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Scattering and the Point Spread Function of the New Generation Space Telescope

Preliminary design work on the New Generation Space Telescope (NGST) is currently under way. This telescope is envisioned as a lightweight, deployable Cassegrain reflector with an aperture of 8 meters, and an effective focal length of 80 meters. It is to be folded into a small-diameter package for launch by an Atlas booster, and unfolded in orbit. The primary is to consist of an octagon with a hole at the center, and with eight segments arranged in a flower petal configuration about the octagon. The comers of the petal-shaped segments are to be trimmed so that the package will fit atop the Atlas booster. This mirror, along with its secondary will focus the light from a point source into an image which is spread from a point by diffraction effects, figure errors, and scattering of light from the surface. The distribution of light in the image of a point source is called a point spread function (PSF). The obstruction of the incident light by the secondary mirror and its support structure, the trimmed corners of the petals, and the grooves between the segments all cause the diffraction pattern characterizing an ideal point spread function to be changed, with the trimmed comers causing the rings of the Airy pattern to become broken up, and the linear grooves causing diffraction spikes running radially away from the central spot, or Airy disk. Any figure errors the mirror segments may have, or any errors in aligning the petals with the central octagon will also spread the light out from the ideal point spread function. A point spread function for a mirror the size of the NGST and having an incident wavelength of 900 nm is considered. Most of the light is confined in a circle with a diameter of 0.05 arc seconds. The ring pattern ranges in intensity from 10(exp -2) near the center to 10(exp -6) near the edge of the plotted field, and can be clearly discerned in a log plot of the intensity. The total fraction of the light scattered from this point spread function is called the total integrated scattering (TIS), and the fraction remaining is called the Strehl ratio. The angular distribution of the scattered light is called the angle resolved scattering (ARS), and it shows a strong spike centered on a scattering angle of zero, and a broad , less intense distribution at larger angles. It is this scattered light, and its effect on the point spread function which is the focus of this study.

Schreur, Julian J.

Track-Level-Compensation Look-Up Table Improves Antenna Pointing Precision

This article presents the improvement of the beam-waveguide antenna pointing accuracy due to the implementation of the track-level-compensation look-up table. It presents the development of the table, from the measurements of the inclinometer tilts to the processing of the measurement data and the determination of the threeaxis alidade rotations. The table consists of three axis rotations of the alidade as a function of the azimuth position. The article also presents the equations to determine the elevation and cross-elevation errors of the antenna as a function of the alidade rotations and the antenna azimuth and elevation positions. The table performance was verified using radio beam pointing data. The pointing error decreased from 4.5 mdeg to 1.4 mdeg in elevation and from 14.5 mdeg to 3.1 mdeg in cross-elevation. I. Introduction The Deep Space Station 25 (DSS 25) antenna shown in Fig. 1 is one of NASA s Deep Space Network beam-waveguide (BWG) antennas. At 34 GHz (Ka-band) operation, it is necessary to be able to track with a pointing accuracy of 2-mdeg root-mean-square (rms). Repeatable pointing errors of several millidegrees of magnitude have been observed during the BWG antenna calibration measurements. The systematic errors of order 4 and lower are eliminated using the antenna pointing model. However, repeatable pointing errors of higher order are out of reach of the model. The most prominent high-order systematic errors are the ones caused by the uneven azimuth track. The track is shown in Fig. 2. Manufacturing and installation tolerances, as well as gaps between the segments of the track, are the sources of the pointing errors that reach over 14-mdeg peak-to-peak magnitude, as reported in [1,2]. This article presents a continuation of the investigations and measurements of the pointing errors caused by the azimuth-track-level unevenness that were presented in [1] and [2], and it presents the implementation results. Track-level-compensation (TLC) look-up tables were created for the DSS 25, DSS 26, DSS 34, and DSS 55 antennas. To date, the most complete and detailed results were obtained for the DSS 25 and DSS 55 antennas. In this article, for brevity of presentation, we present the DSS 25 antenna results only. 1 Communications Ground Systems Section. The research described in this publication was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

Gawronski, W.

Instrument Pointing Capabilities: Past, Present, and Future

This paper surveys the instrument pointing capabilities of past, present and future space telescopes and interferometers. As an important aspect of this survey, we present a taxonomy for "apples-to-apples" comparisons of pointing performances. First, pointing errors are defined relative to either an inertial frame or a celestial target. Pointing error can then be further sub-divided into DC, that is, steady state, and AC components. We refer to the magnitude of the DC error relative to the inertial frame as absolute pointing accuracy, and we refer to the magnitude of the DC error relative to a celestial target as relative pointing accuracy. The magnitude of the AC error is referred to as pointing stability. While an AC/DC partition is not new, we leverage previous work by some of the authors to quantitatively clarify and compare varying definitions of jitter and time window averages. With this taxonomy and for sixteen past, present, and future missions, pointing accuracies and stabilities, both required and achieved, are presented. In addition, we describe the attitude control technologies used to and, for future missions, planned to achieve these pointing performances.

celestial targets

Fine pointing of Laser Beams by using Laser Arrays for Applications to CubeSats

A method of fine pointing of laser beams by using laser arrays has been developed. The telescope system combines a lens system and a VCSEL/Photodetector Array. It does not use moving parts. In computer simulations, it is applied to CubeSats that use body pointing. Body pointing was used by the Aerospace Corporation for CubeSats in LEO in NASA’s Optical Communications and Sensors Demonstration (OCSD) program. Computer simulations of this fine pointing capability have been applied previously to CubeSats in the OCSD program. In this paper, computer simulations of laser pointing using this telescope design are applied to CubeSats in LLO, at 100 km. These CubeSats could form part of the LunaNet, the lunar communications and navigation network, part of the NASA ARTEMIS Program. With more accurate pointing, a laser beam with smaller divergence can be used. For the case of the AeroCube-7B vehicle that was used in the OCSD program, computer simulations will show, for example, that the divergence of the output beam can be reduced from approximately 0.06° FWHM to 0.014°. For the proposed electro-optical system, reaction times to pointing changes and vibrations are on a nanosecond time scale, much faster than those for fine pointing systems that use moving parts such as fast steering mirrors, including MEMS, or that use quad-cell photodetectors to improve the body pointing of the CubeSat. Other possible applications are to Optical Multiple Access (OMA)for simultaneously communicating with ground stations at different locations and to Wavelength-Division Multiplexing (WDM)for increasing data rate transmission.

SMD

Fine Pointing of Laser Beams by Using Laser Arrays for Applications to CubeSats

A method of fine pointing of laser beams by using laser arrays has been developed. The telescope system combines a lens system and a VCSEL/Photodetector Array. It does not use moving parts. In computer simulations, it is applied to CubeSats that use body pointing. Body pointing was used by the Aerospace Corporation for CubeSats in LEO in NASA’s Optical Communications and Sensors Demonstration (OCSD) program. Computer simulations of this fine pointing capability have been applied previously to CubeSats in the OCSD program. In this paper, computer simulations of laser pointing using this telescope design are applied to CubeSats in LLO, at 100 km. These CubeSats could form part of the LunaNet, the lunar communications and navigation network, part of the NASA ARTEMIS Program. With more accurate pointing, a laser beam with smaller divergence can be used. For the case of the AeroCube-7B vehicle that was used in the OCSD program, computer simulations will show, for example, that the divergence of the output beam can be reduced from approximately 0.06° FWHM to 0.014°. For the proposed electro-optical system, reaction times to pointing changes and vibrations are on a nanosecond time scale, much faster than those for fine pointing systems that use moving parts such as fast steering mirrors, including MEMS, or that use quad-cell photodetectors to improve the body pointing of the CubeSat. Other possible applications are to Optical Multiple Access (OMA)for simultaneously communicating with ground stations at different locations and to Wavelength-Division Multiplexing (WDM)for increasing data rate transmission.

HEC

The Baker-Coon-Romans N -point amplitude and an exact field theory limit of the Coon amplitude

We study the N-point Coon amplitude discovered first by Baker and Coon in the 1970s and then again independently by Romans in the 1980s. This Baker-Coon-Romans (BCR) amplitude retains several properties of tree-level string amplitudes, namely duality and factorization, with a q-deformed version of the string spectrum. Although the formula for the N-point BCR amplitude is only valid for q > 1, the four-point case admits a straightforward extension to all q ≥ 0 which reproduces the usual expression for the four-point Coon amplitude. At five points, there are inconsistencies with factorization when pushing q < 1. Despite these issues, we find a new relation between the five-point BCR amplitude and Cheung and Remmen’s four-point basic hypergeometric amplitude, placing the latter within the broader family of Coon amplitudes. Finally, we compute the q → ∞ limit of the N-point BCR amplitudes and discover an exact correspondence between these amplitudes and the field theory amplitudes of a scalar transforming in the adjoint representation of a global symmetry group with an infinite set of non-derivative single-trace interaction terms. This correspondence at q = ∞ is the first definitive realization of the Coon amplitude (in any limit) from a field theory described by an explicit Lagrangian.

1/N Expansion

Splitting regions and shrinking islands from higher point constraints

We study constraints from higher-point amplitudes on 2 → 2 scattering in the context of effective field theory (EFT) using the perturbative numerical S-matrix bootstrap. Specifically, we investigate the class of weakly coupled EFTs with amplitudes that obey the hidden zero and split conditions that are known to hold both for Tr(Φ 3 ) theory and for certain string tree amplitudes, including at 4-point the beta function. Requiring the splitting condition for the 5-point amplitude not only fixes nearly all its contact terms, but it also imposes non-linear constraints among the 4-point EFT Wilson coefficients. When included in the bootstrap, the resulting allowed region consistent with positivity is no longer convex but is restricted to a smaller non-convex region — which has a sharp corner near the string beta function! Assuming the absence of an infinite spin tower at the mass gap, the allowed region bifurcates into a trivial region (with states only above a chosen cutoff) and an island that continues to shrink around the string as more constraints are included in the bootstrap. The numerics indicate that in the absence of single-mass infinite spin towers the string beta function is the unique 4-point amplitude compatible with hidden zero and the 5-point splitting constraints. The analysis provides a prototype example for how features of higher-point amplitudes constrain the bootstrap of 4-point amplitudes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

X-point effects on the ideal MHD modes in tokamaks in the description of dual-poloidal-region safety factor

The flux coordinates with dual-region safety factor (q) in the poloidal direction are developed in this work. The X-point effects on the ideal MHD modes in tokamaks are then analyzed using this coordinate system. Since the X-point effects mainly affect the edge region, the modes localized at the tokamak edge are particularly examined. Two types of modes are studied. The first is related to the conventional peeling or peeling-ballooning modes. The mode existence aligned with the local magnetic field in the poloidally core region as observed experimentally is confirmed. The X points are shown to contribute to a stabilizing effect for the conventionally treated modes with the surface-averaged q and with the tokamak edge portion truncated. The other is the axisymmetric modes localized in the vicinity of X points, which can affect the cross-field-line transport near the X points. The existence of axisymmetric modes points to the possibility of applying a toroidally axisymmetric resonant magnetic perturbation (RMP) in the X-point area for mitigating the edge localized modes, which can be an alternative to the current RMP design. The dual q description also has important implications for the existing non-axisymmetric RMP concept. It helps to understand why the RMP suppression of edge localized modes is difficult to achieve in the double-null tokamak configurations and points to the possibility of further improving the current RMP concept by considering the alignment to the local q.

Fourier analysis

Inverse Segmented Motor Drive Using Dual ANPC Inverters for Common-Mode Voltage and Neutral-Point Current Cancellation

This article proposes an inverse segmented motor drive (SgMD) utilizing dual active neutral point clamped (ANPC) inverters. In the proposed configuration, the neutral point current and common-mode (CM) voltage is topologically canceled, achieving zero total neutral point current and CM voltage under ideal conditions. Also, the zero total neutral point current minimizes the neutral point voltage imbalance in ANPC inverters. The mechanisms behind neutral point current and CM voltage cancellation in the proposed inverse SgMD are first introduced. The modifications to the motor windings for implementing the inverse SgMD are explained, showing that a standard motor can be readily adapted for the proposed configuration. A space vector modulation (SVM) scheme tailored for the proposed topology is presented, along with a carrier-based implementation. Simulation results validate that the proposed topology can achieve zero total CM voltage and neutral point current. It is also shown that the proposed inverse SgMD can reduce neutral point voltage fluctuation by about 90% and RMS current stress in the dc-link capacitors by about 43% compared to the conventional SgMD.

Lee, Sangwhee [ORNL] (ORCID:0000000335490057)

Uncertainty Visualization of Critical Points of 2D Scalar Fields for Parametric and Nonparametric Probabilistic Models

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. Here, in this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

97 MATHEMATICS AND COMPUTING

Crew optimized Shuttle/experiment pointing

The extensive participation of the Shuttle crewmembers (Commander, Pilot, Mission Specialist, and Payload Specialist) in Shuttle/experiment pointing is required to accomplish and enhance payload pointing operations and to optimize associated data collection. For payloads requiring extensive pointing operations, the degree of mission success which can be achieved by the involvement of the crew can not be matched by a combination of remote ground operations and automation. The importance of the use of the crew's manipulative skills, scientific judgment, and flexibility in the alteration of preplanned time lines was clearly demonstrated during the Skylab Apollo Telescope Mount solar experiment operations. The payload pointing operations associated with the Spacelab Instrument Pointing System and the Annular Suspension and Pointing System Gimbal System will also extensively use these crew capabilities. Crew operations will also play a potentially important role in the use of advanced pointing systems to accurately point experiments which have an extensive interaction with the surrounding environment, such as laser experiments.

Holt, A. C.

Shuttle infrared telescope facility pointing and control system

The Shuttle Infrared Telescope Facility (SIRTF) is being designed as a 0.85 m cryogenically cooled telescope capable of a three order of magnitude improvement over currently available infrared instruments. The SIRTF requires that the image at the focal plane be stabilized to better than 0.25 arcsec with an absolute accuracy of 1.0 arcsec. Current pointing-mount performance simulations indicate that neither of these requirements can be met without additional stabilization. The SIRTF pointing and control system will utilize gyro outputs, star field position measurements from a focal plane fine guidance sensor, and a steerable secondary mirror to provide the necessary stabilization and pointing control. The charge coupled device fine guidance sensor tracks multiple stars simultaneously and, through the use of multistar processing algorithms in a high performance microcomputer, generates three-axis attitude errors and gyro-drift estimates to correct the pointing-mount gyros. A high-bandwidth feedforward loop, driven directly from the pointing-mount gyro package, controls the steering mirror in order to correct disturbances not compensated for by the pointing-mount control system. A prototype design for the SIRTF pointing and control system is described in detail. Performance analyses made using a digital simulation of the pointing and control system as well as experimental data obtained in laboratory and field test measurements are presented.

Lorell, K. R.

Configuration trade-offs for the Space Infrared Telescope Facility pointing control system

Conceptual pointing control system designs for the Space Infrared Telescope Facility (SIRTF) are examined in terms of fine guidance pointing and large-angle slewing accuracies. In particular, basic trade-offs between body pointing only and body pointing plus image motion compensation (IMC) are considered using a steady-state linear covariance analysis to compute rms pointing errors. It is shown that body pointing can provide good performance during nominal fine pointing but limits the telescope capability to rapidly slew and acquire targets. Overall, body pointing plus IMC would offer superior performance but must be judged against the difficulties posed by the attitude sensor noise and the higher cost and complexity of IMC. It is recommended that improved sensor designs be pursued while slewing performance be enhanced by a combination of an appropriate command profile and control compensation.

Pue, A. J.

Fine pointing of the Solar Optical Telescope in the Space Shuttle environment

Instruments requiring fine (i.e., sub-arcsecond) pointing, such as the Solar Optical Telescope (SOT), must be equipped with two-stage pointing devices, coarse and fine. Coarse pointing will be performed by a gimbal system, such as the Instrument Pointing System, while the image motion compensation (IMC) will provide fine pointing. This paper describes work performed on the SOT concept design that illustrates IMC as applied to SOT. The SOT control system was modeled in the frequency domain to evaluate performance, stability, and bandwidth requirements. The two requirements of the pointing control, i.e., the 2 arcsecond reproducibility and 0.03 arcsecond rms pointing jitter, can be satisfied by use of IMC at about 20 Hz bandwidth. The need for this high bandwidth is related to Shuttle-induced disturbances that arise primarily from man push-offs and vernier thruster firings. A block diagram of SOT model/stability analysis, schematic illustrations of the SOT pointing system, and a structural model summary are included.

Gowrinathan, S.

Three-dimensional singular points in aerodynamics

When three-dimensional separation occurs on a body immersed in a flow governed by the incompressible Navier-Stokes equations, the geometrical surfaces formed by the three vector fields (velocity, vorticity and the skin-friction) and a scalar field (pressure) become interrelated through topological maps containing their respective singular points and extremal points. A mathematically consistent description of these singular points becomes inevitable when we want to study the geometry of the separation. A separated stream surface requires, for example, the existence of a saddle-type singular point on the skin-friction surface. This singular point is actually, in the proper language of mathematics, a saddle of index two. The index is a measure of the dimension of the outset (set leaving the singular point). Hence, when a saddle of index two is specified, a two dimensional surface that becomes separated from the osculating plane of the saddle is implied. The three-dimensional singular point is interpreted mathematically and the most common aerodynamical singular points are discussed through this perspective.

Unal, Aynur

Equal path, phase shifting, sample point interferometer for monitoring the configuration of surfaces

A system for monitoring the configuration of a surface (e.g., a segmented parabolic surface) using orthogonally placed retroreflectors at sets of points 1, 2, and 3 dispersed throughout the surface with a stationary halfwave plate (HWP) in the front of the one retroreflector at a corner point 3 and a rotating halfwave plate (RHWP) over a source of linearly polarized coherent light, thereby causing the direction of linear polarization to continuously rotate through 360 deg and causing light returned by the retroreflector at point 3 to be continuously phase shifted through 360 deg relative to light returned by retroreflectors at points 1 and 2. The returned light from each set of points 1, 2, and 3 is focused onto a bed-of-nails (BON) phase grating diagonally oriented with respect to the orthogonal orientation of the incident beams from retroreflectors 1, 2, and 3, thereby causing overlap in the light from points 1 and 3 to produce interferometric signals 1,3 and 2,3. Any change in phase of the interferometric signals 1,3 and 2,3 indicates both the magnitude and direction of any change in the position of the retroreflector at point 3 relative to retroreflectors at points 1 and 2.

Manhart, Paul K.

A magnetic isolation and pointing system for the astrometric telescope facility

The astrometric telescope facility (ATF), a 20-meter telescope designed for long-term detection and observation of planetary systems outside of the solar system, is scheduled to be a major user of the Space Station's payload pointing system (PPS) capabilities. However, because the ATF has such a stringent pointing stability specification (as low as 0.01 arcsec error over the frequency range from 5 to 200 hertz) and requires +/- 180-degree roll rotation around the telescope's line of sight, the ATF's utilization of the PPS requires the addition of a mechanism or mechanisms to enhance the basic PPS capabilities. The results of a study conducted to investigate the ATF pointing performance achievable by the addition of a magnetic isolation and pointing (MIPS) system between the PPS upper gimbal and the ATF, and separately, by the addition of a passive isolation system between the Space Station and the PPS base are presented. In addition, the study produced requirements on magnetic force and gap motion as a function of the level of Space Station disturbance. These results were used to support the definition of a candidate MIPS. Pointing performance results from the study indicate that a MIPS can meet the ATF pointing requirements in the presence of a PPS base transitional acceleration of up to 0.018g, with reasonable restrictions placed on the isolation and pointing bandwidths. By contrast, the passive base isolator system must have an unrealistically low isolation bandwidth on all axes (less than 0.1 hertz) to meet ATF pointing requirements. The candidate MIPS is based on an assumed base translational disturbance of 0.01g. The system fits within the available annular region between the PPS and ATF while meeting power and weight limitations and providing the required payload roll motion. Payload data and power services are provided by noncontacting transfer devices.

Smith, Marcie

Report on 3 and 4-point correlation statistics in the COBE DMR anisotrophy maps

As part of the work performed under NASA contract # NAS5-32648, we have computed the 3-point and 4-point correlation functions of the COBE-DNIR 2-year and 4-year anisotropy maps. The motivation for this study was to search for evidence of non-Gaussian statistical fluctuations in the temperature maps: skewness or asymmetry in the case of the 3-point function, kurtosis in the case of the 4-point function. Such behavior would have very significant implications for our understanding of the processes of galaxy formation, because our current models of galaxy formation predict that non-Gaussian features should not be present in the DMR maps. The results of our work showed that the 3-point correlation function is consistent with zero and that the 4-point function is not a very sensitive probe of non-Gaussian behavior in the COBE-DMR data. Our computation and analysis of 3-point correlations in the 2-year DMR maps was published in the Astrophysical Journal Letters, volume 446, page L67, 1995. Our computation and analysis of 3-point correlations in the 4-year DMR maps will be published, together with some additional tests, in the June 10, 1996 issue of the Astrophysical Journal Letters. Copies of both of these papers are attached as an appendix to this report.

Hinshaw, Gary