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NASA NTRS2003

Phase Retrieval Using a Genetic Algorithm on the Systematic Image-Based Optical Alignment Testbed

NASA s Marshall Space Flight Center s Systematic Image-Based Optical Alignment (SIBOA) Testbed was developed to test phase retrieval algorithms and hardware techniques. Individuals working with the facility developed the idea of implementing phase retrieval by breaking the determination of the tip/tilt of each mirror apart from the piston motion (or translation) of each mirror. Presented in this report is an algorithm that determines the optimal phase correction associated only with the piston motion of the mirrors. A description of the Phase Retrieval problem is first presented. The Systematic Image-Based Optical Alignment (SIBOA) Testbeb is then described. A Discrete Fourier Transform (DFT) is necessary to transfer the incoming wavefront (or estimate of phase error) into the spatial frequency domain to compare it with the image. A method for reducing the DFT to seven scalar/matrix multiplications is presented. A genetic algorithm is then used to search for the phase error. The results of this new algorithm on a test problem are presented.

Taylor, Jaime R.↗

NASA NTRS1992

An astrometric study of the Mira variable R Leonis and the occultation binary 19 Leonis

The Multichannel Astrometric Photometer (MAP) was used to determine parallaxes of stars in the region centered on the Mira variable R Leonis. R Leonis, with a parallax of 8.3 +/- 1.0 mas (120 +/- 15 pc), is significantly closer than most recent estimates. At visual wavelengths, its mean physical diameter is 612 +/- 96 times that of the sun. The photocentric motion of R Leonis is not suggestive of either optical or orbital companions, excluding possible secondary components over a wide range of magnitudes as well as orbital periods of up to approximately one decade. Nineteen Leonis, an occultation-speckle binary with a well-determined orbit and a reference star in the R Leonis field, has a distance of 92.6 +/- 12 pc. The 15.2 yr period binary exhibits a slight perturbation during the 4 yr of MAP observations. The similar primary and secondary of this A7 Vn system are 2.41 +/- 0.96 and 2.31 +/- 0.92 solar masses, respectively.

Gatewood, George↗

NASA NTRS1972

Solar experiment alignment system

Sensor system determines absolute alignment of optical axis of experiment package relative to solar vector and provides control information to permit pointing experiment anywhere on solar disc to absolute accuracy of the order of two arc seconds in center and five arc seconds on limb.

Fain, D. L.↗

NASA NTRSDate not supplied

On the New Optical Constants Database (OCdb) and its Importance for the Interpretation of Observational Data

The Optical Constants database(ocdb.smce.nasa.gov) came online in February 2023 and provides complex refractive indices of laboratory-generated organic refractory materials and ices relevant to (exo) planetary and astrophysical environments.The goal of the OCdb is to centralize published optical constants data to facilitate both their access by the scientific community and their use to analyze observational data returned by space missions and ground-based observatories. Computational tools are also under development to facilitate scientific use of the available OCdb optical constants data sets. Investigators generating laboratory optical constants are therefore encouraged to contribute their data to OCdb in order to increase the availability of their data and to enhance the scientific effectiveness of the database. Optical constants are critical input parameters in models (e.g.,radiative transfer, atmospheric, and reflectance spectral models)that are used to simulate the absorption, reflection, and scattering of light due to solid materials present in planetary and astrophysical environments (planets, their satellites, exoplanets, asteroids, comets, protoplanetary disks, etc.), and are key to the compositional interpretation of observations. We will first present the infrastructure of the OCdb and show how to use and contribute to it. We will introduce the two large NASA projects, namely, the Laboratory Astrophysics Directed Work Package and the NASA Center for Optical Constants, that have been instrumental in (i) developing the OCdb, (ii) generating planetary-and astrophysics-relevant ices and organic refractory materials from gas and ice irradiation in the laboratory, and (iii) determining their optical constants for inclusion in OCdb. We will also present two studies that are making use of these optical constants to interpret observations of Titan’s atmosphere and Pluto’s surface. These studies show the importance of measuring optical constants of laboratory-generated materials, and their impact on the models used to analyze and interpret astronomical observations. These studies also demonstrate the essential importance of such a database and the need for optical constants of a broad range of materials and wavelengths to enable the scientific community and to maximize the scientific return from space missions (e.g., Cassini, New Horizons, SOFIA, JWST).

The Optical Constants database↗

NASA NTRS2017

Cryogenic Refractive Index of Heraeus Homosil Glass

This paper reports measurements of the refractive index of Homosil (Heraeus) over the wavelength range of 0.34-3.16 microns and temperature range of 120-335 K. These measurements were performed by using the Cryogenic High Accuracy Refraction Measuring System (CHARMS) facility at the NASAs Goddard Space Flight Center. These measurements were in support of an integrated Structural-Thermal-Optical-Performance (STOP) model that was developed for a field-widened Michelson interferometer that is being built and tested for the High Spectral Resolution Lidar (HSRL) project at the NASA Langley Research Center (LaRC). The cryogenic refractive index measurements were required in order to account for the highly sensitivity performance of the HSRL instrument to changes in refractive index with temperature, temperature gradients, thermal expansion, and deformation due to mounting stresses. A dense coverage of the absolute refractive index over the aforementioned wavelength and temperature ranges was used to determine the thermo-optic coefficient (dn/dT) and dispersion relation (dn/d(lamda)) as a function of wavelength and temperature. Our measurements of Homosil will be compared with measurements of other glasses from the fused silica family studied in CHARMS as well as measurements reported elsewhere in literature.

cryogenic↗

NASA NTRS2017

Cryogenic Refractive Index of Heraeus Homosil Glass

This paper reports measurements of the refractive index of Homosil (Heraeus) over the wavelength range of 0.343.16 m and temperature range of 120335 K. These measurements were performed by using the Cryogenic High Accuracy Refraction Measuring System (CHARMS) facility at the NASAs Goddard Space Flight Center. These measurements were in support of an integrated Structural-Thermal-Optical-Performance (STOP) model that was developed for a field-widened Michelson interferometer that is being built and tested for the High Spectral Resolution Lidar (HSRL) project at the NASA Langley Research Center (LaRC). The cryogenic refractive index measurements were required in order to account for the highly sensitivity performance of the HSRL instrument to changes in refractive index with temperature, temperature gradients, thermal expansion, and deformation due to mounting stresses. A dense coverage of the absolute refractive index over the aforementioned wavelength and temperature ranges was used to determine the thermo-optic coefficient (dndT) and dispersion relation (dnd) as a function of wavelength and temperature. Our measurements of Homosil will be compared with measurements of other glasses from the fused silica family studied in CHARMS as well as measurements reported elsewhere in literature.

Homosil↗

NASA NTRS2010

Crossed, Small-Deflection Energy Analyzer for Wind/Temperature Spectrometer

Determination of neutral winds and ion drifts in low-Earth-orbit missions requires measurements of the angular and energy distributions of the flux of neutrals and ions entering the satellite from the ram direction. The magnitude and direction of the neutral-wind (or ion-drift) determine the location of the maximum in the angular distribution of the flux. Knowledge of the angle of maximum flux with respect to satellite coordinates (pointing) is essential to determine the wind (or ion-drift) vector. The crossed Small-Deflection Energy Analyzer (SDEA) spectrometer (see Figure 1) occupies minimal volume and consumes minimal power. Designed for upper atmosphere/ionosphere investigations at Earth altitudes above 100 km, the spectrometer operates by detecting the angular and energy distributions of neutral atoms/molecules and ions in two mutually perpendicular planes. In this configuration, the two detection planes actually cross at the spectrometer center. It is possible to merge two SDEAs so they share a common optical axis and alternate measurements between two perpendicular planes, and reduce the number of ion sources from two to one. This minimizes the volume and footprint significantly and reduces the ion source power by a factor of two. The area of the entrance aperture affects the number of ions detected/second and also determines the energy resolution. Thermionic emitters require heater power of about 100 mW to produce 1 mA of electron beam current. Typically, electron energy is about 100 eV and requires a 100-V supply for electron acceleration to supply an additional 100 mW of power. Thus, ion source power is at most 200 mW. If two ion sources were to be used, the ion source power would be, at most, 400 mW. Detector power, deflection voltage power, and microcontroller and other functions require less than 150 mW. A WTS (wind/ temperature spectrometer) with two separate optical axes would consume about 650 mW, while the crossed SDEA described here consumes about 350 mW. The entrance aperture has a diameter of 0.004 in. (0.10 mm) to provide the required energy resolution between 0.05 and 0.15. This design (see Figure 2) provides a WTS occupying a volume less than 40 cm(sup 3), on a footprint of diameter about 1.5 in. (38 mm). The Crossed SDEA offers many advantages in the measurements of neutral wind and ion drifts in the Earth's thermosphere. As such, it will be useful in future commercial satellites dedicated to monitoring the ionosphere with a view to improving the integrity and predictability of GPS operations.

Herrero, Federico A.↗

NASA NTRS1984

Determination of the mass of globular cluster X-ray sources

The precise positions of the luminous X-ray sources in eight globular clusters have been measured with the Einstein X-Ray Observatory. When combined with similarly precise measurements of the dynamical centers and core radii of the globular clusters, the distribution of the X-ray source mass is determined to be in the range 0.9-1.9 solar mass. The X-ray source positions and the detailed optical studies indicate that (1) the sources are probably all of similar mass, (2) the gravitational potentials in these high-central density clusters are relatively smooth and isothermal, and (3) the X-ray sources are compact binaries and are probably formed by tidal capture.

Grindlay, J. E.↗

NASA NTRS2004

Spectral Absorption of Solar Radiation by Aerosols during ACE-Asia

As part of the Asian Pacific Regional Aerosol Characterization Experiment (ACE-Asia), the upward and downward spectral solar radiant fluxes were measured with the Spectral Solar Flux Radiometer (SSFR), and the aerosol optical depth was measured with the Ames Airborne Tracking Sunphotometer (AATS-14) aboard the Center for INterdisciplinary Remotely-Piloted Aircraft Studies (CIRPAS) Twin Otter aircraft. IN this paper, we examine the data obtained for two cases: a moderately thick aerosol layer, 12 April, and a relatively thin aerosol case, 16 April 2001. ON both days, the Twin Otter flew vertical profiles in the Korean Strait southeast of Gosan Island. For both days we determine the aerosol spectral absorption of the layer and estimate the spectral aerosol absorption optical depth and single-scattering albedo. The results for 12 April show that the single-scattering albedo increases with wavelength from 0.8 at 400 nm to 0.95 at 900 nm and remains essentially constant from 950 to 1700 nm. On 16 April the amount of aerosol absorption was very low; however, the aerosol single-scattering albedo appears to decrease slightly with wavelength in the visible region. We interpret these results in light of the two absorbing aerosol species observed during the ACE-asia study: mineral dust and black carbon. The results for 12 April are indicative of a mineral dust-black carbon mixture. The 16 April results are possibly caused by black carbon mixed with nonabsorbing pollution aerosols. For the 12 April case we attempt to estimate the relative contributions of the black carbon particles and the mineral dust particles. We compare our results with other estimates of the aerosol properties from a Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) satellite analysis and aerosol measurements made aboard the Twin Otter, aboard the National Oceanic and Atmospheric Administration Ronald H Brown ship, and at ground sites in Gosan and Japan. The results indicate a relatively complicated aerosol mixture of both industrial pollution (including black carbon) and mineral dust. This underscores the need for careful measurements and analysis to separate out the absorption effects of mineral dust and black carbon in the east Asia region.

Bergstrom, R. W.↗

NASA NTRS1997

Microgravity Processing and Photonic Applications of Organic and Polymeric Materials

Some of the primary purposes of this work are to study important technologies, particularly involving thin films, relevant to organic and polymeric materials for improving applicability to optical circuitry and devices and to assess the contribution of convection on film quality in unit and microgravity environments. Among the most important materials processing techniques of interest in this work are solution-based and by physical vapor transport, both having proven gravitational and acceleration dependence. In particular, PolyDiAcetylenes (PDA's) and PhthaloCyanines (Pc's) are excellent NonLinear Optical (NLO) materials with the promise of significantly improved NLO properties through order and film quality enhancements possible through microgravity processing. Our approach is to focus research on integrated optical circuits and optoelectronic devices relevant to solution-based and vapor processes of interest in the Space Sciences Laboratory at the Marshall Space Flight Center (MSFC). Modification of organic materials is an important aspect of achieving more highly ordered structures in conjunction with microgravity processing. Parallel activities include characterization of materials for particular NLO properties and determination of appropriation device designs consistent with selected applications. One result of this work is the determination, theoretically, that buoyancy-driven convection occurs at low pressures in an ideal gas in a thermalgradient from source to sink. Subsequent experiment supports the theory. We have also determined theoretically that buoyancy-driven convection occurs during photodeposition of PDA, an MSFC-patented process for fabricating complex circuits, which is also supported by experiment. Finally, the discovery of intrinsic optical bistability in metal-free Pc films enables the possibility of the development of logic gate technology on the basis of these materials.

Frazier, Donald O.↗

NASA NTRS1972

Optical absorption in fused silica at elevated temperatures during 1.5-MeV electron irradiation

An experimental determination of the optical transmission of Corning 7940 UV and Suprasil 1 and 2 fused silica has been made during 1.5-MeV electron bombardment. The fused silica reached temperatures ranging from 150 to 1000 C. The Lewis Research Center dynamitron provided electron current densities which corresponded to a dose rate of 2.6 to 20 Mrad/sec. The irradiation induced absorption was measured at 215.0, 270.0, and 450.0 nm (2150, 2700, 4500 A). The length of each irradiation was sufficient so that an equilibrium between radiation induced coloration and high temperature annealing was reached. The experimental results indicate a significant optical absorption, with values of the induced absorption coefficient at 215.0 nm (2150 A) of 14.5 to 2.2/cm, at 270.0 nm (2700 A) of 9.7 to 3.0/cm and at 450.0 nm (4500 A) of 3.7 to 0.5/cm. This would make the use of fused silica as the separating wall material in the nuclear light bulb propulsion concept questionable.

Smith, A. B.↗

NASA NTRS2004

The Precision Formation Flying Integrated Analysis Tool (PFFIAT)

Several space missions presently in the concept phase (e.g. Stellar Imager, Submillimeter Probe of Evolutionary Cosmic Structure, Terrestrial Planet Finder) plan to use multiple spacecraft flying in precise formation to synthesize unprecedently large aperture optical systems. These architectures present challenges to the attitude and position determination and control system; optical performance is directly coupled to spacecraft pointing with typical control requirements being on the scale of milliarcseconds and nanometers. To investigate control strategies, rejection of environmental disturbances, and sensor and actuator requirements, a capability is needed to model both the dynamical and optical behavior of such a distributed telescope system. This paper describes work ongoing at NASA Goddard Space Flight Center toward the integration of a set of optical analysis tools (Optical System Characterization and Analysis Research software, or OSCAR) with the Formation Flying Test Bed (FFTB). The resulting system is called the Precision Formation Flying Integrated Analysis Tool (PFFIAT), and it provides the capability to simulate closed-loop control of optical systems composed of elements mounted on multiple spacecraft. The attitude and translation spacecraft dynamics are simulated in the FFTB, including effects of the space environment (e.g. solar radiation pressure, differential orbital motion). The resulting optical configuration is then processed by OSCAR to determine an optical image. From this image, wavefront sensing (e.g. phase retrieval) techniques are being developed to derive attitude and position errors. These error signals will be fed back to the spacecraft control systems, completing the control loop. A simple case study is presented to demonstrate the present capabilities of the tool.

Stoneking, Eric↗

NASA NTRS2004

The Precision Formation Flying Integrated Analysis Tool (PFFIAT)

Several space missions presently in the concept phase (e.g. Stellar Imager, Sub- millimeter Probe of Evolutionary Cosmic Structure, Terrestrial Planet Finder) plan to use multiple spacecraft flying in precise formation to synthesize unprecedently large aperture optical systems. These architectures present challenges to the attitude and position determination and control system; optical performance is directly coupled to spacecraft pointing with typical control requirements being on the scale of milliarcseconds and nanometers. To investigate control strategies, rejection of environmental disturbances, and sensor and actuator requirements, a capability is needed to model both the dynamical and optical behavior of such a distributed telescope system. This paper describes work ongoing at NASA Goddard Space Flight Center toward the integration of a set of optical analysis tools (Optical System Characterization and Analysis Research software, or OSCAR) with the Formation J?lying Test Bed (FFTB). The resulting system is called the Precision Formation Flying Integrated Analysis Tool (PFFIAT), and it provides the capability to simulate closed-loop control of optical systems composed of elements mounted on multiple spacecraft. The attitude and translation spacecraft dynamics are simulated in the FFTB, including effects of the space environment (e.g. solar radiation pressure, differential orbital motion). The resulting optical configuration is then processed by OSCAR to determine an optical image. From this image, wavefront sensing (e.g. phase retrieval) techniques are being developed to derive attitude and position errors. These error signals will be fed back to the spacecraft control systems, completing the control loop. A simple case study is presented to demonstrate the present capabilities of the tool.

Stoneking, Eric↗

NASA NTRS1990

Noncontact measurement of high temperature using optical fiber sensors

The primary goal of this research program was the investigation and application of noncontact temperature measurement techniques using optical techniques and optical fiber methods. In particular, a pyrometer utilizing an infrared optical light pipe and a multiwavelength filtering approach was designed, revised, and tested. This work was motivated by the need to measure the temperatures of small metallic pellets (approximately 3 mm diameter) in free fall at the Microgravity Materials Processing Drop Tube at NASA Marshall Space Flight Center. In addition, research under this program investigated the adaptation of holography technology to optical fiber sensors, and also examined the use of rare-earth dopants in optical fibers for use in measuring temperature. The pyrometer development effort involved both theoretical analysis and experimental tests. For the analysis, a mathematical model based on radiative transfer principles was derived. Key parameter values representative of the drop tube system, such as particle size, tube diameter and length, and particle temperature, were used to determine an estimate of the radiant flux that will be incident on the face of an optical fiber or light pipe used to collect radiation from the incandescent falling particle. An extension of this work examined the advantage of inclining or tilting the collecting fiber to increase the time that the falling particle remains in the fiber field-of-view. Those results indicate that increases in total power collected of about 15 percent may be realized by tilting the fiber. In order to determine the suitability of alternative light pipes and optical fibers, and experimental set-up for measuring the transmittance and insertion loss of infrared fibers considered for use in the pyrometer was assembled. A zirconium fluoride optical fiber and several bundles of hollow core fiber of varying diameters were tested. A prototype two-color pyrometer was assembled and tested at Virginia Tech, and then tested on the Drop Tube at Marshall Space Flight Center. Radiation from 5 mm diameter niobium drops falling in the Drop Tube was successfully detected, and recorded for later analysis. Subsequent analysis indicated that the imaging of light output from the light pipe onto the detector active areas was not identical for both detectors.

Claus, R. O.↗

NASA NTRS1991

Recent spectroscopic findings concerning clay/water interactions at low humidity: Possible applications to models of Martian surface reactivity

A feasibility study assessing the utility of the adaptation of near infrared correlation spectroscopy to quantifying iron and adsorbed water in some clay-based Mars soil analog materials (MarSAM's). The work was intended to constitute Phase 1 of an approach to identifying optical analytical wavelength regions, not only for important mineral classes, but for chemically active centers within them. Many of these centers are common to unrelated mineral classes and of disproportionate influence relative to the mineral structure as a whole in determining the surface reactivity of mineral surfaces. We previously reported linearity between reflectance and total iron and total moisture over a large range of both key variables. We also discovered interesting relationships between the intensity of iron bands and the relative humidity of the systems. These relationships were confirmed. We also show that, in the low humidity range, reflectance is linearly dependent on a different kind of water from that best representing the full humidity range (the kind of water associated, in clays, with surface acidity). These relationships and the sensitivity and capability of quantitation of near infrared data indicate high promise with the production of reactive surface intermediates of products of surface reactions.

Coyne, L.↗

NASA NTRS2000

Evaluation of the Applicability of Solar and Lamp Radiometric Calibrations of a Precision Sun Photometer Operating Between 300 and 1025 nm

Over a period of 3 year a precision Sun photometer (SPM) operating between 300 and 1025 nm was calibrated four times at three different high-mountain sites in Switzerland, Germany, and the United States by means of the Langley-plot technique. We found that for atmospheric window wavelengths the total error (2 sigma-statistical plus systematic errors) of the calibration constants V(sub 0)(lambda), the SPM voltage in the absence of any attenuating atmosphere, can be kept below 1.60% in the UV-A and blue, 0.9% in the mid-visible, and 0.6% in the near-infra red spectral region. For SPM channels within strong water-vapor or ozone absorption bands a modified Langley-plot technique was used to determine V(sub 0)(lambda) with a lower accuracy. Within the same period of time, we calibrated the SPM five times using irradiance standard lamps in the optical labs of the Physikalisch-Meteorologisches Observatorium Davos and World Radiation Center, Switzerland, and of the Remote Sensing Group of the Optical Sciences Center, University of Arizona, Tucson, Arizona. The lab calibration method requires knowledge of the extraterrestrial spectral irradiance. When we refer the standard lamp results to the World Radiation Center extraterrestrial solar irradiance spectrum, they agree with the Langley results within 2% at 6 or 13 SPM wavelengths. The largest disagreement (4.4%) is found for the channel centered at 610 nm. The results of these intercomparisons change significantly when the lamp results are referred to two different extraterrestrial solar irradiance spectra that have become recently available.

Schmid, Beat↗

NASA NTRS2007

Optical Alignment of the JWST ISIM to the OTE Simulator (OSIM): Current Concept and Design Studies

The James Webb Space Telescope's (JWST) Integrated Science Instrument Module (ISIM) contains the observatory's four science instruments and their support subsystems. During alignment and test of the integrated ISIM at NASA's Goddard Space Flight Center (GSFC), the Optical'telescope element SIMulator (OSIM) will be used to optically stimulate the science instruments to verify their operation and performance. In this paper we present the design of two cryogenic alignment fixtures that will be used to determine and verify the proper alignment of OSIM to ISIM during testing at GSFC. These fixtures, the Master Alignment Target Fixture (MAW) and the ISIM Alignment Target Fixture (IATF), will provide continuous, six degree of freedom feedback to OSIM during initial ambient alignment as well as during cryogenic vacuum testing. These fixtures will allow us to position the OSIM and maintain OSIM-ISIM alignment to better than 10 microns in translation and 250 micro-radians in rotation. We will provide a brief overview of the OSIM system and calibration and we will also discuss the relevance of these fixtures in the context of the overall ISIM alignment and verification plan.

Frey, Bradley J.↗

NASA NTRS2012

The Precise Orbit and the Challenge of Long Term Stability

The computation of a precise orbit reference is a fundamental component of the altimetric measurement. Since the dawn of the modern altimeter age, orbit accuracy has been determined by the quality of the GPS, SLR, and DORIS tracking systems, the fidelity of the measurement and force models, and the choice of parameterization for the orbit solutions, and whether a dynamic or a reduced-dynamic strategy is used to calculate the orbits. At the start of the TOPEX mission, the inaccuracies in the modeling of static gravity, dynamic ocean tides, and the nonconservative forces dominated the orbit error budget. Much of the error due to dynamic mismodeling can be compensated by reduced-dynamic tracking techniques depending on the measurement system strength. In the last decade, the launch of the GRACE mission has eliminated the static gravity field as a concern, and the background force models and the terrestrial reference frame have been systematically refined. GPS systems have realized many improvements, including better modeling of the forces on the GPS spacecraft, large increases in the ground tracking network, and improved modeling of the GPS measurements. DORIS systems have achieved improvements through the use of new antennae, more stable monumentation, and of satellite receivers that can track multiple beacons, and as well as through improved modeling of the nonconservative forces. Many of these improvements have been applied in the new reprocessed time series of orbits produced for the ERS satellites, Envisat, TOPEX/Poseidon and the Jason satellites, and as well as for the most recent Cryosat-2 and HY2A. We now face the challenge of maintaining a stable orbit reference for these altimetric satellites. Changes in the time-variable gravity field of the Earth and how these are modelled have been shown to affect the orbit evolution, and the calibration of the altimetric data with tide gauges. The accuracy of the reference frame realizations, and their projection into the future remains a source of error. Other sources of omission error include the geocenter for which no consensus model is as of yet applied. Although progress has been made in nonconservative force modeling through the use of detailed satellite-specific models, radiation pressure modeling, and atmospheric density modeling remain a potential source of orbit error. The longer term influence of variations in the solar and terrestrial radiation fields over annual and solar cycles remains principally untested. Also the long term variation in optical and thermal properties of the space vehicle surfaces would contribute to biases in the orbital frame if ignored. We review the status of altimetric precision orbit determination as exemplified by the recent computations undertaken by the different analysis centers for ERS, Envisat, TOPEX/Poseidon, Jason, Cryosat2 and HY2A, and we provide a perspective on the challenges for future missions such as the Jason-3, SENTINEL-3 and SWOT.

Lemoine, Frank G.↗