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NASA NTRS1984

Light Scattered from Polished Optical Surfaces: Wings of the Point Spread Function

Random figure errors from the polishing process plus particles on the main mirrors in a telescope cause an extended point spread function (PSF) declining approximately as the inverse square of the sine of the angle from a star from about 100 micro-rad to a right angle. The decline in at least one case, and probably in general, proceeds as the inverse cube at smaller angles where the usual focal plane aperture radius is chosen. The photometric error due to misalignment by one Airy ring spacing with an aperture of n rings depends on the net variance in the figure. It is approximately 60/(n+1)(3) when using the data of Kormendy (1973). A typical value is 6 x 10 to the -5th power per ring of misalignment with n = 100 rings. The encircled power may be modulated on a time scale of hours by parts per thousand in a wavelength dependent manner due to relative humidity effects on mirror dust. The scattering according to an inverse power law is due to a random walk in aberration height caused by a multitude of facets and slope errors left by the polishing process. A deviation from such a law at grazing emergence may permit monitoring the dust effects.

Kenknight, C. E.↗

NASA NTRS1999

Parameter Estimation in Astronomy with Poisson-Distributed Data: The (CHI)2(gamma) Statistic - 1

Applying the standard weighted mean formula, [Sigma (sub i)n(sub i)ssigma(sub i, sup -2)], to determine the weighted mean of data, n(sub i), drawn from a Poisson distribution, will, on average, underestimate the true mean by approx. 1 for all true mean values larger than approx.3 when the common assumption is made that the error of the i th observation is sigma(sub i) = max square root of n(sub i), 1).This small, but statistically significant offset, explains the long-known observation that chi-square minimization techniques which use the modified Neyman'chi(sub 2) statistic, chi(sup 2, sub N) equivalent Sigma(sub i)((n(sub i) - y(sub i)(exp 2)) / max(n(sub i), 1), to compare Poisson - distributed data with model values, y(sub i), will typically predict a total number of counts that underestimates the true total by about 1 count per bin. Based on my finding that weighted mean of data drawn from a Poisson distribution can be determined using the formula [Sigma(sub i)[n(sub i) + min(n(sub i), 1)](n(sub i) + 1)(exp -1)] / [Sigma(sub i)(n(sub i) + 1)(exp -1))], I propose that a new chi(sub 2) statistic, chi(sup 2, sub gamma) equivalent, should always be used to analyze Poisson- distributed data in preference to the modified Neyman's chi(exp 2) statistic. I demonstrated the power and usefulness of,chi(sub gamma, sup 2) minimization by using two statistical fitting techniques and five chi(exp 2) statistics to analyze simulated X-ray power - low 15 - channel spectra with large and small counts per bin. I show that chi(sub gamma, sup 2) minimization with the Levenberg - Marquardt or Powell's method can produce excellent results (mean slope errors approx. less than 3%) with spectra having as few as 25 total counts.

Mighell, Kenneth J.↗

NASA NTRS1977

Lightweight reflector assembly

An inexpensive, lightweight reflective assembly member having good optical quality and particularly adaptable to accommodating temperature variations without providing destructive thermal stresses and reflective slope errors is described. The reflective assembly consists of a thin sheet of glass with appropriate reflective coating and a cellular glass block substrate bonded together. The method of fabrication includes abrading the cellular substrate with an abrasive master die to form an appropriate concave surface. An adhesive is applied to the abraded surface and a lamina reflective surface is placed under a uniform pressure to conform the reflective surface onto the desired abraded surface of the substrate.

Argoud, M. J.↗

NASA NTRS1979

Comparative study of solar optics for paraboloidal concentrators

Different analytical methods for computing the flux distribution on the focal plane of a paraboloidal solar concentrator are reviewed. An analytical solution in algebraic form is also derived for an idealized model. The effects resulting from using different assumptions in the definition of optical parameters used in these methodologies are compared and discussed in detail. These parameters include solar irradiance distribution (limb darkening and circumsolar), reflector surface specular spreading, surface slope error, and concentrator pointing inaccuracy. The type of computational method selected for use depends on the maturity of the design and the data available at the time the analysis is made.

Wen, L.↗

NASA NTRS1982

Acurex Parabolic Dish Concentrator (PDC-2)

The design approach, rationale for the selected configuration, and the development status of a cost effective point-focus solar concentrator are discussed. The low-cost concentrator reflective surface design is based on the use of a thin, backsilvered mirror glass reflector bonded to a molded structural plastic substrate. The foundation, support, and drive subassembles are described. A hybrid, two-axis, Sun tracking control system based on microprocessor technology was selected. Coarse synthetic tracking is achieved through a microcomputer-based control system to calculate Sun position for transient periods of cloud cover as well as sundown and sunrise positioning. Accurate active tracking is achieved by two-axis optical sensors. Results of the reflective panel demonstration tests investigating slope error, hail impact survivability, temperature/humidity cycling, longitudinal strength/bending stiffness, and torsional stiffness are discussed.

Overly, P.↗

NASA NTRS1984

A Nomographic Methodology for Use in Performance Trade-Off Studies of Parabolic Dish Solar Power Modules

A simple graphical method was developed to undertake technical design trade-off studies for individual parabolic dish models comprising a two-axis tracking parabolic dish with a cavity receiver and power conversion assembly at the focal point. The results of these technical studies are then used in performing the techno-economic analyses required for determining appropriate subsystem sizing. Selected graphs that characterize the performance of subsystems within the module were arranged in the form of a nomogram that would enable an investigator to carry out several design trade-off studies. Key performance parameters encompassed in the nomogram include receiver losses, intercept factor, engine rating, and engine efficiency. Design and operation parameters such as concentrator size, receiver type (open or windowed aperture), receiver aperture size, operating temperature of the receiver and engine, engine partial load characteristics, concentrator slope error, and the type of reflector surface, are also included in the graphical solution. Cost considerations are not included.

Selcuk, M. K.↗

NASA NTRS1986

Optimization of spherical facets for parabolic solar concentrators

Solar concentrator designs which employ deployable hexagonal panels are being developed for space power systems. An offset optical configuration has been developed which offers significant system level advantages over previously proposed collector designs for space applications. Optical analyses have been performed which show offset reflector intercept factors to be only slightly lower than those for symmetric reflectors with the same slope error. Fluxes on the receiver walls are asymmetric but manageable by varying the tilt angle of the receiver. Greater producibility is achieved by subdividing the hexagonal panels into triangular mirror facets of spherical contour. Optical analysis has been performed upon these to yield near-optimum sizes and radii.

White, J. E.↗

NASA NTRS1986

Correspondence between AXAF TMA X-ray performance and models based upon mechanical and visible light measurements

The AXAF Technology Mirror Assembly (TMA) was characterized prior to X-ray testing by properties measured mechanically or with visible light; these include alignment offsets, roundness and global-axial-slope errors, axial-figure errors with characteristic lengths greater than about five mm, and surface roughness with scale lengths between about 0.005 and 0.5 mm. The X-ray data of Schwartz et al. (1985) are compared with predictions based upon the mechanical and visible light measurements.

Van Speybroeck, L.↗

NASA NTRS1988

Ray tracing optical analysis of offset solar collector for space station solar dynamic system

OFFSET, a detailed ray tracing computer code, was developed at NASA Lewis Research Center to model the offset solar collector for the Space Station solar dynamic electric power system. This model traces rays from 50 points on the face of the Sun to 10 points on each of the 456 collector facets. The triangular facets are modeled with spherical, parabolic, or toroidal reflective surface contour and surface slope errors. The rays are then traced through the receiver aperture to the walls of the receiver. Images of the collector and of the Sun within the receiver produced by this code provide insight into the collector receiver interface. Flux distribution on the receiver walls, plotted by this code, is improved by a combination of changes to aperture location and receiver tilt angle. Power loss by spillage at the receiver aperture is computed and is considerably reduced by using toroidal facets.

Jefferies, Kent S.↗

NASA NTRS1988

Thermal distortion analysis of the space station solar dynamic concentrator

A method was developed to evaluate the thermal distortion of the Space Station Solar Dynamic Concentrator and the effects of thermal distortion on concentrator optical performance. The analytical method includes generating temperature distributions with TRASYS and SINDA models, interfacing the SINDA results with the SINDA-NASTRAN Interface Program (SNIP), calculating thermal distortion with a NASTRAN/PATRAN finite element model, and providing flux distribution maps within the receiver with the ray tracing OFFSET program. Temperature distributions, thermally induced slope errors, and flux distribution maps within the receiver are discussed. Results during a typical orbit indicate that temperatures of the hexagonal panels and triangular facets range between -18 and 99 C (-1 to 210 F), facet rotations are less than 0.2 mrad, and a change in facet radius due to thermal flattening is less than 5 percent. The predicted power loss with thermal distortion effects was less than 0.3 percent. The thermal distortion of the Solar Dynamic concentrator has negligible effect on the flux distribution within the receiver cavity.

Trudell, Jeffrey J.↗

NASA NTRS1987

Solar concentrator advanced development project

A solar dynamic concentrator design developed for use with a solar-thermodynamic power generation module intended for the Space Station is considered. The truss hexagonal panel reflector uses a modular design approach and is flexible in attainable flux profiles and assembly techniques. Preliminary structural, thermal, and optical analysis results are discussed. Accuracy of the surface reflectors should be within 5 mrad rms slope error, resulting in the need for close fabrication tolerances. Significant fabrication issues to be addressed include the facet reflective and protective coating processes and the surface specularity requirements.

Corrigan, Robert D.↗

NASA NTRS1988

X-ray mirror assessment with optical light

The imaging capability of a thin foil X-ray mirror has been examined with optical light, using a laser beam and a wide optical parallel beam. These measurements reveal that: (1) image broadening due to millimeter scale waviness (orange peel) of the aluminum substrate, partly intrinsic to the foil and partly caused during the foil treatment, is 1.2-min of arc half-power diameter (HPD) in two reflections; (2) slope errors due to foil shaping and misalignment cause broadening of 1.6-2.0-min of arc HPD; and (3) total broadening is about 3-min of arc HPD, which is consistent with the broadening of 2.6-min of arc HPD measured with X rays.

Kunieda, Hideyo↗

NASA NTRS1988

Thermal distortion analysis of the Space Station solar dynamic concentrator

Trudell, Jeffery J.↗

NASA NTRS1988

Ray tracing optical analysis of offset solar collector for Space Station solar dynamic system

OFFSET, a detailed ray tracing computer code, was developed at NASA Lewis Research Center to model the offset solar collector for the Space Station solar dynamic electric power system. This model traces rays from 50 points on the face of the sun to 10 points on each of the 456 collector facets. The triangular facets are modeled with spherical, parabolic, or toroidal reflective surface contour and surface slope errors. The rays are then traced through the receiver aperture to the walls of the receiver. Images of the collector and of the sun within the receiver produced by this code provide insight into the collector receiver interface. Flux distribution on the receiver walls, plotted by this code, is improved by a combination of changes to aperture location and receiver tilt angle. Power loss by spillage at the receiver aperture is computed and is considerably reduced by using toroidal facets.

Jefferies, Kent S.↗

NASA NTRS1989

Conceptual design study of a 5 kilowatt solar dynamic Brayton power system using a dome Fresnel lens solar concentrator

The primary project objective was to generate a conceptual design for a nominal 5 kW solar dynamic space power system, which uses a unique, patented, transmittance-optimized, dome-shaped, point-focus Fresnel lens as the optical concentrator. Compared to reflective concentrators, the dome lens allows 200 times larger slope errors for the same image displacement. Additionally, the dome lens allows the energy receiver, the power conversion unit (PCU), and the heat rejection radiator to be independently optimized in configuration and orientation, since none of these elements causes any aperture blockage. Based on optical and thermal trade studies, a 6.6 m diameter lens with a focal length of 7.2 m was selected. This lens should provide 87 percent net optical efficienty at 800X geometric concentration ratio. The large lens is comprised of 24 gores, which compactly stow together during launch, and automatically deploy on orbit. The total mass of the microglass lens panels, the graphite/epoxy support structure, and miscellaneous hardware is about 1.2 kg per square meter of aperture. The key problem for the dome lens approach relates to the selection of a space-durable lens material. For the first time, all-glass Fresnel lens samples were successfully made by a sol-gel casting process.

Oneill, Mark J.↗

NASA NTRS1989

Solar Concentrator Advanced Development Program

The Solar Concentrator Advanced Development Project has successfully designed, fabricated, and tested a full scale prototypical solar dynamic concentrator for space station applications. A Truss Hexagonal Panel reflector was selected as a viable solar concentrator concept to be used for space station applications. This concentrator utilizes a modular design approach and is flexible in attainable flux profiles and assembly techniques. The detailed design of the concentrator, which included structural, thermal and optical analysis, identified the feasibility of the design and specific technologies that were required to fabricate it. The needed surface accuracy of the reflectors surface was found to be very tight, within 5 mrad RMS slope error, and results in very close tolerances for fabrication. To meet the design requirements, a modular structure composed of hexagonal panels was used. The panels, made up of graphite epoxy box beams provided the strength, stiffness and dimensional stability needed. All initial project requirements were met or exceeded by hardware demonstration. Initial testing of structural repeatability of a seven panel portion of the concentrator was followed by assembly and testing of the full nineteen panel structure. The testing, which consisted of theodolite and optical measurements over an assembly-disassembly-reassembly cycle, demonstrated that the concentrator maintained the as-built contour and optical characteristics. The facet development effort within the project, which included developing the vapor deposited reflective facet, produced a viable design with demonstrated optical characteristics that are within the project goals.

Knasel, Don↗

NASA NTRS1990

Finite element analysis of thermal distortion effects on optical performance of solar dynamic concentrator for Space Station Freedom

An analysis was performed to predict the thermal distortion of the solar dynamic concentrator for Space Station Freedom in low earth orbit and to evaluate the effects of that thermal distortion on concentrator on-orbit performance. The analysis required substructural finite element modeling of critical concentrator structural subsystems, structural finite element modeling of the concentrator, mapping of thermal loading onto the structural finite element model, and the creation of specialized postprocessors to assist in interpreting results. Concentrator temperature distributions and thermally induced displacements and slope errors and the resulting receiver flux distribution profiles are discussed. Results determined for a typical orbit indicate that concentrator facet rotations are less than 0.2 mrad and that the change in facet radius due to thermal flattening is less than 5 percent. The predicted power loss due to thermal distortion effects is less than 0.3 percent. As a consequence the thermal distortions of the solar dynamic concentrator in low earth orbit will have a negligible effect on the flux distribution profiles within the receiver.

Doherty, Michael P.↗

NASA NTRS1992

Surface finish quality of the outer AXAF mirror pair based on x ray measurements of the VETA-I

We employ the X-ray measurements of the VETA-I taken at the X-Ray Calibration Facility (XRCF) of the Marshall Space Flight Center (MSFC) to extract information about the surface finish quality of the outermost pair of AXAF mirrors. The particular measurements we consider are one dimensional scans of the core of the point response function (PRF) (full width half maximum (FWHM) scans), the encircled energy as a function of radius, and one dimensional scans of the wings of the PRF. We discuss briefly our ray trace model which incorporates the numerous effects present in the VETA-I test, such as the finite source distance, the size and shape of the X-ray source, the residual gravitational distortions of the optic, the despace of the VETA-I, and particulate contamination. We show how the data constrain the amplitude of mirror surface deviations for spatial frequencies greater than about 0.1 mm(exp -1). Constraints on the average amplitude of circumferential slope errors are derived as well.

Hughes, John P.↗