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At least 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Atomic structural mechanism for ferroelectric-antiferroelectric transformation in perovskite NaNbO 3

Sodium niobate (NaNbO 3 or NN) is described as “the most complex perovskite system,” which exhibits transitions between, as well as coexistence of, several ferroelectrics (FE) and antiferroelectric (AFE) phases at different temperatures. Recently, solid solutions of NN with stabilized AFE phases(s) have gained attention for energy-related applications, such as high-density energy storage and electrocaloric cooling. A better understanding of the atomic mechanisms responsible for AFE/FE phase transitions in NaNbO 3 can enable a more rational design of its solid-solution systems with tunable functional properties. In this work, we have investigated changes in the average and local atomic structure of NN using a combination of x-ray/neutron diffraction and neutron pair-distribution function (PDF) analyses. The Rietveld refinement of the x-ray/neutron-diffraction patterns indicates a coexistence of the FE Q (P2 1 ma) and AFE P (Pbma) phases in the temperature range of 300 K ≤ T ≤ 615K, while PDF analysis indicated that the local structure (r < 8Å) is better described by a P2 1 ma symmetry. Above 615 K, the average structure transitions to an AFE R phase (Pmmn or Pnma), while PDF analysis shows an increased disordering of the octahedral distortions and Na displacements at the local scale. These results indicate that the average P/Q/R phase transitions in NN can be described as a result of complex ordering of distorted octahedral tilts at the nanoscale and off-centered displacements of the Na atoms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1992

Diffractive optics technology and the NASA Geostationary Earth Observatory (GEO)

Diffractive (or binary) optics offers unique capabilities for the development of large-aperture, high-performance, light-weight optical systems. The Geostationary Earth Observatory (GEO) will consist of a variety of instruments to monitor the environmental conditions of the earth and its atmosphere. The aim of this investigation is to analyze the design of the GEO instrument that is being proposed and to identify the areas in which diffractive (or binary) optics technology can make a significant impact in GEO sensor design. Several potential applications where diffractive optics may indeed serve as a key technology for improving the performance and reducing the weight and cost of the GEO sensors have been identified. Applications include the use of diffractive/refractive hybrid lenses for aft-optic imagers, diffractive telescopes for narrowband imaging, subwavelength structured surfaces for anti-reflection and polarization control, and aberration compensation for reflective imaging systems and grating spectrometers.

Morris, G. Michael↗
DOE OSTI2021

Fixed-target serial femtosecond crystallography using in cellulo grown microcrystals

The crystallization of recombinant proteins in living cells is an exciting new approach in structural biology. Recent success has highlighted the need for fast and efficient diffraction data collection, optimally directly exposing intact crystal-containing cells to the X-ray beam, thus protecting the in cellulo crystals from environmental challenges. Serial femtosecond crystallography (SFX) at free-electron lasers (XFELs) allows the collection of detectable diffraction even from tiny protein crystals, but requires very fast sample exchange to utilize each XFEL pulse. Here, an efficient approach is presented for high-resolution structure elucidation using serial femtosecond in cellulo diffraction of micometre-sized crystals of the protein HEX-1 from the fungus Neurospora crassa on a fixed target. Employing the fast and highly accurate Roadrunner II translation-stage system allowed efficient raster scanning of the pores of micro-patterned, single-crystalline silicon chips loaded with living, crystal-containing insect cells. Compared with liquid-jet and LCP injection systems, the increased hit rates of up to 30% and reduced background scattering enabled elucidation of the HEX-1 structure. Using diffraction data from only a single chip collected within 12 min at the Linac Coherent Light Source, a 1.8 Å resolution structure was obtained with significantly reduced sample consumption compared with previous SFX experiments using liquid-jet injection. This HEX-1 structure is almost superimposable with that previously determined using synchrotron radiation from single HEX-1 crystals grown by sitting-drop vapour diffusion, validating the approach. This study demonstrates that fixed-target SFX using micro-patterned silicon chips is ideally suited for efficient in cellulo diffraction data collection using living, crystal-containing cells, and offers huge potential for the straightforward structure elucidation of proteins that form intracellular crystals at both XFELs and synchrotron sources.

Lahey-Rudolph, J. Mia (ORCID:0000000152797267)↗
DOE OSTI2020

Identification of Possible Stellar Companions via Speckle Interferometry in a Sample of Be Stars

We present speckle interferometric measurements of Be stars made with the 1.60 m Perkin-Elmer telescope at the Pico dos Dias Observatory of the Laboratório Nacional de Astrofísica in Brazil. Using three different filters (V, R, and I), we obtained astrometric measurements for 23 stars, during three observing runs allocated in 2017 March, 2018 April, and 2019 July. We identified pairs with angular separation ranging from 0.″10 to 6.″69, including six systems with separations smaller than 1.″0. We estimated a mean error in separation of 15 mas, 1.°2 in position angle, and 0.29 mag for the magnitude difference. We discovered three new possible double systems that are not identified in the literature: HD 174886, HD 159032, and HD 168135 with an average angular separation of 0.″20, 3.″23, and 5.″41, respectively. In addition, we identified four new pairs in multiple systems previously known in the Washington Double Star Catalog. However, for 16 stars of our sample, we did not find evidence of binarity, based on the diffraction-limited resolution, the field of view, and/or the sensitivity of our observations. From the cross-match with data from Gaia Data Release 2, we verified the possibility of some of these systems be gravitationally bound or not.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2009

NASA Tech Briefs, May 2009

Topics covered include: Valve-"Health"-Monitoring System; Microstrip Antenna for Remote Sensing of Soil Moisture and Sea Surface Salinity; Biomedical Wireless Ambulatory Crew Monitor; Wireless Avionics Packet to Support Fault Tolerance for Flight Applications; Aerobot Autonomy Architecture; Submillimeter Confocal Imaging Active Module; Traveling-Wave Maser for 32 GHz; System Synchronizes Recordings from Separated Video Cameras; Piecewise-Planar Parabolic Reflectarray Antenna; Reducing Interference in ATC Voice Communication; EOS MLS Level 1B Data Processing, Version 2.2; Auto-Generated Semantic Processing Services; Geospatial Authentication; Maneuver Automation Software; Event Driven Messaging with Role-Based Subscriptions; Estimating Relative Positions of Outer-Space Structures; Fabricating PFPE Membranes for Capillary Electrophoresis; Linear Actuator Has Long Stroke and High Resolution; Installing a Test Tap on a Metal Battery Case; Fabricating PFPE Membranes for Microfluidic Valves and Pumps; Room-Temperature-Cured Copolymers for Lithium Battery Gel Electrolytes; Catalysts for Efficient Production of Carbon Nanotubes; Amorphous Silk Fibroin Membranes for Separation of CO2; "Zero-Mass" Noninvasive Pressure Transducers; Radial-Electric-Field Piezoelectric Diaphragm Pumps; Ejector-Enhanced, Pulsed, Pressure-Gain Combustor; Suppressing Ghost Diffraction in E-Beam-Written Gratings; Target-Tracking Camera for a Metrology System; Polarimetric Imaging using Two Photoelastic Modulators; Miniature Wide-Angle Lens for Small-Pixel Electronic Camera; Modal Filters for Infrared Interferometry; Mo(3)Sb(7-x)Te(x) for Thermoelectric Power Generation; Two-Dimensional Quantum Model of a Nanotransistor; Scanning Miniature Microscopes without Lenses; Manipulating Neutral Atoms in Chip-Based Magnetic Traps; Expansion Compression Contacts for Thermoelectric Legs; Processing Electromyographic Signals to Recognize Words; Physical Principle for Generation of Randomness; DSN Beowulf Cluster-Based VLBI Correlator; Hybrid NN/SVM Computational System for Optimizing Designs; Criteria for Modeling in LES of Multicomponent Fuel Flow; Computerized Machine for Cutting Space Shuttle Thermal Tiles; Orbiting Depot and Reusable Lander for Lunar Transportation; FPGA-Based Networked Phasemeter for a Heterodyne Interferometer; Aquarius Digital Processing Unit; Three-Dimensional Optical Coherence Tomography; Benchtop Antigen Detection Technique using Nanofiltration and Fluorescent Dyes; Isolation of Precursor Cells from Waste Solid Fat Tissue; Identification of Bacteria and Determination of Biological Indicators; Further Development of Scaffolds for Regeneration of Nerves; Chemically Assisted Photocatalytic Oxidation System; Use of Atomic Oxygen for Increased Water Contact Angles of Various Polymers for Biomedical Applications; Crashworthy Seats Would Afford Superior Protection; Open-Access, Low-Magnetic-Field MRI System for Lung Research; Microfluidic Mixing Technology for a Universal Health Sensor; Microfluidic Extraction of Biomarkers using Water as Solvent; Microwell Arrays for Studying Many Individual Cells; Droplet-Based Production of Liposomes; and Identifying and Inactivating Bacterial Spores

Source record↗
NASA NTRS1987

The laser elevator - Momentum transfer using an optical resonator

In a conventional laser lightsail system the payload is propelled by the momentum imparted to it by the reflection of a laser beam without the use of any propellant. Because of the unfavorable relationship between energy and momentum in a light beam, these systems are very inefficient. The efficiency can be greatly improved, in principle, if the photons that impact the payload mirror are returned to the source and then redirected back toward the payload again. This system, which recirculates the laser beam, is defined as the 'laser elevator'. The gain of the laser elevator over conventional lightsails depends on the number of times the beam is recycled which is limited by the reflectance of the mirrors used, any losses in the transmission of the beam, and diffraction. Due to the increase pathlength of the folded beam, diffraction losses occur at smaller separations of the payload and the source mirror than for conventional lightsail system. The laser elevator has potential applications in launching to low earth orbit, orbital transfer, and rapid interplanetary delivery of small payloads.

Meyer, Thomas R.↗
NASA NTRS1985

Vector diffraction analysis of reflector antennas with mesh surfaces

Reflector antennas with mesh surfaces are used extensively in many satellite and ground antenna systems. A strip-aperture modeling of commonly used mesh surfaces is presented which provides considerable versatility in characterizing the mesh cells. The mesh transmission coefficients are constructed using a Floquet-modal expansion in conjuction with two dominant aperture modes. To account for the mesh local coordinates, the Eulerian angle transformation is invoked to obtain the total induced current on the curved reflector surface. General formulas are presented to show how the solid surface induced current is modified due to the transmission through the mesh. The effects of a variety of mesh configurations on both the co-polar and cross-polar patterns of reflector antennas are studied by numerically evaluating the vector diffraction integral using the Jacobi-Bessel expansion. For some special cases, a comparison is made with the results of the commonly used wire-grid formulation. Many of the numerical data are tailored to the dimensions of a conceptually designed mesh deployable offset reflector of the land mobile satellite system (LMSS).

Rahmat-Samii, Y.↗
NASA NTRS1982

Highly versatile computer-controlled television detector system

A description is presented of a television detector system which has been designed to accommodate a wide range of applications. It is currently being developed for use in X-ray diffraction, X-ray astrophysics, and electron microscopy, but it is also well suited for astronomical observations. The image can be integrated in a large, high-speed memory system, in the memory of a computer system, or the target of the TV tube or CCD array. The detector system consists of a continuously scanned, intensified SIT vidicon with scan and processing electronics which generate a digital image that is integrated in the detector memory. Attention is given to details regarding the camera system, scan control and image processing electronics, the memory system, and aspects of detector performance.

Kalata, K.↗
NASA NTRS2017

An Experimental Flow-Through Assessment of Acidic Fe/Mg Smectite Formation on Early Mars

Orbital observations have detected the phyllosilicate smectite in layered material hundreds of meters thick, intracrater depositional fans, and plains sediments on Mars; however, the detection of carbonate deposits is limited. Instead of neutral/alkaline conditions during the Noachian, early Mars may have experienced mildly acidic conditions derived from volcanic acid-sulfate solutions that allowed Fe/Mg smectite formation but prevented widespread carbonate formation. The detection of acid sulfates (e.g., jarosite) associated with smectite in Mawrth Vallis supports this hypothesis. Previous work demonstrated smectite (saponite) formation in closed hydrologic systems (batch reactor) from basaltic glass at pH 4 and 200°C (Peretyazhko et al., 2016 GCA). This work presents results from alteration of basaltic glass from alkaline to acidic conditions in open hydrologic systems (flow-through reactor). Preliminary experiments exposed basaltic glass to deionized water at 190°C at 0.25 ml/min where solution pH equilibrated to 9.5. These initial high pH experiments were conducted to evaluate the flow-through reactor system before working with lower pHs. Smectite at this pH was not produced and instead X-ray diffraction results consistent with serpentine was detected. Experiments are in progress exposing basaltic glass from pH 8 down to pH 3 to determine what range of pHs could allow for smectite formation in this experimental opensystem. The production of smectite under an experimental open-system at low pHs if successful, would support a significant paradigm shift regarding the geochemical evolution of early Mars: Early Mars geochemical solutions were mildly acidic, not neutral/alkaline. This could have profound implications regarding early martain microbiology where acid conditions instead of neutral/alkaline conditions will require further research in terrestrial analogs to address the potential for biosignature preservation on Mars.

Sutter, Brad↗
DOE OSTI2026

One-dimensional neutron diffraction from layered graphite: Reciprocal space structure and grating behavior

In this work we report observations of one-dimensional neutron diffraction from highly oriented pyrolytic graphite (HOPG), where the scattering angle varies continuously with incident angle following classical grating-like behavior. The 2D polycrystalline structure of HOPG—with highly aligned layers along the 𝑐 axis but random in-plane rotations—creates planes of scattering intensity in reciprocal space at 𝑄 𝑐 =𝑛⁢(2⁢𝜋/𝑑) where 𝑑=3.35Å is the interlayer spacing. As the Ewald sphere sweeps through reciprocal space during sample rotation, it continuously intersects these planes, producing the observed angular dispersion. We observe both first-order (𝑛=1) and second-order (𝑛=2) diffraction at conventional scattering angles (25°–70°), with peak positions that remain temperature-independent between 10 K and 294 K and follow quantitative agreement with momentum conservation 𝑄 𝑐 =𝑘⁢[sin⁡𝜓−sin⁡𝜓 𝑓 ]=𝑛⁢(2⁢𝜋/𝑑). X-ray diffraction under similar conditions shows no comparable behavior, confirming that sharp nuclear-vacuum contrast is essential. While diffraction intensities are weak (∼10 −6 of Bragg peaks), the observations demonstrate how the interplay of atomic-scale periodicity, nuclear contrast, and structural disorder enables observation of continuous diffraction curves at thermal neutron wavelengths, illustrating how HOPG's unique microstructure determines its scattering properties beyond conventional Bragg diffraction.

2-dimensional systems↗
NASA NTRS1992

A new ordered tetragonal phase in the Ti3Al+Nb system

Results are reported from an experimental study of phase stability in a plasma-sprayed Ti3Al+Nb alloy using TEM and electron diffraction techniques. The alloys was produced from Ti3Al+Nb powder via an inductively coupled plasma deposition process. Evidence was found for the ordering of the B2 phase to a structure similar to the DO3-type phase, but with a tetragonal distortion. An ordered tetragonal phase (T) is proposed to account for these observations, and the existence of the B2 - T ordering transformation in the Ti3Al+Nb system is suggested. The T phase can be regarded as a DO3-like phase with a tetragonal distortion. The tegragonality c0/a0 is approximately equal to 1.02, and a0 equals 0.65 +/-0.01 nm.

Hsiung, L. M.↗
NASA NTRS1993

Thermal stress effects in intermetallic matrix composites

Intermetallic matrix composites develop residual stresses from the large thermal expansion mismatch (delta-alpha) between the fibers and matrix. This work was undertaken to: establish improved techniques to measure these thermal stresses in IMC's; determine residual stresses in a variety of IMC systems by experiments and modeling; and, determine the effect of residual stresses on selected mechanical properties of an IMC. X ray diffraction (XRD), neutron diffraction (ND), synchrotron XRD (SXRD), and ultrasonics (US) techniques for measuring thermal stresses in IMC were examined and ND was selected as the most promising technique. ND was demonstrated on a variety of IMC systems encompassing Ti- and Ni-base matrices, SiC, W, and Al2O3 fibers, and different fiber fractions (Vf). Experimental results on these systems agreed with predictions of a concentric cylinder model. In SiC/Ti-base systems, little yielding was found and stresses were controlled primarily by delta-alpha and Vf. In Ni-base matrix systems, yield strength of the matrix and Vf controlled stress levels. The longitudinal residual stresses in SCS-6/Ti-24Al-llNb composite were modified by thermomechanical processing. Increasing residual stress decreased ultimate tensile strength in agreement with model predictions. Fiber pushout strength showed an unexpected inverse correlation with residual stress. In-plane shear yield strength showed no dependence on residual stress. Higher levels of residual tension led to higher fatigue crack growth rates, as suggested by matrix mean stress effects.

Wright, P. K.↗
DOE OSTI2023

Decoding Li + /Na + Exchange Route Toward High-Performance Mn-Based Layered Cathodes for Li-Ion Batteries

Li + /Na + exchange has been extensively explored as an effective method to prepare high-performance Mn-based layered cathodes for Li-ion batteries, since the first report in 1996 by P. G. Bruce (Nature, 1996. 381, 499–500). Understanding the detailed structural changes during the ion-exchange process is crucial to implement the synthetic control of high-performance layered Mn-based cathodes, but less studied. Herein, in situ synchrotron X-ray diffraction, density functional theory calculations, and electrochemical tests are combined to conduct the systemic studies into the structural changes during the ion-exchange process of an Mn-only layered cathode O3-type Li 0.67 [Li 0.22 Mn 0.78 ]O 2 (LLMO) from the corresponding counterpart P3-type Na 0.67 [Li 0.22 Mn 0.78 ]O 2 (NLMO). The temperature-resolved observations combined with theoretical calculations reveal that the Li + /Na + exchange is favorable thermodynamically and composited with two tandem topotactic phase transitions: 1) from NLMO to a layered intermediate through ≈60% of Li + /Na + exchange. 2) then to the final layered product LLMO through further Li insertion. Moreover, the intermediate-dominate composite is obtained by slowing down the exchange kinetics below room temperature, showing better electrochemical performance than LLMO obtained by the traditional molten-salt method. Finally, the findings provide guides for the synthetic control of high-performance Mn-based cathodes under mild conditions.

25 ENERGY STORAGE↗
DOE OSTI2022

Advantages of tandem versus simultaneous operation: The case of isomerization/hydrogenation of terpinolene epoxide to Terpinen-4-ol using a Ni/TiO 2 -SiO 2 bifunctional catalyst

The conversion of terpinolene epoxide to terpinen-4-ol is a desirable chemical transformation for the production of a valuable intermediate. Here this report describes a one-pot, two-step system for the reaction that uses a bifunctional Ni/TiO 2 -SiO 2 catalyst with isomerization and hydrogenation capabilities. The TiO 2 -SiO 2 serves to isomerize the starting epoxide. The Ni component works to hydrogenate the allylic double bond. The tandem system achieves a high 64% yield of terpinen-4-ol. X-ray diffraction analysis showed that TiO 2 -SiO 2 was a mixed binary oxide, and Fourier transform infrared spectroscopy of adsorbed pyridine suggested that acid sites were mainly Lewis acid sites. Electron microscopy showed that the Ni/TiO 2 -SiO 2 catalyst consisted of spherical particles comprising a titanosilicate phase with highly dispersed zero-valent Ni or anatase on the surface. Additionally, there was strong interaction between Ni and the TiO 2 -SiO 2 mixed oxides. Control kinetic experiments demonstrated that the tandem use of the catalysts was more effective than simultaneous operation.

42 ENGINEERING↗
DOE OSTI2023

Re-investigation of high-temperature phase equilibria in Fe-rich Sm–Fe–Ti alloys

Recently renewed attempts to develop high-performance rare-earth-lean permanent magnets based on the Sm(Fe,Ti) 12 compound have drawn attention to the limited knowledge about the high-temperature phase equilibria in the Sm–Fe–Ti system. Experimental investigation of equilibrated alloys with electron probe microanalysis, X-ray diffraction and thermomagnetic analysis revealed several inaccuracies in the currently accepted phase relations at 1000°C and allowed for a revision of the Fe-rich corner of the Sm–Fe–Ti phase diagram. The Sm(Fe,Ti) 12 and Sm 3 (Fe,Ti) 29 phases were found to have more extended Ti ranges of 5.1–9.7 at% and 2.8–6.9 at%, respectively. With increasing of the Ti content, the Curie temperature of the Sm(Fe,Ti) 12 remains nearly constant at 306–312°C, whereas that of the Sm 3 (Fe,Ti) 29 increases from 188°C to 207°C. The low-titanium Sm 3 (Fe,Ti) 29 phase equilibrates not only with the Sm(Fe,Ti) 12 and Sm2(Fe,Ti) 17 phases, but also with (α-Fe) solid solution. Newly demonstrated equilibrium between Sm 2 (Fe,Ti) 17 and TiFe 2 phases makes impossible the earlier reported equilibrium between the Sm 3 (Fe,Ti) 29 and Sm(Fe,Ti) 11 phases. Because of an invariant reaction at 1000 °C, the revised phase diagram also features a class II four-phase equilibrium Sm 3 (Fe,Ti) 29 + TiFe 2 + Sm(Fe,Ti) 12 + Sm 2 (Fe,Ti) 17 . Peritectic decomposition of the Sm(Fe,Ti) 11 phase, which occurs either at 1075°C or at 1087°C, was found to have among its products the Sm(Fe,Ti) 12 phase. Although no such equilibration was attempted, it must be possible to obtain above 1087°C a two-phase state composed of the Sm(Fe,Ti) 12 phase and a liquid – which is important for manufacturing of the Sm(Fe,Ti) 12 - based permanent magnets via the liquid-phase sintering.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Crystal Growth of Quaternary RE 2 EuSi 2 S 8 ( RE = Ce–Nd, Sm, Gd, Tb) Using Flux-Assisted Boron Chalcogen Mixture (BCM) Method: Investigation of Magnetic and Luminescence Properties

A series of quaternary rare-earth containing thiosilicates with the general formula RE 2 EuSi 2 S 8 (RE = Ce–Nd, Sm, Gd, Tb) has been synthesized via the flux-assisted boron chalcogen mixture (BCM) crystal growth method. High-quality single crystals were obtained, and their crystal structures were determined by single-crystal X-ray diffraction. The RE 2 EuSi 2 S 8 series crystallizes in the trigonal system, adopting the space group R-3c. Polycrystalline samples were employed for physical property measurements, including magnetic susceptibility measurements, UV–visible diffuse reflectance, and photoluminescent response. Magnetic data of RE 2 EuSi 2 S 8 ( RE = Ce, Nd, and Gd) were collected over the 2–300 K temperature range. The samples were paramagnetic behavior with negative Weiss constants (θ W = −11.05, −10.55, and −1.35 K respectively). Their thermal stability was investigated using thermogravimetric analysis (TGA). Optical band gaps, estimated from diffuse reflectance spectra, were determined to be 2.2(1) eV for Ce 2 EuSi 2 S 8 , 1.8(1) eV for Nd 2 EuSi 2 S 8 , and 1.7(1) eV for Gd 2 EuSi 2 S 8 respectively. Finally, photoluminescence measurements were collected on Ce 2 EuSi 2 S 8 and Tb 2 EuSi 2 S 8 single crystals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1979

Measurement of the size of the isoplanatic patch using a phase-correcting telescope

In the presence of several-arc-second seeing at Mt. Wilson observatory, a flexible mirror image-sharpening telescope produced diffraction-limited (0.5 arcsec) images of the primary stars in the double star systems of Castor (alpha Gem), Algieba (gamma Leo) and Almach (gamma And). The images of both the primary and the companion star were simultaneously sharpened for Castor (separation 2 arcsec) and Algieba (4 arcsec) but not for Almach (10 arcsec). Thus the size of the isoplanatic patch came to lie between 4 and 10 arcsec. Using a simple model, we conclude that the bulk of the turbulent air responsible for the seeing was situated between 1.1 and 1.7 km above ground.

Pollaine, S.↗
NASA NTRS1982

Tolerance analysis of optical telescopes using coherent addition of wavefront errors

A near diffraction-limited telescope requires that tolerance analysis be done on the basis of system wavefront error. One method of analyzing the wavefront error is to represent the wavefront error function in terms of its Zernike polynomial expansion. A Ramsey-Korsch ray trace package, a computer program that simulates the tracing of rays through an optical telescope system, was expanded to include the Zernike polynomial expansion up through the fifth-order spherical term. An option to determine a 3 dimensional plot of the wavefront error function was also included in the Ramsey-Korsch package. Several assimulation runs were analyzed to determine the particular set of coefficients in the Zernike expansion that are effected by various errors such as tilt, decenter and despace. A 3 dimensional plot of each error up through the fifth-order spherical term was also included in the study. Tolerance analysis data are presented.

Davenport, J. W.↗