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An Overview of the Null-Field Method. II: Convergence and Numerical Stability

In this paper we provide an analysis of the convergence and numerical stability of the null-field method with discrete sources. We show that (i) if the null-field scheme is numerically stable then we can decide whether or not convergence can be achieved; (ii) if the null-field scheme is numerically unstable then we cannot draw any conclusion about the convergence issue; and (iii) the numerical stability is closely related to the property of a tangential system of radiating discrete sources to form a Riesz basis. Our numerical analysis indicates that for prolate spheroids and localized vector spherical wave functions, the null-field scheme is numerically unstable (this system of vector functions does not form a Riesz basis), while for distributed vector spherical wave functions, the numerical instability is not so pronounced (this system of discrete sources almost possesses the property of being a Riesz basis). We also describe an analytical method for computing the surface integrals in the framework of the conventional null-field method with localized vector spherical wave functions which increases the stability of the numerical scheme.

Null-field method↗

Mechanoregulation of Proliferation, Differentiation, Senescence and Survival of Bone Marrow Primary Osteoprecursor Cells

Cell and animal studies conducted onboard the International Space Station and during the Shuttle program have provided extensive data illustrating bone degenerative responses to mechanical unloading in microgravity. Specifically CDKN1a/p21, an inhibitory modulator of cell cycle progression, is upregulated in osteoprecursor cells of the femur during 15-day spaceflight, suggesting that microgravity can block stem cell-based tissue regenerative process at the level of progenitor proliferation and differentiation. To study a potential role for CDKN1a/p21 in regulating osteogenic mechanosensitivity, we cultured primary bone marrow osteoprogenitor cells from CDKN1a/p21-null (p21-null) and wildtype mice with and without mechanical stimulation, and compared their morphological, proliferative, and in-vitro mineralization responses. Structural cell alterations due to mechanical stimulation were assessed by florescence labeling of f-actin cytoskeleton and focal adhesions. Mechanical stimulation of p21-null cells resulted in more pronounced cytoskeletal alignment with the axis of stretch than for wildtype cells. In addition, p21-null cells subjected to stretch loading also formed significantly more focal adhesions than wildtype cells. Combined these findings suggest that p21-null cells are structurally more responsive to stretch stimulation than the wildtype cells. Because osteoprogenitor cells are well known to respond to mechanical stimulation with increased proliferation, we also tested this response in p21-null cells. Results from those experiments show the proliferative capacity of mechanically stimulated p21-null cells far exceeded that of wildtype controls. Specifically, cell counts from 14, and 21 days post mechanical stimulation, show that p21- null cells to have a 4-fold increase in proliferation compared to wildtype. When the p21-null cell differentiation response to mechanical stimulation was evaluated, the p21-null cultuers elicited more extensive mineralization at earlier assessed timepoints than control cultures. Specifically, Von Kossa staining for mineralized matrix showed that the p21-null cells produced more than twice the mineralized surface area of wildtype cells, and at an earlier 7-day time point in culture. Taken together these results suggest that CDKN1a/p21 normally plays a role in negatively regulating osteoprogenitor proliferation and differentiation responses to mechanostimulation in bone. Findings of CDKN1a/p21's increased expression during spaceflight in microgravity also suggest not only a potential molecular mechanism for arresting regenerative bone growth in space, but potentially also a reduced impact for bone-formation-promoting exercise mechanostimulation. The findings described here constitute a novel role for p21 as a regulator of tissue regeneration in response to mechanical load stimulation, and also suggest a new promising molecular target to promote regenerative health in disuse conditions.

gravity↗

Lessons Learned During Cryogenic Optical Testing of the Advanced Mirror System Demonstrators (AMSDs)

Optical testing in a cryogenic environment presents a host of challenges above and beyond those encountered during room temperature testing. The Advanced Mirror System Demonstrators (AMSDs) are 1.4 m diameter, ultra light-weight (<20 kg/mA2), off-axis parabolic segments. They are required to have 250 nm PV & 50 nm RMS surface figure error or less at 35 K. An optical testing system, consisting of an Instantaneous Phase Interferometer (PI), a diffractive null corrector (DNC), and an Absolute Distance Meter (ADM), was used to measure the surface figure & radius-of-curvature of these mirrors at the operational temperature within the X-Ray Calibration Facility (XRCF) at Marshall Space Flight Center (MSFC). The Ah4SD program was designed to improve the technology related to the design, fabrication, & testing of such mirrors in support of NASA s James Webb Space Telescope (JWST). This paper will describe the lessons learned during preparation & cryogenic testing of the AMSDs.

Hadaway, James↗

Multi-Segment Radius Measurement Using an Absolute Distance Meter Through a Null Assembly

This system was one of the test methods considered for measuring the radius of curvature of one or more of the 18 segmented mirrors that form the 6.5 m diameter primary mirror (PM) of the James Webb Space Telescope (JWST). The assembled telescope will be tested at cryogenic temperatures in a 17-m diameter by 27-m high vacuum chamber at the Johnson Space Center. This system uses a Leica Absolute Distance Meter (ADM), at a wavelength of 780 nm, combined with beam-steering and beam-shaping optics to make a differential distance measurement between a ring mirror on the reflective null assembly and individual PM segments. The ADM is located inside the same Pressure-Tight Enclosure (PTE) that houses the test interferometer. The PTE maintains the ADM and interferometer at ambient temperature and pressure so that they are not directly exposed to the telescope s harsh cryogenic and vacuum environment. This system takes advantage of the existing achromatic objective and reflective null assembly used by the test interferometer to direct four ADM beamlets to four PM segments through an optical path that is coincident with the interferometer beam. A mask, positioned on a linear slide, contains an array of 1.25 mm diameter circular subapertures that map to each of the 18 PM segments as well as six positions around the ring mirror. A down-collimated 4 mm ADM beam simultaneously covers 4 adjacent PM segment beamlets and one ring mirror beamlet. The radius, or spacing, of all 18 segments can be measured with the addition of two orthogonally-oriented scanning pentaprisms used to steer the ADM beam to any one of six different sub-aperture configurations at the plane of the ring mirror. The interferometer beam, at a wavelength of 687 nm, and the ADM beamlets, at a wavelength of 780 nm, pass through the objective and null so that the rays are normally incident on the parabolic PM surface. After reflecting off the PM, both the ADM and interferometer beams return to their respective instruments on nearly the same path. A fifth beamlet, acting as a differential reference, reflects off a ring mirror attached to the objective and null and returns to the ADM. The spacings between the ring mirror, objective, and null are known through manufacturing tolerances as well as through an in situ null wavefront alignment of the interferometer test beam with a reflective hologram located near the caustic of the null. Since total path length between the ring mirror and PM segments is highly deterministic, any ADM-measured departures from the predicted path length can be attributed to either spacing error or radius error in the PM. It is estimated that the path length measurement between the ring mirror and a PM segment is accurate to better than 100 m. The unique features of this invention include the differential distance measuring capability and its integration into an existing cryogenic and vacuum compatible interferometric optical test.

Merle, Cormic↗

Three-dimensional kinematic reconnection of plasmoids with nulls

The global nonlinear dynamics of magnetic field lines in plasmoids with a pair of nulls, where B = 0, is studied. The aim of this analysis is to describe the separatrix surfaces on which singularities can occur in ideal magnetohydrodynamics because of topological changes in the field. These separatrix surfaces should locate the boundary layers associated with 3D reconnection in the presence of resistivity or inertia. It is found that the field lines exhibit chaotic scattering with several properties in common with plasmoid models without nulls (in which one component of the magnetic field never changes sign). In particular, the singular surfaces can be fractal, implying complex current density structures down to the dissipation scale. These generic features are expected to exist in typical coronal magnetic geometries exhibiting three-dimensional reconnection and the formation of current sheets.

Lau, Yun-Tung↗

Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines

The present investigation of three-dimensional reconnection of magnetic fields with nulls and of fields with closed lines gives attention to the geometry of the former, with a view to their gamma-line and Sigma-surface structures. The geometric structures of configurations with a pair of type A and B nulls permit reconnection across the null-null lines; these are the field lines which join the two nulls. Also noted is the case of magnetostatic reconnection, in which the magnetic field is time-independent and the electrostatic potential is constant along field lines.

Lau, Yun-Tung↗

Brewster angle of the lunar crust.

Brewster null in reflections of Explorer 35 telemetry transmissions from lunar surface, discussing radiation reflection properties of lunar maria and Flamsteed area

Tyler, G. L.↗

Computer Generated Hologram System for Wavefront Measurement System Calibration

Computer Generated Holograms (CGHs) have been used for some time to calibrate interferometers that require nulling optics. A typical scenario is the testing of aspheric surfaces with an interferometer placed near the paraxial center of curvature. Existing CGH technology suffers from a reduced capacity to calibrate middle and high spatial frequencies. The root cause of this shortcoming is as follows: the CGH is not placed at an image conjugate of the asphere due to limitations imposed by the geometry of the test and the allowable size of the CGH. This innovation provides a calibration system where the imaging properties in calibration can be made comparable to the test configuration. Thus, if the test is designed to have good imaging properties, then middle and high spatial frequency errors in the test system can be well calibrated. The improved imaging properties are provided by a rudimentary auxiliary optic as part of the calibration system. The auxiliary optic is simple to characterize and align to the CGH. Use of the auxiliary optic also reduces the size of the CGH required for calibration and the density of the lines required for the CGH. The resulting CGH is less expensive than the existing technology and has reduced write error and alignment error sensitivities. This CGH system is suitable for any kind of calibration using an interferometer when high spatial resolution is required. It is especially well suited for tests that include segmented optical components or large apertures.

Olczak, Gene↗

Surface characterization and testing II; Proceedings of the Meeting, San Diego, CA, Aug. 10, 11, 1989

Various papers on surface characterization and testing are presented. Individual topics addressed include: simple Hartmann test data interpretation, optimum configuration of the Offner null corrector, system for phase-shifting interferometry in the presence of vibration, fringe variation and visibility in speckle-shearing interferometry, functional integral representation of rough surfaces, calibration of surface heights in an interferometric optical profiler, image formation in common path differential profilometers, SEM of optical surfaces, measuring surface profiles with scanning tunneling microscopes, surface profile measurements of curved parts, high-resolution optical profiler, scanning heterodyne interferometer with immunity from microphonics, real-time crystal axis measurements of semiconductor materials, radial metrology with a panoramic annular lens, surface analysis for the characterization of defects in thin-film processes, Spacelab Optical Viewport glass assembly optical test program for the Starlab mission, scanning differential intensity and phase system for optical metrology.

Greivenkamp, John E.↗

Low-gravity fluid flows

The behavior of fluids in micro-gravity conditions is examined, with particular regard to applications in the growth of single crystals. The effects of gravity on fluid behavior are reviewed, and the advent of Shuttle flights are noted to offer extended time for experimentation and processing in a null-gravity environment, with accelerations resulting solely from maneuvering rockets. Buoyancy driven flows are considered for the cases stable-, unstable-, and mixed-mode convection. Further discussion is presented on g-jitter, surface-tension gradient, thermoacoustic, and phase-change convection. All the flows are present in both gravity and null gravity conditions, although the effects of buoyancy and g-jitter convection usually overshadow the other effects while in a gravity field. Further work is recommended on critical-state and sedimentation processes in microgravity conditions.

Ostrach, S.↗

CGH Figure Testing of Aspherical Mirrors in Cold Vacuums

An established method of room-temperature interferometric null testing of mirrors having simple shapes (e.g., flat, spherical, or spheroidal) has been augmented to enable measurement of errors in the surface figures of off-axis, non-axisymmetric, aspherical mirrors when the mirrors are located inside cryogenic vacuum chambers. The established method involves the use of a computer-generated hologram (CGH), functionally equivalent to a traditional null lens, to modify the laser beam of an imaging interferometer to obtain a reference wavefront that matches the ideal surface figure of a mirror under test. The CGH is inserted at the appropriate position and orientation in the optical path of the imaging interferometer, which, in turn, is appropriately positioned and oriented with respect to the mirror under test. Deviations of the surface figure of the mirror from the ideal surface figure manifest themselves as interference fringes. Interferograms are recorded and analyzed to deduce figure errors.

Chambers, Victor John↗

Effects of Pseudostreamer Boundary Dynamics on Heliospheric Field and Wind

Interchange reconnection has been proposed as a mechanism for the generation of the slow solar wind, and a key contributor to determining its characteristic qualities. In this paper we study the implications of interchange reconnection for the structure of the plasma and field in the heliosphere. We use the Adaptively Refined Magnetohydrodynamic Solver (ARMS) to simulate the coronal magnetic evolution in a coronal topology containing both a pseudostreamer and helmet streamer. We begin with a geometry containing a low-latitude coronal hole that is separated from the main polar coronal hole by a pseudostreamer. We drive the system by imposing rotating flows at the Solar surface within and around the low-latitude coronal hole, which leads to a corrugation (at low altitudes) of the separatrix surfaces that separate open from closed magnetic flux. Interchange reconnection is induced both at the null points and separators of the pseudostreamer, and at the global helmet streamer. Wedemonstrate that a preferential occurrence of interchange reconnection in the “lanes” between our driving cells leads to a filamentary pattern of newly-opened flux in the heliosphere. These flux bundles connect to but extend far from the separatrix-web (S-Web) arcs at the source surface. We propose that the pattern of granular and supergranular flows on the photosphere should leave an observable imprint in the heliosphere.

V Aslanyan↗

Sea-surface temperature and salinity mapping from remote microwave radiometric measurements of brightness temperature

A technique to measure remotely sea surface temperature and salinity was demonstrated with a dual frequency microwave radiometer system. Accuracies in temperature of 1 C and in salinity of part thousand for salinity greater than 5 parts per thousand were attained after correcting for the influence of extraterrestrial background radiation, atmospheric radiation and attenuation, sea-surface roughness, and antenna beamwidth. The radiometers, operating at 1.43 and 2.65 GHz, comprise a third-generation system using null balancing and feedback noise injection. Flight measurements from an aircraft at an altitude of 1.4 km over the lower Chesapeake Bay and coastal areas of the Atlantic Ocean resulted in contour maps of sea-surface temperature and salinity with a spatial resolution of 0.5 km.

Hans-Juergen, C. B.↗

Deep Impact: 19 gigajoules can make quite an impression

Deep Impact will impact the comet Tempel-1 on July 4, 2005. The impact event will be clearly visible from small telescopes on Earth, especially in the IR bands. When combined with observations taken from the Flyby spacecraft, this science data set will provide unique insight into the materials and structure within the comet, and the strength of the surface.

deep impact autonav autonomous navigation↗

Standing waves along a microwave generated surface wave plasma

Two surface wave plasma columns, generated by microwave power in argon at gas pressures of 0.05 torr to 330 torr, interact in the same discharge tube to form standing surface waves. Radial electric field and azimuthal magnetic field outside the discharge tube are measured to be 90 deg out of phase with respect to axial position and to decay exponentially with radial distance from the tube axis. Maximum light emission occurs at the position of maximum azimuthal magnetic field and minimum radial electric field. Electron temperature and density are measured at low pressures with double probes inserted into the plasma at a null of radial electric field. Measured electron densities compare well with those predicted by Gould-Trivelpiece surface wave theory.

Rogers, J.↗

White-Light Nulling Interferometers for Detecting Planets

A report proposes the development of a white-light nulling interferometer to be used in conjunction with a singleaperture astronomical telescope that would be operated in outer space. When such a telescope is aimed at a given star, the interferometer would suppress the light of that star while passing enough light from planets (if any) orbiting the star, to enable imaging or spectroscopic examination of the planets. In a nulling interferometer, according to the proposal, scattered light would be suppressed by spatial filtering in an array of single-mode optical fibers rather than by requiring optical surfaces to be accurate within 1/4,000 wavelength as in a coronagraph or an apodized telescope. As a result, angstrom-level precision would be needed in only the small nulling combiner, and not in large, meter-sized optics. The nulling interferometer could work as an independent instrument in space or in conjunction with a coronagraphic system to detect planets outside our solar system.

Mennesson, Bertrand↗

Measurement of ocean temperature and salinity via microwave radiometry

Sea-surface temperature with an accuracy of 1 C and salinity with an accuracy of 1% were measured with a 1.43 and 2.65 GHz radiometer system after correcting for the influence of cosmic radiation, intervening atmosphere, sea-surface roughness, and antenna beamwidth. The radiometers are a third-generation system using null-balancing and feedback noise injection. Flight measurements from aircraft over bay regions and coastal areas of the Atlantic resulted in contour maps with spatial resolution of 0.5 km.

Blume, H.-J. C.↗

Efficient Implementation of the Invariant Imbedding T-Matrix Method and the Separation of Variables Method Applied to Large Nonspherical Inhomogeneous Particles

Three terms, ''Waterman's T-matrix method'', ''extended boundary condition method (EBCM)'', and ''null field method'', have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIMþSOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIMþSOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIMþSOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIMþSOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging.

Invariant imbedding method↗