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NASA NTRS2008

Mapping the Sedna-Lavinia Region of Venus

Geologic mapping of Venus at 1:5 M scale has shown in great detail the flow complexes of volcanoes, coronae, and shield fields, and the varying structural patterns that differentiate tesserae from corona rims and isolated patches of densely lineated terrain. In most cases, however, the lower-elevation plains between the higher-standing landforms are discriminated only on the basis of potentially secondary features such as late-stage lava flooding or tectonic overprinting. This result, in which volcanoes and tesserae appear as "islands in the sea," places weak constraints on the relative age of large upland regions and the nature of the basement terrain. In this work, we focus on the spatial distribution and topography of densely lineated and tessera units over a large region of Venus, and their relationship to apparently later corona and shield flow complexes. The goal is to identify likely connections between patches of deformed terrain that suggest earlier features of regional extent, and to compare the topography of linked patches with other such clusters as a guide to whether they form larger tracts beneath the plains. Mapping Approach. We are mapping the region from 57S to 57N, 300E-60E. Since the 1:5 M quadrangles emphasize detail of tessera structure and corona/edifice flows, we simply adopt the outlines of these features as they relate to the outcrops of either "densely lineated terrain" or tessera (Fig. 1). The densely lineated material is mapped in many quadrangles based on pervasive structural deformation, typically with a single major axis (in contrast to the overlapping orthogonal patterns on tesserae). This unit definition is often extended to include material of corona rims. We do not at present differentiate between plains units, since earlier efforts show that their most defining attributes may be secondary to the original emplacement (e.g., lobate or sheet-like flooding by thin flow units, tectonic patterns related to regional and localized stress regimes) [1].

Campbell, Bruce A.↗

NASA NTRS2008

Geologic Mapping of the V-36 Thetis Regio Quadrangle: 2008 Progress Report

As a result of mapping, eleven material stratigraphic units and three structural units have been identified and mapped. The material units include (from older to younger): tessera terrain material (tt), material of densely fractured plains (pdf), material of fractured and ridged plains (pfr), material of shield plains (psh), material of plains with wrinkle ridges (pwr), material of smooth plains of intermediate brightness (psi), material of radardark smooth plains (psd), material of lineated plains (pli) material of lobate plains (plo), material of craters having no radar-dark haloes (c1), and material of craters having clear dark haloes (c2). The morphologies and probably the nature of the material units in the study area are generally similar to those observed in other regions of Venus [2]. The youngest units are lobate plains (plo) which here typically look less lobate than in other areas of the planet. Close to them in age are smooth plains which are indeed smooth and represented by two varieties mentioned above. Lineated plains (pli) are densely fractured in a geometrically regular way. Plains with wrinkle ridges, being morphologically similar to those observed in other regions, here occupy unusually small areas. Shield (psh) plains here are also not abundant. Locally they show wrinkle ridging. Fractured and ridged plains (pfr), which form in other regions, the so called ridge belts, are observed as isolated areas of clusters of ridged plains surrounded by other units. Densely fractured plains (pdf) are present in relatively small areas in association with coronae and corona-like features. Tessera terrain (tt) is dissected by structures oriented in two or more directions. Structures are so densely packed that the morphology (and thus nature) of the precursor terrain is not known. Structural units include tessera transitional terrain (ttt), fracture belts (fb) and rifted terrain (rt). Tessera transitional terrain was first identified and mapped by [4] as areas of fractured and ridged plains (pfr) and densely fractured plains (pdf) deformed by transverse faults that made it formally resemble tessera terrain (tt). The obvious difference between units tt and ttt is the recognizable morphology of precursor terrain of unit ttt. Fracture belts are probably ancient rift zones [3]. Rifted terrain (rt), as in other regions of Venus, is so saturated with faults that according to the recommendation of [1, 5] it should be mapped as a structural unit.

Basilevsky, A. T.↗

NASA NTRS2008

Geologic Mapping of Isabella Quadrangle (V-50) and Helen Planitia, Venus

(25-50 S, 180-210 E) is host to numerous coronae and small volcanic centers (paterae and shield fields), focused (Aditi and Sirona Dorsa) and distributed (penetrative north-south trending wrinkle ridges) contractional deformation, and radial and linear extensional structures, all of which contribute materials to and/or deform the expansive surrounding plains (Nsomeka and Wawalag Planitiae). Regional plains, which are a northern extension of regional plains mapped in the Barrymore Quadrangle V-59 [1], dominate the V-50 quadrangle. Previous mapping divided the regional plains into two members: regional plains, members a and b [2]. A re-evaluation of these members has determined that a continuous and consistent unit contact does not exist; however, the majority of this radar unit or surficial unit will still be displayed on the final map as a stipple pattern as it is a prevalent feature of the quadrangle. With minimal tessera or highland material, much of the quadrangle s oldest materials are plains units (the regional plains). Much of these plains are covered with small shield edifices that exhibit a variety of material contributions (or flows). In the northwest, several flows emerge and flow to the southeast from Diana-Dali Chasmata. Local corona- and mons-fed flows superpose the regional plains; however, earlier stages of volcano-tectonic centers marked by arcuate and radial structural elements, including terrain so heavily deformed that it takes on a new appearance, may have developed prior to or concurrently with the region plains. Northtrending deformation belts disrupt the central portion of the map area and wrinkle ridges parallel these larger belts. Isabella crater, in the northeastern quadrant, is highly asymmetric and displays two prominent ejecta blanket morphologies, which generally correlate with distance from the impact structure suggesting that ejecta block size or ejecta blanket thickness may be the cause. The crater floor is very dark and shows no direct connection with the large outflow to the south, which emphasizes the asymmetry observed. Isabella crater ejecta and outflow materials clearly postdate several small craters in the vicinity.

Bleamaster, Leslie F., III↗

NASA NTRS2008

Structural Maps of the V-17 Beta Regio Quadrangle, Venus

These represent slices of the geologic map into 7 time-stratigraphic levels whose descriptions are found in [3-6]. From older to younger they are: 1) Tessera material unit (t), 2) Densely fractured plains material unit (pdf), 3) Fractured and ridged plains material unit (pfr), 4) Tessera transitional terrain structural unit (tt), 5) Fracture belts structural unit (fb), 6) Shield plains (psh) and plains with wrinkle ridges (pwr) material units combined, and 7) Lobate (pl) and smooth (ps) plains material units combined and, approximately contemporaneous with them, the structural unit of rifted terrain (rt). Each slice shows the generalized pattern of structures typical of these units. Figures 1-7 show the seven maps and Figure 8 shows the combined map illustrating what is shown in the seven maps. To visualize the Beta Regio uplift outlines, the major structure of this area, we show the +0.5 km and +2.5 km contour lines, corresponding respectively to the base and the mid-height of the uplift. It is seen in Figures 1-2 and 4 the trends of t, pdf and tt occupy relatively small areas and their structures seen in these small windows appear rather variable and with almost no orientation heritage with time. Figure 3 shows that swarms of ridge belts trend mostly NW and go through the Beta structure with no alignment with it, suggesting that this structure did not yet exist at this time. Figure 5 shows that fracture belts align along the northern base of the Beta uplift suggesting onset of the formation of this structure. Figure 6 shows that wrinkle ridges do not show alignment with the Beta uplift suggesting that this already forming structure was not high enough to exert topographic stress in its vicinity. Figure 7 shows that the Beta uplift has Devana Chasma as an axial rift zone, suggesting a genetic link between the uplift and rifting. Figure 8 shows that structural trends in this area significantly changed with time.

Basilevsky, A. t.↗

NASA NTRS2008

Lunar Geologic Mapping Program: 2008 Update

The NASA Lunar Geologic Mapping Program is underway and a mappers handbook is in preparation. This program for systematic, global lunar geologic mapping at 1:2.5M scale incorporates digital, multi-scale data from a wide variety of sources. Many of these datasets have been tied to the new Unified Lunar Control Network 2005 [1] and are available online. This presentation summarizes the current status of this mapping program, the datasets now available, and how they might be used for mapping on the Moon.

Gaddis, L.↗

NASA NTRS2009

Lunar Mapping and Modeling Project

The Lunar Mapping and Modeling Project (LMMP) has been created to manage the development of a suite of lunar mapping and modeling products that support the Constellation Program (CxP) and other lunar exploration activities, including the planning, design, development, test and operations associated with lunar sortie missions, crewed and robotic operations on the surface, and the establishment of a lunar outpost. The information provided through LMMP will assist CxP in: planning tasks in the areas of landing site evaluation and selection, design and placement of landers and other stationary assets, design of rovers and other mobile assets, developing terrain-relative navigation (TRN) capabilities, and assessment and planning of science traverses. The project draws on expertise from several NASA and non-NASA organizations (MSFC, ARC, GSFC, JPL, CRREL US Army Cold Regions Research and Engineering Laboratory, and the USGS). LMMP will utilize data predominately from the Lunar Reconnaissance Orbiter, but also historical and international lunar mission data (e.g. Apollo, Lunar Orbiter, Kaguya, Chandrayaan-1), as available and appropriate, to meet Constellation s data needs. LMMP will provide access to this data through a single intuitive and easy to use NASA portal that transparently accesses appropriately sanctioned portions of the widely dispersed and distributed collections of lunar data, products and tools. Two visualization systems are being developed, a web-based system called Lunar Mapper, and a desktop client, ILIADS, which will be downloadable from the LMMP portal. LMMP will provide such products as local and regional imagery and DEMs, hazard assessment maps, lighting and gravity models, and resource maps. We are working closely with the LRO team to prevent duplication of efforts and to ensure the highest quality data products. While Constellation is our primary customer, LMMP is striving to be as useful as possible to the lunar science community, the lunar commercial community, the lunar education and public outreach (E/PO) community, and anyone else interested in accessing or utilizing lunar data. A beta version of the portal and visualization systems is expected to be released in late 2009, with a version 1 release planned for early 2011.

Noble, Sarah K.↗

NASA NTRS2009

Mapping Tyrrhena Patera and Hesperia Planum, Mars

Hesperia Planum, characterized by a high concentration of mare-type wrinkle ridges and ridge rings [1-4], encompasses > 2 million sq km in the southern highlands of Mars (Fig. 1). The most common interpretation is that the plains were emplaced as "flood" lavas with total thicknesses of <3 km [4-10]. The wrinkle ridges on its surface make Hesperia Planum the type locale for "Hesperian-aged ridged plains" on Mars [e.g., 9], and recent investigations reveal that wrinkle-ridge formation occurred in more than one episode [4]. Hesperia Planum?s stratigraphic position and crater-retention age [e.g., 9, 11-12] define the base of the Hesperian System. However, results of geologic mapping reveal that the whole of Hesperia Planum is unlikely to be composed of the same materials, emplaced at the same geologic time. To unravel these complexities, we are generating a 1:1.5M-scale geologic map of Hesperia Planum and its surroundings (Fig. 1). We have identified 4 distinct plains units within Hesperia Planum and are attempting to determine the nature and relative ages of these materials (Fig. 2) [13, 14]. The volcano Tyrrhena Patera (22degS, 104degE) is located within Hesperia Planum. Its products are both embayed by, and superpose, Hesperia Planum materials [15, 16]. We were previously funded to generate a 1:1 million scale map of Mars Transverse Mercator (MTM) quadrangles -15257 and -20257, which include the Tyrrhena Patera materials north and west of the Tyrrhena Patera summit. The goal for these maps was to constrain the nature and extent of the Tyrrhena Patera deposits, and to determine the relationship between Tyrrhena Patera materials, Hesperia Planum, and the adjacent highlands [16].

Crown, David A.↗

NASA NTRS2009

New Geologic Map of the Scandia Region of Mars

We have begun work on a sophisti-cated digital geologic map of the Scandia region (Fig. 1) at 1:3,000,000 scale based on post-Viking image and to-pographic datasets. Through application of GIS tools, we will produce a map product that will consist of (1) a printed photogeologic map displaying geologic units and relevant modificational landforms produced by tectonism, erosion, and collapse/mass wasting; (2) a landform geoda-tabase including sublayers of key landform types, attributed with direct measurements of their planform and to-pography using Mars Orbiter Laser Altimeter (MOLA) altimetry data and High-Resolution Stereo Camera (HRSC) digital elevation models (DEMs) and various image datasets; and (3) a series of digital, reconstructed paleostratigraphic and paleotopographic maps showing the inferred distribution and topographic form of materi-als and features during past ages

Tanaka, K. L.↗

NASA NTRS2009

Geologic Mapping of the Medusae Fossae Formation on Mars and the Northern Lowland Plains of Venus

This report summarizes the status of mapping projects supported by NASA grant NNX07AP42G, through the Planetary Geology and Geophysics (PGG) program. The PGG grant is focused on 1:2M-scale mapping of portions of the Medusae Fossae Formation (MFF) on Mars. Also described below is the current status of two Venus geo-logic maps, generated under an earlier PGG mapping grant.

Zimbelman, J. R.↗

NASA NTRS2009

Mars Structural and Stratigraphic Mapping along the Coprates Rise

This geologic mapping project supports a topical study of structures in east Thaumasia associated with the Coprates rise. The study examines cuesta-like features on the east flank of the Coprates rise first identified by Saunders et al. [1]. Mapping combines detailed local stratigraphy, structural geology and topography. Hogbacks and cuestas indicate erosion of tilted rock units. The extent of the erosion will be determined in the course of the mapping. The region of interest lies along the eastern margin of Thaumasia bounded by latitudes -15 and -35 and longitudes 50 to 70 W (Figure 1). Three MTM geologic quadrangles are being compiled for publication by the USGS (-20057, -25057, -30057). All existing data sources are used including THEMIS, MOC, CTX, HiRISE, MOLA and gravity, as well as higher level data available through the PDS data nodes at ASU, UA and Washington University. The extremely valuable ASU JMARS tools are used for analysis of many of the data sets. ArcGIS software has been obtained and is being learned for the map compilation.

Saunders, R Stephen↗

NASA NTRS2010

Geologic Mapping of the Medusae Fossae Formation, Mars, and the Northern Lowland Plains, Venus

This report summarizes the status of mapping projects supported by NASA grant NNX07AP42G, through the Planetary Geology and Geophysics (PGG) program. The PGG grant is focused on 1:2M-scale mapping of portions of the Medusae Fossae Formation (MFF) on Mars. Also described below is the current status of two Venus geologic maps, generated under an earlier PGG mapping grant.

Zimbelman, J. R.↗

NASA NTRS2010

Geologic Map of the Olympia Cavi Region of Mars (MTM 85200): A Summary of Tactical Approaches

The 1:500K-scale geologic map of MTM 85200 - the Olympia Cavi region of Mars - has been submitted for peer review [1]. Physiographically, the quadrangle includes portions of Olympia Rupes, a set of sinuous scarps which elevate Planum Boreum ~800 meters above Olympia Planum. The region includes the high-standing, spiral troughs of Boreales Scopuli, the rugged and deep depressions of Olympia Cavi, and the vast dune fields of Olympia Undae. Geologically, the mapped units and landforms reflect the recent history of repeated accumulation and degradation. The widespread occurrence of both weakly and strongly stratified units implicates the drape-like accumulation of ice, dust, and sand through climatic variations. Similarly, the occurrence of layer truncations, particularly at unit boundaries, implicates punctuated periods of both localized and regional erosion and surface deflation whereby underlying units were exhumed and their material transported and re-deposited. Herein, we focus on the iterative mapping approaches that allowed not only the accommodation of the burgeoning variety and volume of data sets, but also facilitated the efficient presentation of map information. Unit characteristics and their geologic history are detailed in past abstracts [2-3].

Skinner, J. A., Jr.↗

NASA NTRS2010

Rapid Response Flood Water Mapping

Since the beginning of operation of the MODIS instrument on the NASA Terra satellite at the end of 1999, an exceptionally useful sensor and public data stream have been available for many applications including the rapid and precise characterization of terrestrial surface water changes. One practical application of such capability is the near-real time mapping of river flood inundation. We have developed a surface water mapping methodology based on using only bands 1 (620-672 nm) and 2 (841-890 nm). These are the two bands at 250 m, and the use of only these bands maximizes the resulting map detail. In this regard, most water bodies are strong absorbers of incoming solar radiation at the band 2 wavelength: it could be used alone, via a thresholding procedure, to separate water (dark, low radiance or reflectance pixels) from land (much brighter pixels) (1, 2). Some previous water mapping procedures have in fact used such single band data from this and other sensors that include similar wavelength channels. Adding the second channel of data (band 1), however, allows a band ratio approach which permits sediment-laden water, often relatively light at band 2 wavelengths, to still be discriminated, and, as well, provides some removal of error by reducing the number of cloud shadow pixels that would otherwise be misclassified as water.

Fritz Policelli↗

NASA NTRS2010

Five-Year Wilkinson Microwave Anisotropy Probe Observations: Data Processing, Sky Maps, and Basic Results

We present new full-sky temperature and polarization maps in five frequency bands from 23 to 94 GHz, based on data from the first five years of the Wilkinson Microwave Anisotropy Probe (WMAP) sky survey. The new maps are consistent with previous maps and are more sensitive. The five-year maps incorporate several improvements in data processing made possible by the additional years of data and by a more complete analysis of the instrument calibration and in-flight beam response. We present several new tests for systematic errors in the polarization data and conclude that W-band polarization data is not yet suitable for cosmological studies, but we suggest directions for further study. We do find that Ka-band data is suitable for use; in conjunction with the additional years of data, the addition of Ka band to the previously used Q- and V-band channels significantly reduces the uncertainty in the optical depth parameter, tau. Further scientific results from the five-year data analysis are presented in six companion papers and are summarized in Section 7 of this paper. With the five-year WMAP data, we detect no convincing deviations from the minimal six-parameter ACDM model: a flat universe dominated by a cosmological constant, with adiabatic and nearly scale-invariant Gaussian fluctuations. Using WMAP data combined with measurements of Type Ia supernovae and Baryon Acoustic Oscillations in the galaxy distribution, we find (68% CL uncertainties): OMEGA(sub b)h(sup 2) = 0.02267(sup +0.00058)(sub -0.00059), OMEGA(sub c)h(sup 2) = 0.1131 plus or minus 0.0034, OMEGA(sub logical and) = 0.726 plus or minus 0.015, ns = .960 plus or minus 0.013, tau = 0.84 plus or minus 0.016, and DELTA(sup 2)(sub R) = (22.445 plus or minus 0.096) x 10(exp -9) at k = 0.002 Mpc(exp -1). From these we derive sigma(sub 8) = 0.812 plus or minus 0.026, H(sub 0) = 70.5 plus or minus 1.3 kilometers per second Mpc(exp -1), OMEGA(sub b) = 0.0456 plus or minus 0.0015, OMEGA(sub c) = .228 plus or minus 0.013, OMEGA(sub m)h(sup 2) = 0.1358(sup +0.0037)(sub -0.0036), z reion = 10.9 plus or minus 1.4, and t(sub 0) = 13.72 plus or minus 0.12 Gyr. The new limit on the tensor-to-scalar ration is r less than 0.22 (95% CL), while the evidence for a running spectral index is insignificant, dn(sub s)/d ln k = -0.028 plus or minus 0.020 (68% CL). We obtain tight, simultaneous limits on the (constant) dark energy equation of state and the spatial curvature of the universe: -0.14 less than 1 + w less than 0.12 (95% CL) and -0.0179 less than OMEGA(sub k) less than 0.0081 (95% CL). The number of relativistic degrees of freedom, expressed in units of the effective number of neutrino species, is found to be N(sub eff) = 4.4 plus or minus 1.5 (69% CL), consistent with the standard value of 3.04. Models with N(sub eff) = 0 are disfavored at greater than 99% confidence. Finally, new limits on physically motivated primordial non-Gaussianity parameters are -9 less than f(sup local)(sub NL) less than 111 (95% CL) and -151 less than f(sup equal)(sub NL) less than 253 (95% CL) for the local and equilateral models, respectively.

Hinshaw, G.↗

NASA NTRS2011

4 Vesta in Color: High Resolution Mapping from Dawn Framing Camera Images

Rotational surface variations on asteroid 4 Vesta have been known from ground-based and HST observations, and they have been interpreted as evidence of compositional diversity. NASA s Dawn mission entered orbit around Vesta on July 16, 2011 for a year-long global characterization. The framing cameras (FC) onboard the Dawn spacecraft will image the asteroid in one clear (broad) and seven narrow band filters covering the wavelength range between 0.4-1.0 microns. We present color mapping results from the Dawn FC observations of Vesta obtained during Survey orbit (approx.3000 km) and High-Altitude Mapping Orbit (HAMO) (approx.950 km). Our aim is to create global color maps of Vesta using multi spectral FC images to identify the spatial extent of compositional units and link them with other available data sets to extract the basic mineralogy. While the VIR spectrometer onboard Dawn has higher spectral resolution (864 channels) allowing precise mineralogical assessment of Vesta s surface, the FC has three times higher spatial resolution in any given orbital phase. In an effort to extract maximum information from FC data we have developed algorithms using laboratory spectra of pyroxenes and HED meteorites to derive parameters associated with the 1-micron absorption band wing. These parameters will help map the global distribution of compositionally related units on Vesta s surface. Interpretation of these units will involve the integration of FC and VIR data.

Reddy, V.↗

NASA NTRS2011

The CHUVA Lightning Mapping Campaign

The primary science objective for the CHUVA lightning mapping campaign is to combine measurements of total lightning activity, lightning channel mapping, and detailed information on the locations of cloud charge regions of thunderstorms with the planned observations of the CHUVA (Cloud processes of tHe main precipitation systems in Brazil: A contribUtion to cloud resolVing modeling and to the GPM (GlobAl Precipitation Measurement) field campaign. The lightning campaign takes place during the CHUVA intensive observation period October-December 2011 in the vicinity of S o Luiz do Paraitinga with Brazilian, US, and European government, university and industry participants. Total lightning measurements that can be provided by ground-based regional 2-D and 3-D total lightning mapping networks coincident with overpasses of the Tropical Rainfall Measuring Mission Lightning Imaging Sensor (LIS) and the SEVIRI (Spinning Enhanced Visible and Infrared Imager) on the Meteosat Second Generation satellite in geostationary earth orbit will be used to generate proxy data sets for the next generation US and European geostationary satellites. Proxy data, which play an important role in the pre-launch mission development and in user readiness preparation, are used to develop and validate algorithms so that they will be ready for operational use quickly following the planned launch of the GOES-R Geostationary Lightning Mapper (GLM) in 2015 and the Meteosat Third Generation Lightning Imager (LI) in 2017. To date there is no well-characterized total lightning data set coincident with the imagers. Therefore, to take the greatest advantage of this opportunity to collect detailed and comprehensive total lightning data sets, test and validate multi-sensor nowcasting applications for the monitoring, tracking, warning, and prediction of severe and high impact weather, and to advance our knowledge of thunderstorm physics, extensive measurements from lightning mapping networks will be collected in conjunction with electric field mills, field change sensors, high speed cameras and other lightning sensors, dual-polarimetric radars, and aircraft in-situ microphysics which will allow for excellent cross-network inter-comparisons, assessments, and physical understanding.

Goodman, Steven J.↗

NASA NTRS2012

An Effort to Map and Monitor Baldcypress Forest Areas in Coastal Louisiana, Using Landsat, MODIS, and ASTER Satellite Data

This presentation discusses a collaborative project to develop, test, and demonstrate baldcypress forest mapping and monitoring products for aiding forest conservation and restoration in coastal Louisiana. Low lying coastal forests in the region are being negatively impacted by multiple factors, including subsidence, salt water intrusion, sea level rise, persistent flooding, hydrologic modification, annual insect-induced forest defoliation, timber harvesting, and conversion to urban land uses. Coastal baldcypress forests provide invaluable ecological services in terms of wildlife habitat, forest products, storm buffers, and water quality benefits. Before this project, current maps of baldcypress forest concentrations and change did not exist or were out of date. In response, this project was initiated to produce: 1) current maps showing the extent and location of baldcypress dominated forests; and 2) wetland forest change maps showing temporary and persistent disturbance and loss since the early 1970s. Project products are being developed collaboratively with multiple state and federal agencies. Products are being validated using available reference data from aerial, satellite, and field survey data. Results include Landsat TM- based classifications of baldcypress in terms of cover type and percent canopy cover. Landsat MSS data was employed to compute a circa 1972 classification of swamp and bottomland hardwood forest types. Landsat data for 1972-2010 was used to compute wetland forest change products. MODIS-based change products were applied to view and assess insect-induced swamp forest defoliation. MODIS, Landsat, and ASTER satellite data products were used to help assess hurricane and flood impacts to coastal wetland forests in the region.

Spruce, Joseph P.↗

NASA NTRS2012

Variable Sampling Mapping

The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.

Smith, Jeffrey, S.↗