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All sourcesNASA NTRSDOE OSTI
NASA NTRS2006

Effects of diffraction and static wavefront errors on high-contrast imaging from the Thirty Meter Telescope

High-contrast imaging, particularly direct detection of extrasolar planets, is a major science driver for the next generation of extremely large telescopes such as the segmented Thirty Meter Telescope. This goal requires more than merely diffraction-limited imaging, but also attention to residual scattered light from wavefront errors and diffraction effects at the contrast level of 10-8-10-9. Using a wave-optics simulation of adaptive optics and a diffraction suppression system we investigate diffraction from the segmentation geometry, intersegment gaps, obscuration by the secondary mirror and its supports. We find that the large obscurations pose a greater challenge than the much smaller segment gaps. In addition the impact of wavefront errors from the primary mirror, including segment alignment and figure errors, are analyzed. Segment-to-segment reflectivity variations and residual segment figure error will be the dominant error contributors from the primary mirror. Strategies to mitigate these errors are discussed.

segmented mirrors↗
NASA NTRS1975

Fixed-range optimum trajectories for short-haul aircraft

An algorithm, based on the energy-state method, is derived for calculating optimum trajectories with a range constraint. The basis of the algorithm is the assumption that optimum trajectories consist of, at most, three segments: an increasing energy segment (climb); a constant energy segment (cruise); and a decreasing energy segment (descent). This assumption allows energy to be used as the independent variable in the increasing and decreasing energy segments, thereby eliminating the integration of a separate adjoint differential equation and simplifying the calculus of variations problem to one requiring only pointwise extremization of algebraic functions. The algorithm is used to compute minimum fuel, minimum time, and minimum direct-operating-cost trajectories, with range as a parameter, for an in-service CTOL aircraft and for an advanced STOL aircraft. For the CTOL aircraft and the minimum-fuel performance function, the optimum controls, consisting of air-speed and engine power setting, are continuous functions of the energy in both climb and descent as well as near the maximum or cruise energy. This is also true for the STOL aircraft except in the descent where at one energy level a nearly constant energy dive segment occurs, yielding a discontinuity in the airspeed at that energy. The reason for this segment appears to be the relatively high fuel flow at idle power of the engines used by this STOL aircraft. Use of a simplified trajectory which eliminates the dive increases the fuel consumption of the total descent trajectory by about 10 percent and the time to fly the descent by about 19 percent compared to the optimum.

Erzberger, H.↗
NASA NTRS1982

Missing observations in multiyear rotation sampling designs

Because Multiyear estimation of at-harvest stratum crop proportions is more efficient than single year estimation, the behavior of multiyear estimators in the presence of missing acquisitions was studied. Only the (worst) case when a segment proportion cannot be estimated for the entire year is considered. The effect of these missing segments on the variance of the at-harvest stratum crop proportion estimator is considered when missing segments are not replaced, and when missing segments are replaced by segments not sampled in previous years. The principle recommendations are to replace missing segments according to some specified strategy, and to use a sequential procedure for selecting a sampling design; i.e., choose an optimal two year design and then, based on the observed two year design after segment losses have been taken into account, choose the best possible three year design having the observed two year parent design.

Gbur, E. E.↗
NASA NTRS1988

Assembly Test Article (ATA)

The assembly test article (ATA) consisted of two live loaded redesigned solid rocket motor (RSRM) segments which were assembled and disassembled to simulate the actual flight segment stacking process. The test assembly joint was flight RSRM design, which included the J-joint insulation design and metal capture feature. The ATA test was performed mid-November through 24 December 1987, at Kennedy Space Center (KSC), Florida. The purpose of the test was: certification that vertical RSRM segment mating and separation could be accomplished without any damage; verification and modification of the procedures in the segment stacking/destacking documents; and certification of various GSE to be used for flight assembly and inspection. The RSRM vertical segment assembly/disassembly is possible without any damage to the insulation, metal parts, or seals. The insulation J-joint contact area was very close to the predicted values. Numerous deviations and changes to the planning documents were made to ensure the flight segments are effectively and correctly stacked. Various GSE were also certified for use on flight segments, and are discussed in detail.

Ricks, Glen A.↗
NASA NTRS1989

Airplane takeoff and landing performance monitoring system

The invention is a real-time takeoff and landing performance monitoring system which provides the pilot with graphic and metric information to assist in decisions related to achieving rotation speed (V sub R) within the safe zone of the runway or stopping the aircraft on the runway after landing or take off abort. The system processes information in two segments: a pretakeoff segment and a real-time segment. One-time inputs of ambient conditions and airplane configuration information are used in the pretakeoff segment to generate scheduled performance data. The real-time segment uses the scheduled performance data, runway length data and transducer measured parameters to monitor the performance of the airplane throughout the takeoff roll. An important feature of this segment is that it updates the estimated runway rolling friction coefficient. Airplane performance predictions also reflect changes in headwind occurring as the takeoff roll progresses. The system displays the position of the airplane on the runway, indicating runway used and runway available, summarizes the critical information into a situation advisory flag, flags engine failures and off-nominal acceleration performance, and indicates where on the runway particular events such as decision speed (V sub 1), rotation speed (V sub R) and expected stop points will occur based on actual or predicted performance. The display also indicates airspeed, wind vector, engine pressure ratios, second segment climb speed, and balanced field length (BFL). The system detects performance deficiencies by comparing the airplane's present performance with a predicted nominal performance based upon the given conditions.

Middleton, David B.↗
NASA NTRS1989

Optimal trajectories for the aeroassisted flight experiment. Part 4: Data, tables, and graphs

The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. Data, tables, and graphs relative to the following transfers are presented: (IA) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (DA) direct ascent to a 178 NM apogee. For both transfers, two cases are investigated: (1) the bank angle is continuously variable; and (2) the trajectory is divided into segments along which the bank angle is constant. For case (2), the following subcases are studied: two segments, three segments, four segments, and five segments; because the time duration of each segment is optimized, the above subcases involve four, six, eight, and ten parameters, respectively. Presented here are systematic data on a total of ten optimal trajectories (OT), five for Transfer IA and five for Transfer DA. For comparison purposes and only for Transfer IA, a five-segment reference trajectory RT is also considered.

Miele, A.↗
NASA NTRS1997

Tracking hurricane paths

The South East coastal region experiences hurricane threat for almost six months in every year. To improve the accuracy of hurricane forecasts, meteorologists would need the storm paths of both the present and the past. A hurricane path can be established if we could identify the correct position of the storm at different times right from its birth to the end. We propose a method based on both spatial and temporal image correlations to locate the position of a storm from satellite images. During the hurricane season, the satellite images of the Atlantic ocean near the equator are examined for the hurricane presence. This is accomplished in two steps. In the first step, only segments with more than a particular value of cloud cover are selected for analysis. Next, we apply image processing algorithms to test the presence of a hurricane eye in the segment. If the eye is found, the coordinate of the eye is recorded along with the time stamp of the segment. If the eye is not found, we examine adjacent segments for the existence of hurricane eye. It is probable that more than one hurricane eye could be found from different segments of the same period. Hence, the above process is repeated till the entire potential area for hurricane birth is exhausted. The subsequent/previous position of each hurricane eye will be searched in the appropriate adjacent segments of the next/previous period to mark the hurricane path. The temporal coherence and spatial coherence of the images are taken into account by our scheme in determining the segments and the associated periods required for analysis.

Prabhakaran, Nagarajan↗
NASA NTRS2001

Analysis and Verification of HET 1 m Mirror Deflections Due to Edge Sensor Loading

The ninety-one 1 m mirror segments which comprise the McDonald Observatory Hobby Eberly Telescope (HET) primary mirror have been observed to drift out of alignment in an unpredictable manner in response to time variant temperature deviations. A Segment Alignment Maintenance System (SAMS) is being developed to detect and correct this segment-to-segment drift using sensors mounted at the edges of the mirror segments. However, the segments were not originally designed to carry the weight of edge sensors. Thus, analyses and tests were conducted as part of the SAMS design to estimate the magnitude and shape of the edge sensor induced deformations as well as the resultant optical performance. Interferometric testing of a 26 m radius of curvature HET mirror segment was performed at the Marshall Space Flight Center using several load conditions to verify the finite element analyses.

Stallcup, Michael A.↗
NASA NTRS2001

Internal Flow Simulation of Enhanced Performance Solid Rocket Booster for the Space Transportation System

An enhanced performance solid rocket booster concept for the space shuttle system has been proposed. The concept booster will have strong commonality with the existing, proven, reliable four-segment Space Shuttle Reusable Solid Rocket Motors (RSRM) with individual component design (nozzle, insulator, etc.) optimized for a five-segment configuration. Increased performance is desirable to further enhance safety/reliability and/or increase payload capability. Performance increase will be achieved by adding a fifth propellant segment to the current four-segment booster and opening the throat to accommodate the increased mass flow while maintaining current pressure levels. One development concept under consideration is the static test of a "standard" RSRM with a fifth propellant segment inserted and appropriate minimum motor modifications. Feasibility studies are being conducted to assess the potential for any significant departure in component performance/loading from the well-characterized RSRM. An area of concern is the aft motor (submerged nozzle inlet, aft dome, etc.) where the altered internal flow resulting from the performance enhancing features (25% increase in mass flow rate, higher Mach numbers, modified subsonic nozzle contour) may result in increased component erosion and char. To assess this issue and to define the minimum design changes required to successfully static test a fifth segment RSRM engineering test motor, internal flow studies have been initiated. Internal aero-thermal environments were quantified in terms of conventional convective heating and discrete phase alumina particle impact/concentration and accretion calculations via Computational Fluid Dynamics (CFD) simulation. Two sets of comparative CFD simulations of the RSRM and the five-segment (IBM) concept motor were conducted with CFD commercial code FLUENT. The first simulation involved a two-dimensional axi-symmetric model of the full motor, initial grain RSRM. The second set of analyses included three-dimensional models of the RSRM and FSM aft motors with four-degree vectored nozzles.

Ahmad, Rashid A.↗
NASA NTRS1997

Application-Controlled Demand Paging for Out-of-Core Visualization

In the area of scientific visualization, input data sets are often very large. In visualization of Computational Fluid Dynamics (CFD) in particular, input data sets today can surpass 100 Gbytes, and are expected to scale with the ability of supercomputers to generate them. Some visualization tools already partition large data sets into segments, and load appropriate segments as they are needed. However, this does not remove the problem for two reasons: 1) there are data sets for which even the individual segments are too large for the largest graphics workstations, 2) many practitioners do not have access to workstations with the memory capacity required to load even a segment, especially since the state-of-the-art visualization tools tend to be developed by researchers with much more powerful machines. When the size of the data that must be accessed is larger than the size of memory, some form of virtual memory is simply required. This may be by segmentation, paging, or by paged segments. In this paper we demonstrate that complete reliance on operating system virtual memory for out-of-core visualization leads to poor performance. We then describe a paged segment system that we have implemented, and explore the principles of memory management that can be employed by the application for out-of-core visualization. We show that application control over some of these can significantly improve performance. We show that sparse traversal can be exploited by loading only those data actually required. We show also that application control over data loading can be exploited by 1) loading data from alternative storage format (in particular 3-dimensional data stored in sub-cubes), 2) controlling the page size. Both of these techniques effectively reduce the total memory required by visualization at run-time. We also describe experiments we have done on remote out-of-core visualization (when pages are read by demand from remote disk) whose results are promising.

Cox, Michael↗
NASA NTRS2003

Radio Frequency Trap for Containment of Plasmas in Antimatter Propulsion Systems Using Rotating Wall Electric Fields

A containment apparatus for containing a cloud of charged particles comprises a cylindrical vacuum chamber having a longitudinal axis. Within the vacuum chamber is a containment region. A magnetic field is aligned with the longitudinal axis of the vacuum chamber. The magnetic field is time invariant and uniform in strength over the containment region. An electric field is also aligned with the longitudinal axis of the vacuum chamber and the magnetic field. The electric field is time invariant, and forms a potential well over the containment region. One or more means are disposed around the cloud of particles for inducing a rotating electric field internal to the vacuum chamber. The rotating electric field imparts energy to the charged particles within the containment region and compress the cloud of particles. The means disposed around the outer surface of the vacuum chamber for inducing a rotating electric field are four or more segments forming a segmented ring, the segments conforming to the outer surface of the vacuum chamber. Each of the segments is energized by a separate alternating voltage. The sum of the voltages imposed on each segment establishes the rotating field. When four segments form a ring, the rotating field is obtained by a signal generator applying a sinusoidal signal phase delayed by 90,180 and 270 degrees in sequence to the four segments.

Sims, William Herbert, III↗
NASA NTRS2004

High Efficiency Thermoelectric Radioisotope Power Systems

The work performed and whose results presented in this report is a joint effort between the University of New Mexico s Institute for Space and Nuclear Power Studies (ISNPS) and the Jet Propulsion Laboratory (JPL), California Institute of Technology. In addition to the development, design, and fabrication of skutterudites and skutterudites-based segmented unicouples this effort included conducting performance tests of these unicouples for hundreds of hours to verify theoretical predictions of the conversion efficiency. The performance predictions of these unicouples are obtained using 1-D and 3-D models developed for that purpose and for estimating the actual performance and side heat losses in the tests conducted at ISNPS. In addition to the performance tests, the development of the 1-D and 3-D models and the development of Advanced Radioisotope Power systems for Beginning-Of-Life (BOM) power of 108 We are carried out at ISNPS. The materials synthesis and fabrication of the unicouples are carried out at JPL. The research conducted at ISNPS is documented in chapters 2-5 and that conducted at JP, in documented in chapter 5. An important consideration in the design and optimization of segmented thermoelectric unicouples (STUs) is determining the relative lengths, cross-section areas, and the interfacial temperatures of the segments of the different materials in the n- and p-legs. These variables are determined using a genetic algorithm (GA) in conjunction with one-dimensional analytical model of STUs that is developed in chapter 2. Results indicated that when optimized for maximum conversion efficiency, the interfacial temperatures between various segments in a STU are close to those at the intersections of the Figure-Of-Merit (FOM), ZT, curves of the thermoelectric materials of the adjacent segments. When optimizing the STUs for maximum electrical power density, however, the interfacial temperatures are different from those at the intersections of the ZT curves, but close to those at the intersections the characteristic power, CP, curves of the thermoelectric materials of the adjacent segments (CP = T(sup 2)Zk and has a unit of W/m). Results also showed that the number of the segments in the n- and p-legs of the STUs optimized for maximum power density are generally fewer than when the same unicouples are optimized for maximum efficiency. These results are obtained using the 1-D optimization model of STUs that is detailed in chapter 2. A three-dimensional model of STUs is developed and incorporated into the ANSYS commercial software (chapter 3). The governing equations are solved, subject to the prescribed

El-Genk, Mohamed↗
NASA NTRS2006

Precision Linear Actuators for the Spherical Primary Optical Telescope Demonstration Mirror

The Spherical Primary Optical Telescope (SPOT) is an ongoing research effort at Goddard Space Flight Center developing wavefront sensing and control architectures for future space telescopes. The 03.5 m SPOT telescope primary mirror is comprised20f 6, 0.86 m hexagonal mirror segments arranged in a single ring, with the central segment missing . The mirror segments are designed for laboratory use and are not light-weighted to reduce cost. Each primary mirror segment is actuated and has tip, tilt, and piston rigid body motions. Additionally, the radius of curvature of each mirror segment may be varied mechanically3. To provide these degrees of freedom, the SPOT mirror segment assembly requires linear actuators capable of 10 nm resolution over a total stroke of 5 mm. These actuators must withstand high static loads as they must support the mirror segment, which has a mass of approx.100 kg. A stepper motor driving a differential satellite roller screw was designed to meet these demanding requirements. Initial testing showed that the actuator is capable of sub-micron repeatability over the entire 6mm range, and was limited by 100-200 nm measurement noise levels present in the facility. Further testing must be accomplished in an isolated facility with a measurement noise floor of < 5 nm. Such a facility should be ready for use at GSFC in the early summer of 2006, and will be used to better characterize this actuator.

Budinoff, Jason↗
NASA NTRS2006

Precision Linear Actuators for the Spherical Primary Optical Telescope Demonstration Mirror

The Spherical Primary Optical Telescope (SPOT) is an ongoing research effort at Goddard Space Flight Center developing wavefront sensing and control architectures for future space telescopes. The 03.5-m SPOT telescope primary mirror is comprise9 of six 0.86-m hexagonal mirror segments arranged in a single ring, with the central segment missing. The mirror segments are designed for laboratory use and are not lightweighted to reduce cost. Each primary mirror segment is actuated and has tip, tilt, and piston rigid-body motions. Additionally, the radius of curvature of each mirror segment may be varied mechanically. To provide these degrees of freedom, the SPOT mirror segment assembly requires linear actuators capable of <lO-nm resolution over a total stroke of 5 mm. These actuators must withstand high static loads as they must support the mirror segment, which has a mass of -100 kg. A stepper motor driving a differential satellite roller screw was designed to meet these demanding requirements. Initial testing showed that the actuator is capable of sub-micron repeatability over the entire 6-mm range, and was limited by 100-200 nm measurement noise levels present in the facility. Further testing must be accomplished in an isolated facility with a measurement noise floor of <5 nm. Such a facility should be ready for use at GSFC in the early summer of 2006, and will be used to better characterize this actuator.

Budinoff, Jason↗
NASA NTRS2010

Wavefront Control and Image Restoration with Less Computing

PseudoDiversity is a method of recovering the wavefront in a sparse- or segmented- aperture optical system typified by an interferometer or a telescope equipped with an adaptive primary mirror consisting of controllably slightly moveable segments. (PseudoDiversity should not be confused with a radio-antenna-arraying method called pseudodiversity.) As in the cases of other wavefront- recovery methods, the streams of wavefront data generated by means of PseudoDiversity are used as feedback signals for controlling electromechanical actuators of the various segments so as to correct wavefront errors and thereby, for example, obtain a clearer, steadier image of a distant object in the presence of atmospheric turbulence. There are numerous potential applications in astronomy, remote sensing from aircraft and spacecraft, targeting missiles, sighting military targets, and medical imaging (including microscopy) through such intervening media as cells or water. In comparison with prior wavefront-recovery methods used in adaptive optics, PseudoDiversity involves considerably simpler equipment and procedures and less computation. For PseudoDiversity, there is no need to install separate metrological equipment or to use any optomechanical components beyond those that are already parts of the optical system to which the method is applied. In Pseudo- Diversity, the actuators of a subset of the segments or subapertures are driven to make the segments dither in the piston, tilt, and tip degrees of freedom. Each aperture is dithered at a unique frequency at an amplitude of a half wavelength of light. During the dithering, images on the focal plane are detected and digitized at a rate of at least four samples per dither period. In the processing of the image samples, the use of different dither frequencies makes it possible to determine the separate effects of the various dithered segments or apertures. The digitized image-detector outputs are processed in the spatial-frequency (Fourier-transform) domain to obtain measures of the piston, tip, and tilt errors over each segment or subaperture. Once these measures are known, they are fed back to the actuators to correct the errors. In addition, measures of errors that remain after correction by use of the actuators are further utilized in an algorithm in which the image is phase-corrected in the spatial-frequency domain and then transformed back to the spatial domain at each time step and summed with the images from all previous time steps to obtain a final image having a greater signal-to-noise ratio (and, hence, a visual quality) higher than would otherwise be attainable.

Lyon, Richard G.↗
NASA NTRS2004

Hexagonal Pixels and Indexing Scheme for Binary Images

A scheme for resampling binaryimage data from a rectangular grid to a regular hexagonal grid and an associated tree-structured pixel-indexing scheme keyed to the level of resolution have been devised. This scheme could be utilized in conjunction with appropriate image-data-processing algorithms to enable automated retrieval and/or recognition of images. For some purposes, this scheme is superior to a prior scheme that relies on rectangular pixels: one example of such a purpose is recognition of fingerprints, which can be approximated more closely by use of line segments along hexagonal axes than by line segments along rectangular axes. This scheme could also be combined with algorithms for query-image-based retrieval of images via the Internet. A binary image on a rectangular grid is generated by raster scanning or by sampling on a stationary grid of rectangular pixels. In either case, each pixel (each cell in the rectangular grid) is denoted as either bright or dark, depending on whether the light level in the pixel is above or below a prescribed threshold. The binary data on such an image are stored in a matrix form that lends itself readily to searches of line segments aligned with either or both of the perpendicular coordinate axes. The first step in resampling onto a regular hexagonal grid is to make the resolution of the hexagonal grid fine enough to capture all the binaryimage detail from the rectangular grid. In practice, this amounts to choosing a hexagonal-cell width equal to or less than a third of the rectangular- cell width. Once the data have been resampled onto the hexagonal grid, the image can readily be checked for line segments aligned with the hexagonal coordinate axes, which typically lie at angles of 30deg, 90deg, and 150deg with respect to say, the horizontal rectangular coordinate axis. Optionally, one can then rotate the rectangular image by 90deg, then again sample onto the hexagonal grid and check for line segments at angles of 0deg, 60deg, and 120deg to the original horizontal coordinate axis. The net result is that one has checked for line segments at angular intervals of 30deg. For even finer angular resolution, one could, for example, then rotate the rectangular-grid image +/-45deg before sampling to perform checking for line segments at angular intervals of 15deg.

Johnson, Gordon G.↗
NASA NTRS2012

Generating Ground Reference Data for a Global Impervious Surface Survey

We are engaged in a project to produce a 30m impervious cover data set of the entire Earth for the years 2000 and 2010 based on the Landsat Global Land Survey (GLS) data set. The GLS data from Landsat provide an unprecedented opportunity to map global urbanization at this resolution for the first time, with unprecedented detail and accuracy. Moreover, the spatial resolution of Landsat is absolutely essential to accurately resolve urban targets such as buildings, roads and parking lots. Finally, with GLS data available for the 1975, 1990, 2000, and 2005 time periods, and soon for the 2010 period, the land cover/use changes due to urbanization can now be quantified at this spatial scale as well. Our approach works across spatial scales using very high spatial resolution commercial satellite data to both produce and evaluate continental scale products at the 30m spatial resolution of Landsat data. We are developing continental scale training data at 1m or so resolution and aggregating these to 30m for training a regression tree algorithm. Because the quality of the input training data are critical, we have developed an interactive software tool, called HSegLearn, to facilitate the photo-interpretation of high resolution imagery data, such as Quickbird or Ikonos data, into an impervious versus non-impervious map. Previous work has shown that photo-interpretation of high resolution data at 1 meter resolution will generate an accurate 30m resolution ground reference when coarsened to that resolution. Since this process can be very time consuming when using standard clustering classification algorithms, we are looking at image segmentation as a potential avenue to not only improve the training process but also provide a semi-automated approach for generating the ground reference data. HSegLearn takes as its input a hierarchical set of image segmentations produced by the HSeg image segmentation program [1, 2]. HSegLearn lets an analyst specify pixel locations as being either positive or negative examples, and displays a classification of the study area based on these examples. For our study, the positive examples are examples of impervious surfaces and negative examples are examples of non-impervious surfaces. HSegLearn searches the hierarchical segmentation from HSeg for the coarsest level of segmentation at which selected positive example locations do not conflict with negative example locations and labels the image accordingly. The negative example regions are always defined at the finest level of segmentation detail. The resulting classification map can be then further edited at a region object level using the previously developed HSegViewer tool [3]. After providing an overview of the HSeg image segmentation program, we provide a detailed description of the HSegLearn software tool. We then give examples of using HSegLearn to generate ground reference data and conclude with comments on the effectiveness of the HSegLearn tool.

Tilton, James C.↗
NASA NTRS2016

Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

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