerical and actual interferograms of a spherical discontinuity of refractive index are presented. The theory was developed to test the practicality and limits of using three-dimensional computed tomography to process optical diagnostic data for internal fluid dynamics.

Sampling in Flat Detector Fan Beam Tomography

In fan beam tomography, functions in

Imaging spheres with general incident wavefronts using a dipole decomposition

\mathbb{R}^2

A fast algorithm to compute the -line through points inside a helix cylinder

are reconstructed from integrals along rays which emanate from source points on a circle exterior to the object. The ray from each source can be parameterized either by the angle subtended with the ray through the origin or by the location of intersection with a line through the origin perpendicular to the central ray. The former models a curved detector and the latter a flat detector. Requirements for reconstructing an essentially bandlimited function from regular samples acquired with a curved detector are well known [F. Natterer, SIAM J. Appl. Math., 53 (1993), pp. 358–380]. These results are extended to the flat detector. The essential bandregion of flat fan beam transform of an essentially bandlimited function is computed and shown to be a superset of the scaled version of the corresponding bandregion of the curved fan beam transform of the function. Sampling conditions for the flat fan beam transform follow and differ from those appearing in the li...

Extended low contrast detectability for radiographic imaging systems

Although scattering for spheres with plane wave illumination was solved precisely by Mie in 1909, often it is of interest to image spheres with non-planar illumination. An extension of Mie theory which incorporates non-planar illumination requires knowledge of the coefficients for a spherical harmonic expansion of the incident wavefront about the center of the sphere. These coefficients have been determined for a few special cases, such as Gaussian beams, which have a relatively simple model. Using a vectorized Huygens principle, a general vector wavefront can be represented as a superposition of dipole sources. We have computed the spherical wave function expansion coefficients of an arbitrarily placed dipole and hence the scattering from a sphere illuminated by a general wavefront can be computed. As a special case, Mies solution of plane wave scattering was recovered. POtential applications include scattering with partially coherent illumination. Experimental results from the scattering from polystyrene spheres using Koehler illumination show agreement with numerical tests.

Method and apparatus for determining correlation between spatial coordinates in breast

In the context of helical cone-beam CT, Danielsson et al. discovered that for each point interior to the cylindrical surface containing a given helix, there is exactly one line segment passing through the point which intersects two points less than one turn apart on the helix. This segment is called a π-line. A new constructive algebraic proof of this result is presented along with a fast algorithm to compute the endpoints of the 71-line through an arbitrary point in the interior of the helix cylinder. This proof exposes the geometry of the decomposition of a cylinder interior as a disjoint union of π-lines.