Results for “Correctness proofs” — Page 7

NASA NTRS2003

Adaptive Nulling: A New Enabling Technology for Interferometric Exoplanet

Deep, stable nulling of starlight requires careful control of the amplitudes and phases of the beams that are being combined. The detection of earth-like planets using the interferometer architectures currently being considered for the Terrestrial Planet Finder mission require that the E-field amplitudes are balanced at the level of approx. 0.1%, and the phases are controlled at the level of 1 mrad (corresponding to approx.1.5 nm for a wavelength of 10 microns). These conditions must be met simultaneously at all wavelengths across the science band, and for both polarization states, imposing unrealistic tolerances on the symmetry between the optical beamtrains. We introduce the concept of a compensator that is inserted into the beamtrain, which can adaptively correct for the mismatches across the spectrum, enabling deep nulls with realistic, imperfect optics. The design presented uses a deformable mirror to adjust the amplitude and phase of each beam as an arbitrary function of wavelength and polarization. A proof-of-concept experiment will be conducted at visible/near-IR wavelengths, followed by a system operating in the Mid-IR band.

planet detection↗

NASA NTRS2009

Design Aspects of the VLBI2010 System - Progress Report of the IVS VLBI2010 Committee

This report summarizes the progress made in developing the next generation VLBI system, dubbed the VLBI2010 system. The VLBI2010 Committee of the International VLBI Service for Geodesy and Astrometry (IVS) worked on the design aspects of the new system. The report covers Monte Carlo simulations showing the impact of the new operating modes on the final products. A section on system considerations describes the implications for the VLBI2010 system parameters by considering the new modes and system-related issues such as sensitivity, antenna slew rate, delay measurement error. RF1, frequency requirements, antenna deformation, and source structure corrections_ This is followed by a description of all major subsystems and recommendations for the network, station. and antenna. Then aspects of the feed, polarization processing. calibration, digital back end, and correlator subsystems are covered. A section is dedicated to the NASA. proof-of-concept demonstration. Finally, sections tm operational considerations, on risks and fallback options, and on the next steps complete the report.

Petrachenko, Bill↗

NASA NTRS1979

Definition of Mutually Optimum NDI and Proof Test Criteria for 2219 Aluminum Pressure Vessels. Volume 2: Optimization and Fracture Studies

Certain behavioral aspects associated with fracture and crack extension that cannot be studied using other techniques were evaluated with the ultrasonic method. Characterization of collimated beam techniques showed that significant beam width reduction could be accomplished. Techniques for collimation are given. The crack-opening displacement-gage correction-factor study showed that displacement resulting from crack opening and that from plasticity could be readily differentiated. Crack closure studies using both ultrasonic and crack-opening displacement measurements showed an opening and closing behavior associated with load-unload curves. The results of this work were in general agreement with the closure concepts of Elber. Ultrasonic measurements used to study the nature of flaw extension characteristics associated with failure of the ligament between the flaw front and back surface showed that penetration could occur by an abrupt fracturing after subcritical growth or by continuous growth.

Schwartzberg, F. R.↗

NASA NTRS2009

Deriving Safety Cases for the Formal Safety Certification of Automatically Generated Code

We present an approach to systematically derive safety cases for automatically generated code from information collected during a formal, Hoare-style safety certification of the code. This safety case makes explicit the formal and informal reasoning principles, and reveals the top-level assumptions and external dependencies that must be taken into account; however, the evidence still comes from the formal safety proofs. It uses a generic goal-based argument that is instantiated with respect to the certified safety property (i.e., safety claims) and the program. This will be combined with a complementary safety case that argues the safety of the framework itself, in particular the correctness of the Hoare rules with respect to the safety property and the trustworthiness of the certification system and its individual components. Keywords: Automated code generation, Hoare logic, formal code certification, safety case, Goal Structuring Notation.

Basir, Nurlida↗

NASA NTRS2016

Limb-Nadir Matching Using Non-Coincident NO2 Observations: Proof of Concept and the OMI-minus-OSIRIS Prototype Product

A variant of the limb-nadir matching technique for deriving tropospheric NO2 columns is presented in which the stratospheric component of the NO2 slant column density (SCD) measured by the Ozone Monitoring Instrument (OMI) is removed using non-coincident profiles from the Optical Spectrograph and InfraRed Imaging System (OSIRIS). In order to correct their mismatch in local time and the diurnal variation of stratospheric NO2, OSIRIS profiles, which were measured just after sunrise, were mapped to the local time of OMI observations using a photochemical boxmodel. Following the profile time adjustment, OSIRIS NO2 stratospheric vertical column densities (VCDs) were calculated. For profiles that did not reach down to the tropopause, VCDs were adjusted using the photochemical model. Using air mass factors from the OMI Standard Product (SP), a new tropospheric NO2 VCD product - referred to as OMI-minus-OSIRIS (OmO) - was generated through limb-nadir matching. To accomplish this, the OMI total SCDs were scaled using correction factors derived from the next-generation SCDs that improve upon the spectral fitting used for the current operational products. One year, 2008, of OmO was generated for 60 deg S to 60 deg N and a cursory evaluation was performed. The OmO product was found to capture the main features of tropospheric NO2, including a background value of about 0.3 x 10(exp 15) molecules per sq cm over the tropical Pacific and values comparable to the OMI operational products over anthropogenic source areas. While additional study is required, these results suggest that a limb-nadir matching approach is feasible for the removal of stratospheric NO2 measured by a polar orbiter from a nadir-viewing instrument in a geostationary orbit such as Tropospheric Emissions: Monitoring of Pollution (TEMPO) or Sentinel-4.

Photochemical Boxmodel↗

NASA NTRS1986

Review of methodology and technology available for the detection of extrasolar planetary systems

Anyone undertaking an interstellar voyage might wish to be assured of the existence of a safe planetary harbor at the other end! Aside from the obvious interest of the participants in this Symposium, astronomers and astrophysicists are also eager to detect and study other planetary systems in order to better understand the formation of our own Solar System. Scientists involved in the search for extraterrestrial intelligence argue that planets suitable for the evolution of life may abound elsewhere within our own Milky Way Galaxy. On theoretical grounds, they are probably correct, but they lack any observational support. For in spite of decades of claimed astrometric detections of planetary companions and the recent exciting and tantalizing observations from the IRAS satellite and the IR speckle observations of Van Biesbroeck 8 and other cool stars, there is no unambiguous proof for the existence of another planetary system beyond our own. In this paper we review the various methods for detecting extrasolar planets and briefly describe the Earth and space based technology currently available and discuss the near-term plans to implement these different search techniques. In each case an attempt is made to identify the limiting source of systematic error inherent to the methodology and to assess the potential for technological improvements.

Non-NASA Center↗

NASA NTRS2009

A Mathematical Basis for the Safety Analysis of Conflict Prevention Algorithms

In air traffic management systems, a conflict prevention system examines the traffic and provides ranges of guidance maneuvers that avoid conflicts. This guidance takes the form of ranges of track angles, vertical speeds, or ground speeds. These ranges may be assembled into prevention bands: maneuvers that should not be taken. Unlike conflict resolution systems, which presume that the aircraft already has a conflict, conflict prevention systems show conflicts for all maneuvers. Without conflict prevention information, a pilot might perform a maneuver that causes a near-term conflict. Because near-term conflicts can lead to safety concerns, strong verification of correct operation is required. This paper presents a mathematical framework to analyze the correctness of algorithms that produce conflict prevention information. This paper examines multiple mathematical approaches: iterative, vector algebraic, and trigonometric. The correctness theories are structured first to analyze conflict prevention information for all aircraft. Next, these theories are augmented to consider aircraft which will create a conflict within a given lookahead time. Certain key functions for a candidate algorithm, which satisfy this mathematical basis are presented; however, the proof that a full algorithm using these functions completely satisfies the definition of safety is not provided.

Maddalon, Jeffrey M.↗

NASA NTRS2021

Transmission Telescope Optical Dynamic Alignment

The Integrated Radio Optical Communication System (iROC) is designed to transmit data between Mars and Earth by means of radio waves at 32.67 GHz (Ka Band) and laser beam at 1550 nm, both transmitted via a combined teletenna. The iROC terminal will provide ‘beaconless’ operations to allow full function from the outer planets. In order to point without the aid of an uplink beacon, the proof of concept presented here is addressing the need for an accurate determination and control of the relative position of the laser beam with respect to a reference star. The experiment presented simulates a surrogate transmission telescope system in laboratory setting and presents the model used in the correction of the outgoing beam. The results of the model show a nonlinear dependence between the outgoing and the reference beam, indicating the necessity of a minimum of two metrology instruments placed along the optical system for increased pointing precision.

optical communication↗

NASA NTRS2010

The Potential of Small Space Telescopes for Exoplanet Observations

The imaging of faint exoplanets near bright stars requires the development of very high contrast detection techniques, including both precise wavefront control and deep starlight rejection. A system-level proof-of-principle experiment carried out at at the Palomar Observatory has recently demonstrated that exoplanets can be detected very near stars even with a fairly small (1.5 m diameter) telescope aperture, such as someday might be used by a first space-based exoplanet imaging mission. Using fine-scale wavefront correction across this small aperture, together with fine pointing and focus control, pre- and post-detection speckle reduction, and a vector vortex coronagraph, it has been possible to achieve extremely good starlight rejection within a small number of diffractions beams of the stellar position. This performance has recently allowed the imaging of the three HR8799 planets and the HD32297 disk, thus providing a first system-level validation of the steps needed to achieve high-contrast observations at very small angles. These results thus serve to highlight the potential of small space telescopes aiming at high-contrast exoplanet observations. Specifically, a small-angle coronagraph enables the use of smaller telescopes, thus potentially reducing mission cost significantly.

coronagraphy↗

NASA NTRS2014

On Formulations of Discontinuous Galerkin and Related Methods for Conservation Laws

A formulation for the discontinuous Galerkin (DG) method that leads to solutions using the differential form of the equation (as opposed to the standard integral form) is presented. The formulation includes (a) a derivative calculation that involves only data within each cell with no data interaction among cells, and (b) for each cell, corrections to this derivative that deal with the jumps in fluxes at the cell boundaries and allow data across cells to interact. The derivative with no interaction is obtained by a projection, but for nodal-type methods, evaluating this derivative by interpolation at the nodal points is more economical. The corrections are derived using the approximate (Dirac) delta functions. The formulation results in a family of schemes: different approximate delta functions give rise to different methods. It is shown that the current formulation is essentially equivalent to the flux reconstruction (FR) formulation. Due to the use of approximate delta functions, an energy stability proof simpler than that of Vincent, Castonguay, and Jameson (2011) for a family of schemes is derived. Accuracy and stability of resulting schemes are discussed via Fourier analyses. Similar to FR, the current formulation provides a unifying framework for high-order methods by recovering the DG, spectral difference (SD), and spectral volume (SV) schemes. It also yields stable, accurate, and economical methods.

Huynh, H. T.↗

NASA NTRS2012

Failure Analysis of T-38 Aircraft Burst Hydraulic Aileron Return Line

During maintenance troubleshooting for fluctuating hydraulic pressures, a technician found that a right hand aileron return line, on the flight hydraulic side, was ruptured (Fig. 1, 2). This tubing is part of the Hydraulic Flight Control Aileron Return Reducer to Aileron Manifold and is suspected to be original to the T-38 Talon trainer aircraft. Ailerons are small hinged sections on the outboard portion of a wing used to generate rolling motion thereby banking the aircraft. The ailerons work by changing the effective shape of the airfoil of the outer portion of the wing [1]. The drawing, Northrop P/N 3-43033-55 (6/1960), specifies that the line is made from 0.375 inch OD, aluminum 5052-0 tubing with a 0.049 inch wall thickness. WW-T-787 requires the tube shall be seamless and uniform in quality and temper [2]. The test pressure for this line is 3000 psi, and the operational pressure for this line is estimated to be between 45 psi and 1500 psi based on dynamic loading during flight. Examination of the fracture surface found evidence of arrest bands originating on the inner diameter (Fig 3). Ductile dimples are observed on the tube fractures (Fig. 4). The etched cross-section revealed thinning and work-hardening in the burst region (Fig. 5). The wall thickness just outside the work-hardened fracture region measured 0.035". Barlow's Formula: P = 2St/D, where P is burst pressure, S is allowable stress, t is wall thickness and D is the outer diameter of tube. Using the ultimate tensile strength of 28 ksi and a measured wall thickness of 0.035 inches at burst, P = 5.2 ksi (burst pressure). Using the yield of 13 ksi (YS) for aluminum 5052-0, plastic deformation will happen at P = 2.4 ksi suggesting plastic deformation occurred at a proof pressure of 3.0 ksi. Conclusion: The burst resulted from high stress, low-cycle fatigue. Evidence of arrest bands originating on the inner diameter. Fracture is predominately shear dimples, characteristic of high load ductile fractures (Fig 6). Section wall reduction in the burst region. Plastic deformation and thinning of the out-of-specification tube wall likely happened during the initial proof testing years ago. Metallography of tubing away from rupture site confirmed tubing was seamless. Based on the tube microstructure, it is likely that the initial wall thickness was about 30 % thinner than the requirement of 0.049 inches. Fracture initiated on the ID and progressed to the OD (shear lip). The tube is made of the correct material of 5052-0 aluminum as verified using Optical Emission Spectroscopy (Table 2). The tubing hardness tested 77 HV100 (77 HRE). This hardness is slightly above the requirement for 70 HRE maximum for aluminum 5052-0 in AMS 2658C [3].

Martinez, J. E.↗

NASA NTRS1995

Non-standard analysis and embedded software

One model for computing in the future is ubiquitous, embedded computational devices analogous to embedded electrical motors. Many of these computers will control physical objects and processes. Such hidden computerized environments introduce new safety and correctness concerns whose treatment go beyond present Formal Methods. In particular, one has to begin to speak about Real Space software in analogy with Real Time software. By this we mean, computerized systems which have to meet requirements expressed in the real geometry of space. How to translate such requirements into ordinary software specifications and how to carry out proofs is a major challenge. In this talk we propose a research program based on the use of no-standard analysis. Much detail remains to be carried out. The purpose of the talk is to inform the Formal Methods community that Non-Standard Analysis provides a possible avenue to attack which we believe will be fruitful.

Platek, Richard↗

NASA NTRS1994

Advanced End-to-end Simulation for On-board Processing (AESOP)

Developers of data compression algorithms typically use their own software together with commercial packages to implement, evaluate and demonstrate their work. While convenient for an individual developer, this approach makes it difficult to build on or use another's work without intimate knowledge of each component. When several people or groups work on different parts of the same problem, the larger view can be lost. What's needed is a simple piece of software to stand in the gap and link together the efforts of different people, enabling them to build on each other's work, and providing a base for engineers and scientists to evaluate the parts as a cohesive whole and make design decisions. AESOP (Advanced End-to-end Simulation for On-board Processing) attempts to meet this need by providing a graphical interface to a developer-selected set of algorithms, interfacing with compiled code and standalone programs, as well as procedures written in the IDL and PV-Wave command languages. As a proof of concept, AESOP is outfitted with several data compression algorithms integrating previous work on different processors (AT&T DSP32C, TI TMS320C30, SPARC). The user can specify at run-time the processor on which individual parts of the compression should run. Compressed data is then fed through simulated transmission and uncompression to evaluate the effects of compression parameters, noise and error correction algorithms. The following sections describe AESOP in detail. Section 2 describes fundamental goals for usability. Section 3 describes the implementation. Sections 4 through 5 describe how to add new functionality to the system and present the existing data compression algorithms. Sections 6 and 7 discuss portability and future work.

Mazer, Alan S.↗

NASA NTRS2012

Satellite Ocean Biology: Past, Present, Future

Since 1978 when the first satellite ocean color proof-of-concept sensor, the Nimbus-7 Coastal Zone Color Scanner, was launched, much progress has been made in refining the basic measurement concept and expanding the research applications of global satellite time series of biological and optical properties such as chlorophyll-a concentrations. The seminar will review the fundamentals of satellite ocean color measurements (sensor design considerations, on-orbit calibration, atmospheric corrections, and bio-optical algorithms), scientific results from the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) and Moderate resolution Imaging Spectroradiometer (MODIS) missions, and the goals of future NASA missions such as PACE, the Aerosol, Cloud, Ecology (ACE), and Geostationary Coastal and Air Pollution Events (GeoCAPE) missions.

McClain, Charles R.↗

NASA NTRS2015

An Experimental Investigation of the Flow Physics Associated With End Wall Losses and Large Rotor Tip Clearances as Found in the Rear Stages of a High Pressure Compressor

The focus of this work was to characterize the fundamental flow physics and the overall performance effects due to increased rotor tip clearance heights in axial compressors. Data have been collected in the three-stage axial research compressor at Purdue University with a specific focus on analyzing the multistage effects resulting from the tip leakage flow. Three separate rotor tip clearance heights were studied with nominal tip clearance heights of 1.5%, 3.0%, and 4.0% based on a constant annulus height. Overall compressor performance was investigated at four corrected speedlines (100%, 90%, 80%, and 68%) for each of the three tip clearance configurations using total pressure and total temperature rakes distributed throughout the compressor. The results have confirmed results from previous authors showing a decrease of total pressure rise, isentropic efficiency, and stall margin which is approximately linear with increasing tip clearance height. The stall inception mechanisms have also been evaluated at the same corrected speeds for each of the tip clearance configurations. Detailed flow field measurements have been collected at two loading conditions, nominal loading (NL) and high loading (HL), on the 100% corrected speedline for the smallest and largest tip clearance heights (1.5% and 4.0%). Steady detailed radial traverses of total pressure at the exit of each stator row have been supported by flow visualization techniques to identify regions of flow recirculation and separation. Furthermore, detailed radial traverses of time-resolved total pressures at the exit of each rotor row have been measured with a fast-response pressure probe. These data have helped to quantify the size of the leakage flow at the exit of each rotor. Thermal anemometry has also been implemented to evaluate the time-resolved three-dimensional components of velocity throughout the compressor and calculate blockage due to the rotor tip leakage flow throughout the compressor. These measurements have also been used to calculate streamwise vorticity. Time-resolved static pressure measurements have been collected over the rotor tips for all rotors with each of the three tip clearance configurations for up to five loading conditions along the 100% corrected speedline using fast-response piezoresistive pressure sensors. These time-resolved static pressure measurements, as well as the time-resolved total pressures and velocities have helped to reveal a profound influence of the upstream stator vane on the size and shape of the rotor tip leakage flow. Finally, a novel particle image velocimetry (PIV) technique has been developed as a proof-of- concept. In contrast to PIV methods that have been typically been utilized for turbomachinery applications in the past, the method used for this study introduced the laser light through the same access window that was also used to image the flow. This new method addresses potential concerns related to the intrusive laser-introducing techniques that have typically been utilized by other authors in the past. Ultimately, the data collected for this project represent a unique data set which contributes to build a better understanding of the tip leakage flow field and its associated loss mechanisms. These data will facilitate future engine design goals leading to small blade heights in the rear stages of high pressure compressors and aid in the development of new blade designs which are desensitized to the performance penalties attributed to rotor tip leakage flows.

turbomachinery↗

NASA NTRS2015

An Experimental Investigation of the Flow Physics Associated With End Wall Losses and Large Rotor Tip Clearances as Found in the Rear Stages of a High Pressure Compressor

The focus of this work was to characterize the fundamental flow physics and the overall performance effects due to increased rotor tip clearance heights in axial compressors. Data have been collected in the three-stage axial research compressor at Purdue University with a specific focus on analyzing the multistage effects resulting from the tip leakage flow. Three separate rotor tip clearance heights were studied with nominal tip clearance heights of 1.5%, 3.0%, and 4.0% based on a constant annulus height. Overall compressor performance was investigated at four corrected speedlines (100%, 90%, 80%, and 68%) for each of the three tip clearance configurations using total pressure and total temperature rakes distributed throughout the compressor. The results have confirmed results from previous authors showing a decrease of total pressure rise, isentropic efficiency, and stall margin which is approximately linear with increasing tip clearance height. The stall inception mechanisms have also been evaluated at the same corrected speeds for each of the tip clearance configurations. Detailed flow field measurements have been collected at two loading conditions, nominal loading (NL) and high loading (HL), on the 100% corrected speedline for the smallest and largest tip clearance heights (1.5% and 4.0%). Steady detailed radial traverses of total pressure at the exit of each stator row have been supported by flow visualization techniques to identify regions of flow recirculation and separation. Furthermore, detailed radial traverses of time-resolved total pressures at the exit of each rotor row have been measured with a fast-response pressure probe. These data have helped to quantify the size of the leakage flow at the exit of each rotor. Thermal anemometry has also been implemented to evaluate the time-resolved three-dimensional components of velocity throughout the compressor and calculate blockage due to the rotor tip leakage flow throughout the compressor. These measurements have also been used to calculate streamwise vorticity. Time-resolved static pressure measurements have been collected over the rotor tips for all rotors with each of the three tip clearance configurations for up to five loading conditions along the 100% corrected speedline using fast-response piezoresistive pressure sensors. These time-resolved static pressure measurements, as well as the time-resolved total pressures and velocities have helped to reveal a profound influence of the upstream stator vane on the size and shape of the rotor tip leakage flow. Finally, a novel particle image velocimetry (PIV) technique has been developed as a proof-of- concept. In contrast to PIV methods that have been typically been utilized for turbomachinery applications in the past, the method used for this study introduced the laser light through the same access window that was also used to image the flow. This new method addresses potential concerns related to the intrusive laser-introducing techniques that have typically been utilized by other authors in the past. Ultimately, the data collected for this project represent a unique data set which contributes to build a better understanding of the tip leakage flow field and its associated loss mechanisms. These data will facilitate future engine design goals leading to small blade heights in the rear stages of high pressure compressors and aid in the development of new blade designs which are desensitized to the performance penalties attributed to rotor tip leakage flows.

Berdanier, Reid A.↗

NASA NTRS2001

Observations of Ocean Primary Productivity Using MODIS

Measuring the magnitude and variability of oceanic net primary productivity (NPP) represents a key advancement toward our understanding of the dynamics of marine ecosystems and the role of the ocean in the global carbon cycle. MODIS observations make two new contributions in addition to continuing the bio-optical time series begun with Orbview-2's SeaWiFS sensor. First, MODIS provides weekly estimates of global ocean net primary productivity on weekly and annual time periods, and annual empirical estimates of carbon export production. Second, MODIS provides additional insight into the spatial and temporal variations in photosynthetic efficiency through the direct measurements of solar-stimulated chlorophyll fluorescence. The two different weekly productivity indexes (first developed by Behrenfeld & Falkowski and by Yoder, Ryan and Howard) are used to derive daily productivity as a function of chlorophyll biomass, incident daily surface irradiance, temperature, euphotic depth, and mixed layer depth. Comparisons between these two estimates using both SeaWiFS and MODIS data show significant model differences in spatial distribution after allowance for the different integration depths. Both estimates are strongly dependence on the accuracy of the chlorophyll determination. In addition, an empirical approach is taken on annual scales to estimate global NPP and export production. Estimates of solar stimulated fluorescence efficiency from chlorophyll have been shown to be inversely related to photosynthetic efficiency by Abbott and co-workers. MODIS provides the first global estimates of oceanic chlorophyll fluorescence, providing an important proof of concept. MODIS observations are revealing spatial patterns of fluorescence efficiency which show expected variations with phytoplankton photo-physiological parameters as measured during in-situ surveys. This has opened the way for research into utilizing this information to improve our understanding of oceanic NPP variability. Deriving the ocean bio-optical properties places severe demands on instrument performance (especially band to band precision) and atmospheric correction. Improvements in MODIS instrument characterization and calibration over the first 16 mission months have greatly improved the accuracy of the chlorophyll input fields and FLH, and therefore the estimates of NPP and fluorescence efficiency. Annual estimates now show the oceanic NPP accounts for 40-50% of the global total NPP, with significant interannual variations related to large scale ocean processes. Spatial variations in ocean NPP, and exported production, have significant effects on exchange of CO2 between the ocean and atmosphere. Further work is underway to improve both the primary productivity model functions, and to refine our understanding of the relationships between fluorescence efficiency and NPP estimates. We expect that the MODIS instruments will prove extremely useful in assessing the time dependencies of oceanic carbon uptake and effects of iron enrichment, within the global carbon cycle.

Esaias, Wayne E.↗

NASA NTRSDate not supplied

Initial Findings in Full-Shell Active Optics

The realization of active full-shell x-ray optics will provide ground-breaking capability for future missions. Future X-ray missions, such as Lynx, require high angular-resolution, large effective area, and as wide a field of view(FOV) as possible. It is currently not possible to perform high-resolution imaging of both wide and narrow FOVs with a single X-ray telescope. In this paper, we discuss the use of actuators to switch the optical surface of full-shell x-ray optics between prescriptions optimized for narrow-field and wide-field viewing, as well as correct for low-spatial-frequency errors in the optics. Previously, a pathfinder was developed using finite-element modeling(FEM). Using a combination of the model’s influence functions, the capacity of active full-shell optics was shown to switch between prescriptions with 92% accuracy. Another benefit of the analytical pathfinder was its ability to correct low-spatial frequency errors, which comprise a large percentage of the MSFC full-shell x-ray optics root-mean-square (RMS) slope error. In order to verify the pathfinder, a surface-parallel actuator was bonded to a nickel-replicated coupon. After the actuator was bonded to the coupon, the slope of the surface was measured while the actuator was activated. The proof-of-concept demonstrator development, the influence function data, and the resulting implications on the analytical pathfinder are reported and discussed.

X-ray optics↗