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NASA NTRS2018

The Harmonized Landsat and Sentinel-2 Surface Reflectance Data Set

The Harmonized Landsat and Sentinel-2 (HLS) project is a NASA initiative aiming to produce a VirtualConstellation (VC) of surface reflectance (SR) data acquired by the Operational Land Imager (OLI) and MultiSpectral Instrument (MSI) aboard Landsat 8 and Sentinel-2 remote sensing satellites, respectively. The HLS products are based on a set of algorithms to obtain seamless products from both sensors (OLI and MSI): atmospheric correction, cloud and cloud-shadow masking, spatial co-registration and common gridding, bidirectional reflectance distribution function normalization and spectral bandpass adjustment. Three products are derivedfrom the HLS processing chain: (i) S10: full resolution MSI SR at 10 m, 20 m and 60 m spatial resolutions; (ii)S30: a 30 m MSI Nadir BRDF (Bidirectional Reflectance Distribution Function)-Adjusted Reflectance (NBAR);(iii) L30: a 30 m OLI NBAR. All three products are processed for every Level-1 input products from Landsat 8/OLI (L1T) and Sentinel-2/MSI (L1C). As of version 1.3, the HLS data set covers 10.35 million km2 and spans from first Landsat 8 data (2013); Sentinel-2 data spans from October 2015. The L30 and S30 show a good consistency with coarse spatial resolution products, in particular MODIS Collection 6 MCD09CMG products (overall deviations do not exceed 11%) that are used as a reference for quality assurance. The spatial co-registration of the HLS is improved compared to original Landsat 8 L1T and Sentinel 2A L1C products, for which misregistration issues between multi-temporal data are known. In particular, the resulting computed circular errors at 90% for the HLS product are 6.2 m and 18.8 m, for S10 and L30 products, respectively. The main known issue of the current data set remains the Sentinel-2 cloud mask with many cloud detection omissions. The cross-comparison with MODIS was used to flag products with most evident non-detected clouds. A time series outlier filtering approach is suggested to detect remaining clouds. Finally, several time series are presented to highlight the high potential of the HLS data set for crop monitoring.

Landsat Sentinel-2↗
NASA NTRS2021

Chapter 13: Errors and Uncertainties Associated with Quasi-Global Satellite Precipitation Products

Measuring precipitation on a global scale is only possible from satellite platforms. Satellite precipitation estimates are based on geosynchronous infrared sensors on geostationary satellites, characterized by high sampling frequency, and polar-orbiting microwave sensors on low-Earth-orbiting satellites with less-frequent sampling. Assessing satellite product performance is fundamental to infer the reliability of such estimates and effectively use them in water resources management, extreme event characterization, disease control, or weather forecasting. Nevertheless, errors and uncertainties associated with satellite precipitation products are often masked due to temporal and spatial sampling, as well as bias-corrections against a reference dataset. Moreover, the verification of satellite precipitation products is easier over land areas, where rain gauges and ground radars are available as benchmark, but extremely limited over the oceans. Substantial work still remains to better quantify relative and absolute errors and uncertainties within satellite-based precipitation products over land and oceans.

Viviana Maggioni↗
NASA NTRS2024

PRODEM: An Annual Series of Summer DEMs (2019 through 2022) of the Marginal Areas of the Greenland Ice Sheet

Surface topography across the marginal zone of the Greenland Ice Sheet is constantly evolving in response to changing weather, season, climate, and ice dynamics. However, current digital elevation models (DEMs) for the ice sheet are usually based on data from a multi-year period, thus obscuring these changes over time. Here we present four 500 m resolution summer DEMs (PRODEMs) of the Greenland Ice Sheet marginal zone for 2019 through 2022. The PRODEMs cover the marginal zone from the ice edge to 50 km inland, hence capturing all Greenland outlet glaciers. Each PRODEM is based on data fusion of CryoSat-2 radar altimetry and ICESat-2 laser altimetry using regionally varying kriging of elevation anomalies relative to ArcticDEM. The PRODEMs are validated using leave-one-out cross-validation, and PRODEM19 is further validated against an external data set, showcasing their ability to correctly represent surface elevations within the associated spatially varying prediction uncertainties. We observe a general lowering of surface elevations during the 4-year PRODEM period, but the spatial pattern of change is highly complex and with annual changes superimposed. The PRODEMs enable detailed studies of the marginal ice sheet elevation changes. With their high spatio-temporal resolution, the PRODEMs will be of value to a wide range of researchers and users studying ice sheet dynamics and monitoring how the ice sheet responds to changing environmental conditions. PRODEMs from summer 2019 through 2022 are available at https://doi.org/10.22008/FK2/52WWHG (Winstrup, 2024), and we plan to annually update the product henceforth.

Digital Elevation Models↗
NASA NTRS2013

Characterization and Correction of Aquarius Long Term Calibration Drift Using On-Earth Brightness Temperature Refernces

The Aquarius/SAC-D mission was launched on June 10, 2011 from Vandenberg Air Force Base. Aquarius consists of an L-band radiometer and scatterometer intended to provide global maps of sea surface salinity. One of the main mission objectives is to provide monthly global salinity maps for climate studies of ocean circulation, surface evaporation and precipitation, air/sea interactions and other processes. Therefore, it is critical that any spatial or temporal systematic biases be characterized and corrected. One of the main mission requirements is to measure salinity with an accuracy of 0.2 psu on montly time scales which requires a brightness temperature stability of about 0.1K, which is a challenging requirement for the radiometer. A secondary use of the Aquarius data is for soil moisture applications, which requires brightness temperature stability at the warmer end of the brightness temperature dynamic range. Soon after launch, time variable drifts were observed in the Aquarius data compared to in-situ data from ARGO and models for the ocean surface salinity. These drifts could arise from a number of sources, including the various components of the retrieval algorithm, such as the correction for direct and reflected galactic emission, or from the instrument brightness temperature calibration. If arising from the brightness temperature calibration, they could have gain and offset components. It is critical that the nature of the drifts be understood before a suitable correction can be implemented. This paper describes the approach that was used to detect and characterize the components of the drift that were in the brightness temperature calibration using on-Earth reference targets that were independent of the ocean model.

Aquarius↗
NASA NTRS2023

A Multi-Pixel Split-Window Approach to Sea Surface Temperature Retrieval from Thermal Imagers with Relatively High Radiometric Noise: Preliminary Studies

In the following decade(s), a set of satellite missions carrying thermal infrared (TIR) imagers with a relatively high noise equivalent differential temperature (NEdT) are expected, e.g., the high resolution TIR imagers flying on the future Thermal infraRed Imaging Satellite for High-resolution Natural resource Assessment (TRISHNA), Land Surface Temperature Monitoring (LSTM) and NASA-JPL/ASI Surface Biology and Geology Thermal (SBG) missions or the secondary payload on board the ESA Earth Explorer 10 Harmony. The instruments on board these missions are expected to be characterized by an NEdT of ⪆0.1 K. In order to reduce the impact of radiometric noise on the retrieved sea surface temperature (SST), this study investigates the possibility of applying a multi-pixel atmospheric correction based on the hypotheses that (i) the spatial variability scales of radiatively active atmospheric variables are, on average, larger than those of the SST and (ii) the effect of atmosphere is accounted for via the split window (SW) difference. Based on 32 Sentinel 3 SLSTR case studies selected in oceanic regions where SST features are mainly driven by meso to sub-mesoscale turbulence (e.g., corresponding to major western boundary currents), this study documents that the local spatial variability of the SW difference term on the scale of ≃3 × 3 km2 is comparable with the noise associated with the SW difference. Similarly, the power spectra of the SW term are shown to have, for small scales, the behavior of white noise spectra. On this basis, we suggest to average the SW term and to use it for the atmospheric correction procedure to reduce the impact of radiometric noise. In principle, this methodology can be applied on proper scales that can be dynamically defined for each pixel. The applicability of our findings to high-resolution TIR missions is discussed and an example of an application to ECOSTRESS data is reported.

sea surface temperature↗
NASA NTRS1987

Analyses and assessments of span wise gust gradient data from NASA B-57B aircraft

Analysis of turbulence measured across the airfoil of a Cambera B-57 aircraft is reported. The aircraft is instrumented with probes for measuring wind at both wing tips and at the nose. Statistical properties of the turbulence are reported. These consist of the standard deviations of turbulence measured by each individual probe, standard deviations and probability distribution of differences in turbulence measured between probes and auto- and two-point spatial correlations and spectra. Procedures associated with calculations of two-point spatial correlations and spectra utilizing data were addressed. Methods and correction procedures for assuring the accuracy of aircraft measured winds are also described. Results are found, in general, to agree with correlations existing in the literature. The velocity spatial differences fit a Gaussian/Bessel type probability distribution. The turbulence agrees with the von Karman turbulence correlation and with two-point spatial correlations developed from the von Karman correlation.

Frost, Walter↗
NASA NTRS2020

Airborne Radiometry for Calibration, Validation, and Research in Oceanic, Coastal, and Inland Waters

Present-day ocean color satellite sensors, which principally provide reliable data on chlorophyll, sediments, and colored dissolved organic material in the open ocean, are not well suited for coastal and inland water studies for a variety of reasons, including coarse spatial and spectral resolution plus challenges with atmospheric correction. National Aeronautics and Space Administration (NASA) airborne mission concepts tested in 2011, 2013, 2017, and 2018 over Monterey Bay, CA, and nearby inland waters have demonstrated the feasibility of improving airborne monitoring and research activities in case-1 and case-2 aquatic ecosystems through the combined use of state-of-the-art above- and in-water measurement capabilities. These competencies have evolved through time to produce a sensor-web approach: imaging spectrometer, microradiometers, and a sun photometer (airborne) with their analogous algorithms, and with corresponding in-water radiometers and ground-based sun photometry. The NASA airborne instrument suite and mission concept demonstrations, leveraging high quality above- and in-water data, significantly improves the fidelity as well as the spatial and spectral resolution of observations for studying and monitoring water quality in oceanic, coastal, and inland water ecosystems. The goal of this series of projects was to develop and fly a portable airborne sensor suite for NASA science missions focusing on a gradient of water types from oligotrophic to turbid waters addressing the challenges of an optically complex coastal ocean zone and inland waters. The airborne radiometry in this range of aquatic conditions and sites has supported improved results of studies of water quality and biogeochemistry and provides capabilities for research areas such as ocean productivity and biogeochemistry; aquatic impacts of coastal landscape alteration; coastal, estuarine, and inland waters ecosystem productivity; atmospheric correction; and regional climate variability.

atmospheric correction↗
NASA NTRS2021

Impact of environmental attributes on the uncertainty in MAIAC/MODIS AOD retrievals: A comparative analysis

This work examines the impact of different environmental attributes on the uncertainty in satellite-based Aerosol Optical Depth (AOD) retrieval against the benchmark Aerosol Robotic Network (AERONET) AOD measurements at 21 sites across North Africa, California and Germany, in the years 2007–2017. As a first step, we studied the effects of spatial averaging the Multi-Angle Implementation of Atmospheric Correction (MAIAC) AOD retrievals, and of temporal averaging the AERONET AOD around the satellite (Aqua) overpass, on the agreement between the two products. AERONET AOD averaging over a time-window of ±15 min around the satellite overpass and the 1 ×1 km2 spatial grid of MAIAC were found to provide the best AOD retrieval performance. Next, MAIAC AOD were stratified according to different co-measured environmental attributes (aerosol loading, dominant particle size, vegetation cover, and prevailing particle type) and analyzed against the AERONET AOD. The envelope of the expected retrieval error varied considerably among different environmental attributes categories, with more accurate AOD retrievals obtained over highly vegetated areas (i.e. less surface reflectance) than over arid areas. Moreover, the retrieval accuracy was found to be sensitive to the aerosol loading and particle size, with a large bias between the MAIAC and AERONET AOD during high aerosol loading of coarse particles. In addition, the retrieval accuracy of MAIAC AOD was found to depend on the aerosol type due to the aerosol model assumptions regarding their optical properties.

AOD RETRIEVAL↗
NASA NTRS2006

Thermal Band Atmospheric Correction Using Atmospheric Profiles Derived from Global Positioning System Radio Occultation and the Atmospheric Infrared Sounder

This Rapid Prototyping Capability study explores the potential to use atmospheric profiles derived from GPS (Global Positioning System) radio occultation measurements and by AIRS (Atmospheric Infrared Sounder) onboard the Aqua satellite to improve surface temperature retrieval from remotely sensed thermal imagery. This study demonstrates an example of a cross-cutting decision support technology whereby NASA data or models are shown to improve a wide number of observation systems or models. The ability to use one data source to improve others will be critical to the GEOSS (Global Earth Observation System of Systems) where a large number of potentially useful systems will require auxiliary datasets as input for decision support. Atmospheric correction of thermal imagery decouples TOA radiance and separates surface emission from atmospheric emission and absorption. Surface temperature can then be estimated from the surface emission with knowledge of its emissivity. Traditionally, radiosonde sounders or atmospheric models based on radiosonde sounders, such as the NOAA (National Oceanic & Atmospheric Administration) ARL (Air Resources Laboratory) READY (Real-time Environmental Application and Display sYstem), provide the atmospheric profiles required to perform atmospheric correction. Unfortunately, these types of data are too spatially sparse and too infrequently taken. The advent of high accuracy, global coverage, atmospheric data using GPS radio occultation and AIRS may provide a new avenue for filling data input gaps. In this study, AIRS and GPS radio occultation derived atmospheric profiles from the German Aerospace Center CHAMP (CHAllenging Minisatellite Payload), the Argentinean Commission on Space Activities SAC-C (Satellite de Aplicaciones Cientificas-C), and the pair of NASA GRACE (Gravity Recovery and Climate Experiment) satellites are used as input data in atmospheric radiative transport modeling based on the MODTRAN (MODerate resolution atmospheric TRANsmittance) radiative transport software to separate out the atmospheric component of measured top of atmosphere radiance. Simulated water bodies across a variety of MODTRAN model atmospheres including desert, mid-latitude, tropical and sub-artic conditions provide test bed conditions. Atmospherically corrected radiance and surface temperature results were compared to those obtained using traditional radiosonde balloon data and models. In general, differences between the different techniques were less than 2 percent indicating the potential value satellite derived atmospheric profiles have to atmospherically correct thermal imagery.

Pagnutti, Mary↗
NASA NTRS1976

A LANDSAT digital image rectification system

DIRS is a digital image rectification system for the geometric correction of LANDSAT multispectral scanner digital image data. DIRS removes spatial distortions from the data and brings it into conformance with the Universal Transverse Mercator (UTM) map projection. Scene data in the form of landmarks are used to drive the geometric correction algorithms. Two dimensional least squares polynominal and spacecraft attitude modeling techniques for geometric mapping are provided. Entire scenes or selected quadrilaterals may be rectified. Resampling through nearest neighbor or cubic convolution at user designated intervals is available. The output products are in the form of digital tape in band interleaved, single band or CCT format in a rotated UTM projection. The system was designed and implemented on large scale IBM 360 computers.

Vanwie, P.↗
NASA NTRS1991

The measurement of atmospheric water vapor - Radiometer comparison and spatial variations

Two water vapor radiometer (WVR) experiments were conducted to evaluate whether such instruments are both suitable and necessary to correct for propagation effects that are induced by precipitable water vapor (PWV) on signals from GPS and VLBI. WVRs are suitable for these corrections if they provide wet path delays to better than 0.5 cm. They are needed if spatial variations of PWV result in complicated, direction-dependent propagation effects that are too complex to be parametrized in the GPS or VLBI geodetic solution. The suitability of radiometers was first addressed by comparing six airport WVRs for two weeks. While two WVRs showed an average wet path delay bias of only 0.1 cm, others were biased by 1-3 cm relative to each other and relative to radiosondes. The second experiment addressed the question whether radiometers are needed for the detection of inhomogeneities in the wet delay. Three JPL D-series radiometers were operated at three sites 50 km apart. The WVRs simultaneously sampled PWV at different azimuths and elevations in search of spatial variations of PWV. On one day of this second experiment evidence was found for spatial variations of the wet path delay as high as 20 percent of the total wet path delay.

Rocken, C.↗
NASA NTRS2012

Multi-Angle Implementation of Atmospheric Correction for MODIS (MAIAC). Part 3: Atmospheric Correction

This paper describes the atmospheric correction (AC) component of the Multi-Angle Implementation of Atmospheric Correction algorithm (MAIAC) which introduces a new way to compute parameters of the Ross-Thick Li-Sparse (RTLS) Bi-directional reflectance distribution function (BRDF), spectral surface albedo and bidirectional reflectance factors (BRF) from satellite measurements obtained by the Moderate Resolution Imaging Spectroradiometer (MODIS). MAIAC uses a time series and spatial analysis for cloud detection, aerosol retrievals and atmospheric correction. It implements a moving window of up to 16 days of MODIS data gridded to 1 km resolution in a selected projection. The RTLS parameters are computed directly by fitting the cloud-free MODIS top of atmosphere (TOA) reflectance data stored in the processing queue. The RTLS retrieval is applied when the land surface is stable or changes slowly. In case of rapid or large magnitude change (as for instance caused by disturbance), MAIAC follows the MODIS operational BRDF/albedo algorithm and uses a scaling approach where the BRDF shape is assumed stable but its magnitude is adjusted based on the latest single measurement. To assess the stability of the surface, MAIAC features a change detection algorithm which analyzes relative change of reflectance in the Red and NIR bands during the accumulation period. To adjust for the reflectance variability with the sun-observer geometry and allow comparison among different days (view geometries), the BRFs are normalized to the fixed view geometry using the RTLS model. An empirical analysis of MODIS data suggests that the RTLS inversion remains robust when the relative change of geometry-normalized reflectance stays below 15%. This first of two papers introduces the algorithm, a second, companion paper illustrates its potential by analyzing MODIS data over a tropical rainforest and assessing errors and uncertainties of MAIAC compared to conventional MODIS products.

Lyapustin, A.↗
NASA NTRS1976

A Landsat Digital Image Rectification System

DIRS is a Digital Image Rectification System for the geometric correction of Landsat Multispectral Scanner digital image data. DIRS removes spatial distortions from the data and brings it into conformance with the Universal Transverse Mercator (UTM) map projection. Scene data in the form of landmarks or Ground Control Points (GCPs) are used to drive the geometric correction algorithms. The system offers extensive capabilities for 'shade printing' to aid in the determination of GCPs. Affine, two dimensional least squares polynominal and spacecraft attitude modeling techniques for geometric mapping are provided. Entire scenes or selected quadralaterals may be rectified. Resampling through nearest neighbor or cubic convolution at user designated intervals is available. The output products are in the form of digital tape in band interleaved, single band or CCT format in a rotated UTM projection. The system was designed and implemented on large scale IBM 360 computers with at least 300-500K bytes of memory for user application programs and five nine track tapes plus direct access storage.

Van Wie, P.↗
NASA NTRS1987

Intrinsic frequency spectra of short gravity-capillary waves obtained from temporal measurements of wave height on a lake

Intrinsic frequency spectra of water waves in the range of 6-17 Hz were obtained as a function of both wind speed and wind stress from point measurements of wave height. In a lake with a limited fetch, there are two types of surface motions causing Doppler shift in the frequencies of short waves: orbital velocity of long waves and surface wind drift. The former was estimated from long-wave amplitude by using a linear wave theory. The error in this estimate is of the order of the long-wave slope, and for this work it is typically 10 percent. The latter was approximated by the friction velocity. The friction velocity could be either taken as 3 percent of the mean wind speed measured at a height of 10 m or obtained from direct measurements of the wind stress. The surface drift velocities obtained by these two approaches were found to be in close agreement. Doppler frequency shift can be corrected in either the frequency or the equivalent spatial domain. The two techniques were found to produce comparable results. Experimental results showed that the spectral energy of short waves rapidly increased in response to increasing winds and jumped up by an order of magnitude when wave breaking occurred.

Atakturk, S. S.↗
NASA NTRS1994

A preliminary tidal analysis of TOPEX/POSEIDON altimetry

Approximately 12 months of data from the TOPEX/POSEIDON satellite altimeter mission are analyzed for the major short-period oceanic tides. A harmonic analysis is performed on data captured within bins defined on a deep-ocean grid, which, owing to tidal aliasing considerations, must have a relatively coarse spatial resolution. Our analysis is in terms of corrections to the Schwiderski and Cartwright-Ray models, and it confirms many of the Schwiderski differences previously reported by Cartwright and Ray. Our differences with respect to the Geosat-based Cartwright and Ray model form a sectorial pattern in M(sub 2) with high/low differences separated roughly 180 deg in longitude. We suggest that these sectorial errors were most likely induced by Geosat's relatively large orbit error. Comparisons to independent data validate the improved TOPEX/POSEIDON solutions; in-situ 'ground truth' shows M(sub 2) root mean square (RMS) differences of 4.10 cm (Schwiderski), 3.86 cm (cartwright and Ray), 2.63 cm (this paper). Global rates of energy dissipation confirm earlier estimates for M(sub 2), and show improved agreement with satellite tracking studies for K(sub 1) and S(sub 2). These preliminary exercises confirm that TOPEX/POSEIDON should results in a new generation of improved global tidal models.

Schrama, E. J. O.↗
NASA NTRS1997

Microwave Remote Sensing of Soil Moisture for Estimation of Soil Properties

Surface soil moisture dynamics was derived using microwave remote sensing, and employed to estimate soil physical and hydraulic properties. The L-band ESTAR radiometer was employed in an airborne campaign over the Little Washita watershed, Oklahoma during June 10-18, 1992. Brightness temperature (TB) data were employed in a soil moisture inversion algorithm which corrected for vegetation and soil effects. Analyses of spatial TB and soil moisture dynamics during the dry-down period revealed a direct relationship between changes in TB, soil moisture and soil texture. Extensive regression analyses were carried out which yielded statistically significant quantitative relationships between ratio of percent sand to percent clay (RSC, a term derived to quantify soil texture) and saturated hydraulic conductivity (Ksat) in terms of change components of TB and surface soil moisture. Validation of results indicated that both RSC and Ksat can be estimated with reasonable accuracy. These findings have potential applications for deriving spatial distributions of RSC and Ksat over large areas.

Mattikalli, Nandish M.↗
NASA NTRS2002

The Gas Production Rate and Coma Structure of Comet C/1995 01 (Hale-Bopp)

The University of Wisconsin-Madison and NASA-Goddard conducted a comprehensive multi-wavelength observing campaign of coma emissions from comet Hale-Bopp, including OH 3080 A, [O I] 6300 A, H2O(+) 6158 A, H Balmer-alpha 6563 A, NH2 6330 A, [C I] 9850 A CN 3879 A, C2 5141 A, C3 4062 A, C I 1657 A, and the UV and optical continua. In this work, we concentrate on the results of the H2O daughter studies. Our wide-field OH 3080 A measured flux agrees with other, similar observations and the expected value calculated from published water production rates using standard H2O and OH photochemistry. However, the total [O I] 6300 A flux determined spectroscopically over a similar field-of-view was a factor of 3 - 4 higher than expected. Narrow-band [O I] images show this excess came from beyond the H2O scale length, suggesting either a previously unknown source of [O I] or an error in the standard OH + upsilon to O((sup I)D) + H branching ratio. The Hale-Bopp OH and [O I] distributions, both of which were imaged to cometocentric distances greater than 1 x 10(exp 6) km, were more spatially extended than those of comet Halley (after correcting for brightness differences), suggesting a higher bulk outflow velocity. Evidence of the driving mechanism for this outflow is found in the H(alpha) line profile, which was narrower than in comet Halley (though likely because of opacity effects, not as narrow as predicted by Monte-Carlo models). This is consistent with greater collisional coupling between the suprathermal H photodissociation products and Hale-Bopp's dense coma. Presumably because of mass loading of the solar wind by ions and ions by the neutrals, the measured acceleration of H2O(+) down the ion tail was much smaller than in comet Halley. Tailward extensions in the azimuthal distributions of OH 3080 A, [O I], and [C I], as well as a Doppler asymmetry in the [O I] line profile, suggest ion-neutral coupling. While the tailward extension in the OH can be explained by increased neutral acceleration, the [O I] 6300 A and [C I] 9850 A emissions show 13% and less than 200% excesses in this direction (respectively), suggesting a non-negligible contribution from dissociative recombination of CO(+) and/or electron collisional excitation. Thus, models including the effects of photo-and collisional chemistry are necessary for the full interpretation of these data.

Morgenthaler, Jeffrey P.↗
NASA NTRS2004

Liquid Crystal on Silicon Wavefront Corrector

A low cost, high resolution, liquid crystal on silicon, spatial light modulator has been developed for the correction of huge aberrations in an optical system where the polarization dependence and the chromatic nature are tolerated. However, the overall system performance suggests that this device is also suitable for real time correction of aberration in human eyes. This device has a resolution of 1024 x 768, and is driven by an XGA display driver. The effective stroke length of the device is 700 nm and 2000 nm for the visible and IR regions of the device, respectively. The response speeds are 50 Hz and 5 Hz, respectively, which are fast enough for real time adaptive optics for aberrations in human eyes. By modulating a wavefront of 2 pi, this device can correct for arbitrary high order wavefront aberrations since the 2-D pixel array is independently controlled by the driver. The high resolution and high accuracy of the device allow for diffraction limited correction of the tip and tilt or defocus without an additional correction loop. We have shown that for every wave of aberration, an 8 step blazed grating is required to achieve high diffraction efficiency around 80%. In light of this, up to 125 waves peak to valley of tip and tilt can be corrected if we choose the simplest aberration. Corrections of 34 waves of aberration, including high order Zernicke terms in a high magnification telescope, to diffraction limited performance (residual wavefront aberration less than 1/30 lambda at 632.8 nm) have been observed at high efficiency.

Pouch, John↗