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All sources NASA NTRS DOE OSTI

NASA NTRS1993

Data analysis for GOPEX image frames

The data analysis based on the image frames received at the Solid State Imaging (SSI) camera of the Galileo Optical Experiment (GOPEX) demonstration conducted between 9-16 Dec. 1992 is described. Laser uplink was successfully established between the ground and the Galileo spacecraft during its second Earth-gravity-assist phase in December 1992. SSI camera frames were acquired which contained images of detected laser pulses transmitted from the Table Mountain Facility (TMF), Wrightwood, California, and the Starfire Optical Range (SOR), Albuquerque, New Mexico. Laser pulse data were processed using standard image-processing techniques at the Multimission Image Processing Laboratory (MIPL) for preliminary pulse identification and to produce public release images. Subsequent image analysis corrected for background noise to measure received pulse intensities. Data were plotted to obtain histograms on a daily basis and were then compared with theoretical results derived from applicable weak-turbulence and strong-turbulence considerations. Processing steps are described and the theories are compared with the experimental results. Quantitative agreement was found in both turbulence regimes, and better agreement would have been found, given more received laser pulses. Future experiments should consider methods to reliably measure low-intensity pulses, and through experimental planning to geometrically locate pulse positions with greater certainty.

Levine, B. M.↗

NASA NTRS1994

A monolithic Si bolometer array for the Caltech Submillimeter Observatory

We are developing a submillimeter continuum camera for the Caltech Submillimeter Observatory (CSO) located on Mauna Kea. The camera will employ a monolithic Si bolometer array which was developed by Moseley et al. at the NASA Goddard Space Flight Center (GSFC). The camera will be cooled to a temperature of about 300 mK in a He-3 cryostat, and will operate primarily at wavelengths of 350 and 450 micrometers. We plan to use a bolometer array with 1x24 directly illuminated pixels, each pixel of dimension 1x2 sq mm, which is about half of the F/4 beam size at these wavelengths. Each pixel is 10 to 12 micrometers thick and is supported only by four thin Si legs formed by wet chemical etch. The pixels are doped n-type by phosphorus implantation, compensated by boron implantation. Signals from the bolometer pixels are first amplified by cryogenically cooled FET's. The signals are further amplified by room-temperature amplifiers and then separately digitized by 16 bit A/D converters with differential inputs. The outputs of the A/D converters are fed into a digital signal processing board via fiber-optic cables. The electronics and data acquisition system were designed by the Goddard group. We will report the status of this effort.

Wang, Ning↗

NASA NTRS2005

Connecting Black Hole States and Accertion Flow Geometry

Under this program, INTEGRAL made four observations of the Galactic black hole X-ray binary GRO 51655-40 in outburst. Our team made a number of supporting observations simultaneously in the radio, optical, and X-ray bands. The data have been processed by INTEGRAL and efforts to make a preliminary reduction and analysis of the data are underway. As the data have only been in house for a month at the time of writing, there are no significant results to report at this time, apart from the fact that the source appears to have been detected clearly even up to an energy of 200 keV.

Teegarden, Bonnard↗

NASA NTRS1996

Second International Airborne Remote Sensing Conference and Exhibition

The conference provided four days of displays and scientific presentations on applications, technology, a science of sub-orbital data gathering and analysis. The twelve displayed aircraft equipped with sophisticated instrumentation represented a wide range of environmental and reconnaissance missions,including marine pollution control, fire detection, Open Skies Treaty verification, thermal mapping, hydrographical measurements, military research, ecological and agricultural observations, geophysical research, atmospheric and meterological observations, and aerial photography. The U.S. Air Force and the On-Site Inspection Agency displayed the new Open Skies Treaty verification Boeing OC 135B that promotes international monitoring of military forces and activities. SRl's Jetstream uses foliage and ground penetrating SAR for forest inventories, toxic waste delineation, and concealed target and buried unexploded ordnance detection. Earth Search Sciences's Gulfstream 1 with prototype miniaturized airborne hyperspectral imaging equipment specializes in accurate mineral differentiation, low-cost hydrocarbon exploration, and nonproliferation applications. John E. Chance and the U.S. Army Corps of Engineers displayed the Bell 2 helicopter with SHOALS that performs hydrographic surveying of navigation projects, coastal environment assessment, and nautical charting surveys. Bechtel Nevada and U.S. DOE displayed both the Beech King AIR B-200 platform equipped to provide first response to nuclear accidents and routine environmental surveillance, and the MBB BO-105 helicopter used in spectral analysis for environmental assessment and military appraisal. NASA Ames Research Center's high-altitude Lockheed ER-2 assists in earth resources monitoring research in atmospheric chemistry, oceanography, and electronic sensors; ozone and greenhouse studies and satellite calibration and data validation. Ames also showcased the Learjet 24 Airborne Observatory that completed missions in Venus cloud cover analysis, Quadantid meteor shower studies, extra-solar far infrared ionic structure lines measurement, Cape Kennedy launch support, and studies in air pollution, The Products and Services Exhibit showcased new sensor and image processing technologies, aircraft data collection services, unmanned vehicle technology, platform equipment, turn-key services, software a workstations, GPS services, publications, and processing and integration systems by 58 exhibitors. The participation of aircraft users and crews provided unique dialogue between those who plan data collection a operate the remote sensing technology, and those who supply the data processing and integration equipment. Research results using hyperspectral imagery, radar and optical sensors, lidar, digital aerial photography, a integrated systems were presented. Major research and development programs and campaigns we reviewed, including CNR's LARA Project and European Space Agency's 1991-1995 Airborne Campaign. The pre-conference short courses addressed airborne video, photogrammetry, hyperspectral data analysis, digital orthophotography, imagery and GIS integration, IFSAR, GPS, and spectrometer calibration.

Source record↗

NASA NTRS1973

Simultaneous observation solutions for NASA-MOTS and SPEOPT station positions on the North American datum

Simultaneous observations of the GEOS-I and II flashing lamps by the NASA MOTS and SPEOPT cameras on the North American Datum (NAD) were analyzed using geometrical techniques to provide an adjustment of the station coordinates. Two separate adjustments were obtained. An optical data only solution was computed in which the solution scale was provided by the Rosman-Mojave distance obtained from a dynamic station solution. In a second adjustment, scaling was provided by processing simultaneous laser ranging data from Greenbelt and Wallops Island in a combined optical-laser solution. Comparisons of these results with previous GSFC dynamical solutions indicate an rms agreement on the order of 4 meters or better in each coordinate. Comparison with a detailed gravimetric geoid of North America yields agreement of 3 meters or better for mainland U.S. stations and 7 and 3 meters, respectively, for Bermuda and Puerto Rico.

Reece, J. S.↗

DOE OSTI2024

Performance of plane wavefront Fizeau interferometers in power spectral density measurements with tilted plane optics

Binary pseudo-random array (BPRA) test samples are useful devices for calibrating the instrument transfer function (ITF) of Fizeau interferometers, interferometric microscopes, and other optical and non-optical surface and wavefront metrology instruments. The intrinsic white noise character of the power spectral density (PSD) function of the BPRA pattern simplifies the extraction of the ITF from the measured PSD. The ITF determined in a dedicated calibration experiment can be used to reconstruct the surface height profile from the measured data, effectively enhancing the instrument’s spatial resolution. For a high confidence reconstruction procedure, a reliable analytical model of the IFT is desirable. Usually, the model accounts for the contributions to the ITF related the imperfections of the instrument’s optical and detector systems. Here, we experimentally demonstrate that in the case of surface height metrology with Fizeau interferometers, the PSD measurements and, therefore, the efficacy of the ITF calibration of the tool, are strongly affected by the instrument data acquisition and processing procedures, as well as by the shape of the optic under test and its alignment with respect to the interferometer.

Yashchuk, V V↗

NASA NTRS1999

Space Weathering in the Fine Size Fractions of Lunar Soils: Soil Maturity Effects

The effects of space weathering on the optical properties of lunar materials have been well documented. These effects include a reddened continuum slope, lowered albedo, and attenuated absorption features in reflectance spectra of lunar soils as compared to finely comminuted rocks from the same Apollo sites. However, the regolith processes that cause these effects are not well known, nor is the petrographic setting of the products of these processes fully understood. A Lunar Soil Characterization Consortium has been formed with the purpose of systematically integrating chemical and mineralogical data with the optical properties of lunar soils. Understanding space-weathering effects is critical in order to fully integrate the lunar sample collection with remotely-sensed data from recent robotic missions (e.g., Lunar Prospector, Clementine, and Galileo) We have shown that depositional processes (condensation of impact-derived vapors, sputter deposits, accreted impact material, e.g., splash glass, spherules, etc.) are a major factor in the modification of the optical surfaces of lunar regolith materials. In mature soils, it is the size and distribution of the nanophase metal in the soil grains that has the major effect on optical properties. In this report, we compare and contrast the space-weathering effects in an immature and a mature soil with similar elemental compositions. For this study, we analyzed <10 micron sieve fractions of two Apollo 17 soils, 79221 (mature, Is/FeO = 81) and 71061 (immature, Is/FeO = 14). Details of the sieving procedures and allocation scheme are given else where. The results of other detailed chemical, mineralogical, and spectroscopic analyses of these soil samples are reported elsewhere. A representative sample of each soil was embedded in low-viscosity epoxy, and thin sections (about 70nm thick) were obtained through ultra microtomy. The thin sections used for these analyses typically contained cross sections of up to 500 individual grains. The thin sections were studied using a JEOL 2010 transmission electron microscope (TEM) equipped with a thin window energy-dispersive X-ray (EDX) spectrometer. An individual thin section was selected from each soil, and for each grain in the section we determined (1) the elemental composition by EDX; (2) whether the grain was crystalline or glassy using electron diffraction and darkfield imaging; (3) the presence or absence of rims and accreted material; and (4) the distribution of nanophase Fe where present. Most of the categories are self-evident; however, we divide the agglutinate derived material into agglutinitic glass (glass with approximately the same composition as the bulk soil that contains nanophase Fe with or without vesicles) and agglutinate fragments, which are composed of crystalline grains and agglutinitic glass. Lithic fragments are defined as polymineralic grains with no glass. Pyroxene grains have been divided into high- and low-Ca groups. As expected, there are a number of differences in the petrography of the <10-microns fractions of 79221 and 71061 given the great difference in their respective maturities, but we focus here on two major distinctions: agglutinate content and the number of grains with micropatina. Slightly over 50% of the particles in 79221 consist of agglutinitic glass and agglutinate fragments, while the remainder are predominantly crystalline mineral grains. The agglutinic glass particles contain abundant nanophase Fe and vesicles. Angular particles are rare, with most showing smooth, rounded exteriors, Of the mineral grains analyzed thus far, over 90% of the grains have amorphous rims that contain nanophase Fe (these rims are believed to have formed by vapor deposition and irradiation effects). The nanophase Fe in these rims probably accounts for a significant fraction of the increase in Is/FeO measured in these size fractions. In addition to the rims, the majority of particles also show abundant accreted material in the form of glass splashes and spherules that also contain nanophase Fe. In stark contrast, the surfaces of the mineral grains in the 71061 sample are relatively prisitine, as only about 14% of the mineral grains in the sample exhibited amorphous rims. Furthermore, the mineral particles are more angular and show greater surface roughness than in the mature sample. Accreted material on particle surfaces is rare. Agglutinitic material is a major component of the 71061 sample; however, nanophase Fe and vesicles are not as well developed as in the 79221 sample. It is now recognized that nanophase Fe is probably the main agent in modifying the optical properties of lunar soil grains. The most important result of this study is the observation that in the fine size fractions of mature soils, nearly every grain has nanophase Fe within 100 run of the particle surface. (Additional Information contained in original)

Keller, L. P.↗

NASA NTRSDate not supplied

High Temperature Material Property Data and Challenges to Thermal Process Model Predictions and In-Situ/Ex-Situ Measurements for Metallic Additive Manufacturing

Understanding and predicting performance properties of parts produced by metallic additive manufacturing has improved significantly over the past decade; however, difficult to measure material properties and process outcomes continue to be challenges. The qualification or certification of aerospace parts require extensive measures to quantify variable part properties in order to buy down the risk of component failure. The variability, inherent to the additive manufacturing, process adds unwanted uncertainty in the production of load critical structural components. Process modeling has proven valuable in providing predictions and context for understanding outcomes of the additive manufacturing process; however, these physically informed process models require material properties at temperatures that are difficult to measure and rarely available. Further, calibrating or validating such models is difficult because the process itself is challenging to measure. This talk will explore some of the challenges resulting from difficult to acquire input data by relating thermal process model predictions to in-situ and ex-situ optical microscopy measurements.

Process Model↗

NASA NTRS2003

Refinement of Protocols for Measuring the Apparent Optical Properties of Seawater

Ocean color satellite missions, like the Sea-viewing Wide Field-of-view Sensor (SeaWiFS) or the Moderate Resolution Imaging Spectroradiometer (MODIS) projects, are tasked with acquiring a global ocean color data set, validating and monitoring the accuracy and quality of the data, processing the radiometric data into geophysical units using a set of atmospheric and bio-optical algorithms, and distributing the final products to the scientific community. The long-standing requirement of the SeaWiFS Project, for example, is to produce spectral water-leaving radiances, LW(lambda), to within 5% absolute (lambda denotes wavelength) and chlorophyll a concentrations to within 35% (Hooker and Esaias 1993), and most ocean color sensors have the same or similar requirements. Although a diverse set of activities are required to ensure the accuracy requirements are met (Hooker and McClain 2000), the perspective here is with field observations. The accurate determination of upper ocean apparent optical properties (AOPs) is essential for the vicarious calibration of ocean color data and the validation of the derived data products, because the sea-truth measurements are used to evaluate the satellite observations (Hooker and McClain 2000). The uncertainties with in situ AOP measurements have various sources: a) the sampling procedures used in the field, including the environmental conditions encountered; b) the absolute characterization of the radiometers in the laboratory; c) the conversion of the light signals to geophysical units in a processing scheme, and d) the stability of the radiometers in the harsh environment they are subjected to during transport and use. Assuming ideal environmental conditions, so this aspect can be neglected, the SeaWiFS ground-truth uncertainty budget can only be satisfied if each uncertainty is on the order of 1-2%, or what is generally referred to as 1% radiometry. In recent years, progress has been made in estimating the magnitude of some of these uncertainties and in defining procedures for minimizing them. For the SeaWiFS Project, the first step was to convene a workshop to draft the SeaWiFS Ocean Optics Protocols (hereafter referred to as the Protocols). The Protocols initially adhered to the Joint Global Ocean Flux Study (JGOFS) sampling procedures (JGOFS 1991) and defined the standards for optical measurements to be used in SeaWiFS calibration and validation activities (Mueller and Austin 1992). Over time, the Protocols were revised (Mueller and Austin 1995), and then recurringly updated on essentially an annual basis (Mueller 2000, 2002, and 2003) as part of the Sensor Inter-comparison and Merger for Biological and Interdisciplinary Oceanic Studies (SIMBIOS) project. 98

Hooker, Stanford B.↗

NASA NTRS2009

Software Development to Assist in the Processing and Analysis of Data Obtained Using Fiber Bragg Grating Interrogation Systems

A fiber Bragg grating is a portion of a core of a fiber optic strand that has been treated to affect the way light travels through the strand. Light within a certain narrow range of wavelengths will be reflected along the fiber by the grating, while light outside that range will pass through the grating mostly undisturbed. Since the range of wavelengths that can penetrate the grating depends on the grating itself as well as temperature and mechanical strain, fiber Bragg gratings can be used as temperature and strain sensors. This capability, along with the light-weight nature of the fiber optic strands in which the gratings reside, make fiber optic sensors an ideal candidate for flight testing and monitoring in which temperature and wing strain are factors. The purpose of this project is to research the availability of software capable of processing massive amounts of data in both real-time and post-flight settings, and to produce software segments that can be integrated to assist in the task as well.

Hicks, Rebecca↗

NASA NTRS2006

Symmetric Phase Only Filtering for Improved DPIV Data Processing

The standard approach in Digital Particle Image Velocimetry (DPIV) data processing is to use Fast Fourier Transforms to obtain the cross-correlation of two single exposure subregions, where the location of the cross-correlation peak is representative of the most probable particle displacement across the subregion. This standard DPIV processing technique is analogous to Matched Spatial Filtering, a technique commonly used in optical correlators to perform the crosscorrelation operation. Phase only filtering is a well known variation of Matched Spatial Filtering, which when used to process DPIV image data yields correlation peaks which are narrower and up to an order of magnitude larger than those obtained using traditional DPIV processing. In addition to possessing desirable correlation plane features, phase only filters also provide superior performance in the presence of DC noise in the correlation subregion. When DPIV image subregions contaminated with surface flare light or high background noise levels are processed using phase only filters, the correlation peak pertaining only to the particle displacement is readily detected above any signal stemming from the DC objects. Tedious image masking or background image subtraction are not required. Both theoretical and experimental analyses of the signal-to-noise ratio performance of the filter functions are presented. In addition, a new Symmetric Phase Only Filtering (SPOF) technique, which is a variation on the traditional phase only filtering technique, is described and demonstrated. The SPOF technique exceeds the performance of the traditionally accepted phase only filtering techniques and is easily implemented in standard DPIV FFT based correlation processing with no significant computational performance penalty. An "Automatic" SPOF algorithm is presented which determines when the SPOF is able to provide better signal to noise results than traditional PIV processing. The SPOF based optical correlation processing approach is presented as a new paradigm for more robust cross-correlation processing of low signal-to-noise ratio DPIV image data."

Wernet, Mark P.↗

NASA NTRS1985

Airborne atmospheric electricity experiments

During the 1984 U2 spring flight program, lightning spectra were measured in the wavelengths from 380 nm to 900 nm with a temporal resolution of 5 ms. With this capability, researchers simultaneously acquired both visible near-infrared lightning spectra on a pulse to pulse basis, so that the spectral variability within a flash, as well as flash to flash variations, can be studied. Preliminary results suggest that important variations do occur, particularly in the strengths of the hydrogen and singly ionized nitrogen emission lines. Also, the results have revealed significant differences in the integrated energy distributions between the lightning spectra measured above clouds and the spectral measurements of cloud-to-ground lightning made at the ground. In particular, the ratio of the energy in the near-IR to that in the visible is around 1 to 2 for cloud top spectra versus about 1/3 for surface observations. Detailed analyses of the 1984 lightning spectral data is being conducted. This data should provide improved understanding about the optical transmission properties of thunderclouds and the physics of the lightning discharge process. Efforts continue on developing and testing background signal removal algorithms using U2 spectometer and optical array sensor day-flight data sets. The goal of this research is to develop an algorithm satisfying Lightning Mapper Sensor requirements.

Blakeslee, R. J.↗

NASA NTRS2012

Experimental Evaluation of the "Polished Panel Optical Receiver" Concept on the Deep Space Network's 34 Meter Antenna

The potential development of large aperture ground-based "photon bucket" optical receivers for deep space communications has received considerable attention recently. One approach currently under investigation proposes to polish the aluminum reflector panels of 34-meter microwave antennas to high reflectance, and accept the relatively large spotsize generated by even state-of-the-art polished aluminum panels. Here we describe the experimental effort currently underway at the Deep Space Network (DSN) Goldstone Communications Complex in California, to test and verify these concepts in a realistic operational environment. A custom designed aluminum panel has been mounted on the 34 meter research antenna at Deep-Space Station 13 (DSS-13), and a remotely controlled CCD camera with a large CCD sensor in a weather-proof container has been installed next to the subreflector, pointed directly at the custom polished panel. Using the planet Jupiter as the optical point-source, the point-spread function (PSF) generated by the polished panel has been characterized, the array data processed to determine the center of the intensity distribution, and expected communications performance of the proposed polished panel optical receiver has been evaluated.

photon counting detection↗

NASA NTRS1971

Simultaneous solution for the masses of the principal planets from analysis of optical, radar, and radio tracking data.

The Jet Propulsion Laboratory has developed a set of computer programs known as the Solar System Data Processing System (SSDPS) which is employed in improving the ephemerides of the major planets and for improving the values of several associated astronomical constants. A group of solutions for the masses of the major planets, together with the AU and radii of Mercury, Venus, and Mars, is presented. These solutions based upon optical, radar, and spacecraft radio tracking data are preliminary. The relative power of radar and radio tracking data vis-a-vis purely optical data in a solution is shown. The problems which could arise by adopting solutions based upon a single data type are demonstrated.

Lieske, J. H.↗

DOE OSTI2021

KS4A-Omics1.0_FspDS682

Soil fungi facilitate the translocation of inorganic nutrients from soil minerals to other microorganisms and plants. This ability is particularly advantageous in impoverished soils, because fungal mycelial networks can bridge otherwise spatially disconnected and inaccessible nutrient hotspots. However, the molecular mechanisms underlying fungal mineral weathering and transport through soil remains poorly understood. Here, we addressed this knowledge gap by directly visualizing nutrient acquisition and transport through fungal hyphae in a mineral doped soil micromodel using a multimodal imaging approach. Here, we observed how a representative of common saprotrophic soil fungi, Fusarium sp. DS 682, exhibited a mechanosensory response (thigmotropism) around obstacles and through pore spaces (~12 μm) in the presence of minerals.This study establishes the significance of fungal biology and nutrient translocation mechanisms in maintaining fungal growth under water and nutrient limitations in a soil-like microenvironment, using a high-throughput multi-omic analysis approach. Data package KS4A-Omics.1.0_FspDS682 (Publication: Fungal Mineral Weathering Mechanisms Revealed Through Direct Molecular Visualization) contents reported here are the first version (1.0) and contain pre- and post-processed data using high throughput data capture technologies for multi-omic analysis and integration, this data package contains raw and post-processed experimental data for X-Ray Absorption Near Edge Structure Spectroscopy (XANES/XRF), Optical Microscopy, Proteomics, Scanning Electron Microscope (SEM), Time-of-Flight Secondary Ion Mass Spectroscopy (ToF-SIMS), X-Ray Diffraction Spectroscopy (XRD) files, and X- Ray Photoelectron Spectroscopy (XPS) using EMSL capabilities. This data package DOI contains a comprehensive collection of high-throughput multi-omics data and process metadata catalog. Support files include additional data download contents “Read Me” with dataset descriptor information and data source method application ontologies (see data dictionary section). Reported data download content is structured for compliance with reported guidelines provided by community standard initiatives and publisher stakeholder policies supporting FAIR data principles.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Two-colour dissipative solitons and breathers in microresonator second-harmonic generation

Frequency conversion of dissipative solitons associated with the generation of broadband optical frequency combs having a tooth spacing of hundreds of giga-hertz is a topical challenge holding the key to practical applications in precision spectroscopy and data processing. The work in this direction is underpinned by fundamental problems in nonlinear and quantum optics. Here, we present the dissipative two-colour bright-bright and dark-dark solitons in a quasi-phase-matched microresonator pumped for the second-harmonic generation in the near-infrared spectral range. We also found the breather states associated with the pulse front motion and collisions. The soliton regime is found to be typical in slightly phase-mismatched resonators, while the phase-matched ones reveal broader but incoherent spectra and higher-order harmonic generation. Soliton and breather effects reported here exist for the negative tilt of the resonance line, which is possible only via the dominant contribution of second-order nonlinearity.

42 ENGINEERING↗

NASA NTRS2016

Development and Implementation of a Generic Analysis Template for Structural-Thermal-Optical-Performance Modeling

Performance-related effects of system level temperature changes can be a key consideration in the design of many types of optical instruments. This is especially true for space-based imagers, which may require complex thermal control systems to maintain alignment of the optical components. Structural-Thermal-Optical-Performance (STOP) analysis is a multi-disciplinary process that can be used to assess the performance of these optical systems when subjected to the expected design environment. This type of analysis can be very time consuming, which makes it difficult to use as a trade study tool early in the project life cycle. In many cases, only one or two iterations can be performed over the course of a project. This limits the design space to best practices since it may be too difficult, or take too long, to test new concepts analytically. In order to overcome this challenge, automation, and a standard procedure for performing these studies is essential. A methodology was developed within the framework of the Comet software tool that captures the basic inputs, outputs, and processes used in most STOP analyses. This resulted in a generic, reusable analysis template that can be used for design trades for a variety of optical systems. The template captures much of the upfront setup such as meshing, boundary conditions, data transfer, naming conventions, and post-processing, and therefore saves time for each subsequent project. A description of the methodology and the analysis template is presented, and results are described for a simple telescope optical system.

Scola, Salvatore↗

NASA NTRS1993

Inverting Image Data For Optical Testing And Alignment

Data from images produced by slightly incorrectly figured concave primary mirror in telescope processed into estimate of spherical aberration of mirror, by use of algorithm finding nonlinear least-squares best fit between actual images and synthetic images produced by multiparameter mathematical model of telescope optical system. Estimated spherical aberration, in turn, converted into estimate of deviation of reflector surface from nominal precise shape. Algorithm devised as part of effort to determine error in surface figure of primary mirror of Hubble space telescope, so corrective lens designed. Modified versions of algorithm also used to find optical errors in other components of telescope or of other optical systems, for purposes of testing, alignment, and/or correction.

Shao, Michael↗