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DOE OSTI2018

Behavior of the maximum likelihood in quantum state tomography

Quantum state tomography on a d-dimensional system demands resources that grow rapidly with d. They may be reduced by using model selection to tailor the number of parameters in the model (i.e., the size of the density matrix). Most model selection methods typically rely on a test statistic and a null theory that describes its behavior when two models are equally good. Here, we consider the loglikelihood ratio. Because of the positivity constraint ρ ≥ 0, quantum state space does not generally satisfy local asymptotic normality (LAN), meaning the classical null theory for the loglikelihood ratio (the Wilks theorem) should not be used. Thus, understanding and quantifying how positivity affects the null behavior of this test statistic is necessary for its use in model selection for state tomography. We define a new generalization of LAN, metric-projected LAN, show that quantum state space satisfies it, and derive a replacement for the Wilks theorem. In addition to enabling reliable model selection, our results shed more light on the qualitative effects of the positivity constraint on state tomography.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Final Technical Report for NSF/DOE partnership grant 1004284/ER54905/SC0004660: 2011- 2013

Research has been performed on two topics: (1) Nonlinear time-dependent phenomena in the regime of electron magnetohydrodynamics (EMHD). (2) Plasma structures forming ”bubbles”. The latter are regions of localized density depletions or enhancements separated from the ambient plasma by sheaths or double layers. Three-dimensional magnetic null points can also be considered as ”magnetic bubbles”. Nonlinear EMHD fields are generated by pulsed magnetic loops. The magnetic field varies in time faster than an ion cyclotron period, hence interacts only with electrons. Space charge electric fields are created when magnetic forces try to separate electrons from ions. Electric and magnetic forces nearly balance to keep the plasma quasi neutral. This leads to rotational electron motions, i.e. Hall currents and associated magnetic perturbations. When the time scale falls between the ion and electron cyclotron period the magnetic perturbation is convected in the whistler mode. When the time-varying magnetic field exceeds the background magnetic field the whistler mode becomes highly nonlinear since its properties depend on the total magnetic field. When the time-varying magnetic field creates magnetic null points or null lines EMHD breaks down. Electrons can be accelerated in null lines which dissipated magnetic energy like in magnetic reconnection. Energized electrons with anisotropic distributions create secondary whistler instabilities. These effects have been observed in field topologies resembling spheromaks and field-reversed configurations (FRCs). The whistler mode propagation near magnetic nulls is not trivial when the field gradients and wavelength are comparable. Ray tracing is inappropriate when the WKB approximation breaks down. Experiments have been started to map wave propagation on curved field lines with null points. Initial results show that whistlers in highly nonuniform fields have highly oblique phase velocities but the energy flow remains dominantly along the field. Density bubbles are created by anode discharges, typically forming spherical ”fireballs” bounded by a double layer. In a magnetized plasma the shape becomes cylindrical, in nonuniform magnetic fields many asymmetric fireball shapes are possible. Due to electron energization the fireball plasma has higher density and temperature than the ambient plasma. The double layer can also be produced by a high transparency positively biased grid. Instabilities arise from the electron transit through the plasma bubble and the double layer. When a permanent magnet is biased positively the electrons perform ExB drifts in the equatorial plane between the poles. Electron drift modes are excited with a high spectral contents. Similarly, a negatively biased magnet produces a disk-shaped plasma bubble. The cold magnet emits secondary electrons due to the impact of energetic ions. Such magnetron discharges exhibit a variety of instabilities which affect the cross-field transport and sputtering applications. This report will summarize the main effects observed and provide references to more detailed publications.

, nonlinear time-dependent phenomena↗

DOE OSTI2026

Magnetohydrodynamic Wave Mode Conversion in a Pseudostreamer Structure

The interaction of a fast magnetoacoustic wave with a magnetic null point in a pseudostreamer magnetic configuration is modeled. The incident fast wave is excited by an impulsive velocity driver located in the corona outside the Alfvén-acoustic equipartition layer. The fast wave front experiences refraction and wraps around the null point, while the front segment approaching the null point along the magnetic bisector passes through it. In the equipartition layer surrounding the null point, part of the fast wave energy is converted into slow magnetoacoustic waves. Slow waves propagate outward from the null point along the magnetic separatrices. The fronts of slow waves exhibit a characteristic chevron shape. The fast-to-slow mode conversion efficiency increases with the width of the initial perturbation, following a power-law dependence with an index of approximately 1.06. For initial wave amplitudes below about 10% of the local Alfvén speed, the dependence of the conversion efficiency on the initial amplitude is weak. After interacting with the null point, the amplitudes of the fast waves decrease significantly owing to energy conversion and the spreading of wave energy over a broad spatial domain. In contrast, the energy of slow waves remains concentrated in the vicinity of the magnetic separatrices, resulting in less pronounced geometric attenuation of these waves. These findings are consistent with observational reports of the interaction of a coronal fast wave with a pseudostreamer.

Zhong, Yu [Univ. of Warwick, Coventry (United King↗

NASA NTRS1990

The Hubble Space Telescope optical systems failure report

The findings of the Hubble Space Telescope Optical Systems Board of Investigation are reported. The Board was formed to determine the cause of the flaw in the telescope, how it occurred, and why it was not detected before launch. The Board conducted its investigation to include interviews with personnel involved in the fabrication and test of the telescope, review of documentation, and analysis and test of the equipment used in the fabrication of the telescope's mirrors. The investigation proved that the primary mirror was made in the wrong shape (a 0.4-wave rms wavefront error at 632.8 nm). The primary mirror was manufactured by the Perkin-Elmer Corporation (Hughes Danbury Optical Systems, Inc.). The critical optics used as a template in shaping the mirror, the reflective null corrector (RNC), consisted of two small mirrors and a lens. This unit had been preserved by the manufacturer exactly as it was during the manufacture of the mirror. When the Board measured the RNC, the lens was incorrectly spaced from the mirrors. Calculations of the effect of such displacement on the primary mirror show that the measured amount, 1.3 mm, accounts in detail for the amount and character of the observed image blurring. No verification of the reflective null corrector's dimensions was carried out by Perkin-Elmer after the original assembly. There were, however, clear indications of the problem from auxiliary optical tests made at the time. A special optical unit called an inverse null corrector, designed to mimic the reflection from a perfect primary mirror, was built and used to align the apparatus; when so used, it clearly showed the error in the reflective null corrector. A second null corrector was used to measure the vertex radius of the finished primary mirror. It, too, clearly showed the error in the primary mirror. Both indicators of error were discounted at the time as being themselves flawed. The Perkin-Elmer plan for fabricating the primary mirror placed complete reliance on the reflective null corrector as the only test to be used in both manufacturing and verifying the mirror's surface with the required precision. This methodology should have alerted NASA management to the fragility of the process and the possibility of gross error. Such errors had been seen in other telescope programs, yet no independent tests were planned, although some simple tests to protect against major error were considered and rejected. During the critical time period, there was great concern about cost and schedule, which further inhibited consideration of independent tests.

Source record↗

NASA NTRS2012

Integrated Optics Achromatic Nuller for Stellar Interferometry

This innovation will replace a beam combiner, a phase shifter, and a mode conditioner, thus simplifying the system design and alignment, and saving weight and space in future missions. This nuller is a dielectric-waveguide-based, four-port asymmetric coupler. Its nulling performance is based on the mode-sorting property of adiabatic asymmetric couplers that are intrinsically achromatic. This nuller has been designed, and its performance modeled, in the 6.5-micrometer to 9.25-micrometer spectral interval (36% bandwidth). The calculated suppression of starlight for this 15-cm-long device is 10(exp -5) or better through the whole bandwidth. This is enough to satisfy requirements of a flagship exoplanet-characterization mission. Nulling interferometry is an approach to starlight suppression that will allow the detection and spectral characterization of Earth-like exoplanets. Nulling interferometers separate the light originating from a dim planet from the bright starlight by placing the star at the bottom of a deep, destructive interference fringe, where the starlight is effectively cancelled, or nulled, thus allowing the faint off-axis light to be much more easily seen. This process is referred to as nulling of the starlight. Achromatic nulling technology is a critical component that provides the starlight suppression in interferometer-based observatories. Previously considered space-based interferometers are aimed at approximately 6-to-20-micrometer spectral range. While containing the spectral features of many gases that are considered to be signatures of life, it also offers better planet-to-star brightness ratio than shorter wavelengths. In the Integrated Optics Achromatic Nuller (IOAN) device, the two beams from the interferometer's collecting telescopes pass through the same focusing optic and are incident on the input of the nuller.

Ksendzov, Alexander↗

NASA NTRS2006

Measuring Extended Structure in Stars Using the Keck Interferometer Nuller

The Keck Interferometer Nuller is designed to detect faint off-axis mid-infrared light a few tens to a few hundreds of milliarcseconds from a bright central star. The starlight is suppressed by destructive combination along the long (85 m) baseline, which produces a fringe spacing of 25 mas at a wavelength of 10 m, with the central null crossing the position of the star. The strong, variable mid-infrared background is subtracted using interferometric phase chopping along the short (5 m) baseline. This paper presents an overview of the observing and data reduction strategies used to produce a calibrated measurement of the off-axis light. During the observations, the instrument cycles rapidly through several calibration and measurement steps, in order to monitor and stabilize the phases of the fringes produced by the various baselines, and to derive the fringe intensity at the constructive peak and destructive null along the long baseline. The data analysis involves removing biases and coherently demodulating the short-baseline fringe with the long-baseline fringe tuned to alternate between constructive and destructive phases, combining the results of many measurements to improve the sensitivity, and estimating the part of the null leakage signal which is associated with the finite angular size of the central star. Comparison of the results of null measurements on science target and calibrator stars permits the instrumental leakage - the "system null leakage" - to be removed and the off-axis light to be measured.

nulling interferometry↗

NASA NTRS2005

Accessing Small Inner Working Angles with a Rotating Sub-Aperture Nuller

A new approach to high contrast observations near bright stars with a single-aperture telescope is discussed, which is based on the idea of a rotating separated-aperture nulling interferometer. The approach can be described as a rotating sub-aperture nuller, because it nulls two or more sub-apertures within a single telescope's pupil, and uses baseline rotation to modulate the signals from off-axis sources in a manner similar to that of potential space-based nulling interferometers. The sub-aperture beams can be combined in a number of ways, including a fiber nuller and a rotational shearing interferometer. Such a rotating nulling coronagraph has two great advantages. First, it can be used on a ground-based telescope to test signal reconstruction approaches pertinent to potential space-based nulling interferometers. Moreover, it also has the potential to enable ground-based coronagraphic observations of faint off-axis companions very close to bright stars.

coronagraphy↗

DOE OSTI2022

Transverse spin in the light-ray OPE

We study a product of null-integrated local operators O 1 and O 2 on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious d – 2 dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin J 1 + J 2 – 1. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins J 1 + J 2 – 1 + n, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin 3 (as described by Hofman and Maldacena), but also novel terms with spin 5, 7, 9, etc. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in N = 4 SYM, finding perfect agreement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

Syndecan-4 shedding impairs macrovascular angiogenesis in diabetes mellitus

Purpose: Syndecan-4 (synd4) is a ubiquitous heparan sulfate proteoglycan cell surface receptor that modulates cell proliferation, migration, mechanotransduction, and endocytosis. The extracellular domain of synd4 sheds heavily in acute inflammation, but the shedding of synd4 in chronic inflammation, such as diabetes mellitus (DM), is still undefined. We investigated the alterations of synd4 endothelial expression in DM and the influence of impaired synd4 signaling on angiogenesis in human umbilical vein endothelial cells (HUVECs), diabetic rats, synd4 null mice, and db/db mice. Material and methods: HUVECs were incubated with advanced glycation end products (AGEs). Western blot analysis was used to determine synd4 protein expression and ELISA was used to detect soluble synd4 fragments. The concentration of synd4 in the aortic endothelia of diabetic rats was detected by immunohistochemical staining. Aortic ring assays were performed to study the process of angiogenesis in the diabetic rats and in synd4 null and db/db mice. Recombinant adenoviruses containing the synd4 gene or null were constructed to enhance synd4 aortic expression in db/db mice. Results: Western blot analysis showed decreased expression of the synd4 extracellular domain in HUVECs, and ELISA detected increased soluble fragments of synd4 in the media. Synd4 endothelial expression in the aortas of diabetic rats was decreased. Aortic ring assay indicated impaired angiogenesis in synd4 null and db/db mice, which was partially reversed by synd4 overexpression in db/db mice. Conclusion: Synd4 shedding from vascular endothelial cells played an important role in the diabetes-related impairment of angiogenesis. -- Highlights: •Synd4 shedding from endothelial cells is accelerated under the stimulation of AGEs. •Extracellular domain of synd4 is diminished in the endothelium of DM rats. •Aortic rings of synd4 null mice showed impaired angiogenesis. •Overexpression of synd4 partly rescues macrovascular angiogenesis in db/db mice.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

The snowflake divertor

The snowflake magnetic configuration is characterized by the presence of two closely spaced poloidal field nulls that create a characteristic hexagonal (reminiscent of a snowflake) separatrix structure. The magnetic field properties and the plasma behaviour in the snowflake are determined by the simultaneous action of both nulls, this generating a lot of interesting physics, as well as providing a chance for improving divertor performance. One of the most interesting effects of the snowflake geometry is the heat flux sharing between multiple divertor channels. The authors summarise experimental results obtained with the snowflake configuration on several tokamaks. Wherever possible, relation to the existing theoretical models is described. Divertor concepts utilizing the properties of a snowflake configuration are briefly discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

BMS in cosmology

Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

DYNAMIC EVOLUTION OF AN X-SHAPED STRUCTURE ABOVE A TRANS-EQUATORIAL QUADRUPOLE SOLAR ACTIVE REGION GROUP

In the solar corona, magnetic reconnection usually takes place at the singular configuration of the magnetic field, in particular near a magnetic null, owing to its high susceptibility to perturbations. In this Letter, we report a rare X-shaped structure, encompassing a magnetic null, above a trans-equatorial quadrupole active region group that is well observed by the Atmospheric Imaging Assembly (AIA). The observations show that this X-shaped structure is visible in all AIA EUV passbands and stably exists for days. However, possibly induced by flare activities at the northern part of the quadrupole active region group, the X-shaped structure starts to destabilize while a jet erupts near its center at ∼15:05 UT on 2013 October 7. Through nonlinear force-free field modeling, we identify a magnetic null that is above the quadrupole polarities and well corresponds to the X-shaped structure. After the jet eruption, the temperature and emission measure of the plasma near the X-shaped structure rise from ∼2.3 MK and ∼1.2 × 10{sup 27} cm{sup –5} at 15:01 UT to ∼5.4 MK and ∼3.7 × 10{sup 27} cm{sup –5} at 15:36 UT, respectively, revealed by the differential emission measure analysis, indicating that magnetic reconnection most likely takes place there to heat the plasma. Moreover, the height of the null increases ∼10 Mm, which is most likely due to the partial opening of the field lines near the fan surface that makes the null underneath rise to seek a new equilibrium.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2017

Mapping of orthogonal 2D flux coordinates for two nearby magnetic X-points to logically rectangular domains

The behavior of plasmas in configurations with magnetic null points is of potential interest for a number of systems. Such nulls, sometimes referred to as X-points, a name strictly valid only for wellseparated nulls where magnetic separatrices cross at a right angle, may occur in only one component of the magnetic field, such as the poloidal field in a tokamak. Numerical simulations are often used to study and predict turbulence and transport in such systems. For cases with strong magnetic field such that the ion and electron gyro-frequencies are much larger that particle collision frequencies, there is a strong anisotropy in the plasma transport along the magnetic field compared to across the field. Because of the strong anisotropy, it is often advantageous for simulations to use a coordinate system based on magnetic flux surfaces together with a coordinate orthogonal to the flux surfaces. This report presents the topological considerations needed to construct the mapping on an orthogonal flux-surface mesh onto a logically rectangular domain often used in simulation codes of the divertor region of tokamaks having two nearby X-points, thus extending the mapping now common single-null or well-separated double nullpoint cases with one null located at the top and bottom of the device. This extension is especially relevant to study the capability of snowflake divertors in tokamaks for reducing the peak heat flux of exhaust plasma on the target plates [1-3]. The analysis presented here follows the analytic description of the poloidal magnetic field, B pol , near two closely-spaced X-points given by Ryutov [1-3]. This analysis is applicable to experimental devices where the two X-points are generated by distributed poloidal field coils and the plasma core current. This analytic description is used to identify topological features of an orthogonal mesh. A key parameter that specifies the various topology changes is the poloidal angle between the primary X-point and the second X-point, and the changes are associated with a set of critical angles. Understanding these changes leads to the final step in the mesh construction by identifying the locations of various regions or patches in configuration space and in a corresponding logically rectangular index space. UEDGE [4] and other 2-D fluid plasma simulation codes [5-7] describe the edge plasma of toroidally symmetric tokamak configurations with one or more X-points in a divertor region. The 2-D spatial mesh is usually based on a magnetic configuration produced by an MHD equilibrium code such as EFIT and written out as one or more “eqdsk” files. As illustrated in Fig. 1, the domain of the simulated plasma consists of several flux tubes bounded by poloidal magnetic flux surfaces. The number and spacing of the flux surfaces defines the “radial” resolution of the mesh. The “radial” direction is locally orthogonal to flux surfaces; the “poloidal” direction is locally parallel to flux surfaces. The “poloidal” resolution of the mesh is defined by the number of cells in the poloidal direction between adjacent flux surfaces. For boundary plasma transport codes used for tokamak configurations such as UEDGE it is convenient, though not necessary, to assume that all flux tubes have the same number of poloidal cells so the mesh is logically rectangular in index space, but does possess internal boundaries linking different sub-rectangles in the computational domain. The following sections of this report describe indexing schemes that map tokamak magnetic configurations with one or more x-points in the divertor region(s) onto a rectangular index space. Simulation results from the UEDGE code illustrate the schemes for a few configurations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Composing preconditioners for multiphysics PDE systems with applications to Generalized MHD

New patch smoothers or relaxation techniques are developed for solving linear matrix equations coming from systems of discretized partial differential equations (PDEs). One key linear solver challenge for many PDE systems arises when the resulting discretization matrix has a near null space that has a large dimension, which can occur in generalized magnetohydrodynamic (GMHD) systems. Patch-based relaxation is highly effective for problems when the null space can be spanned by a basis of locally supported vectors. The patch-based relaxation methods that we develop can be used either within an algebraic multigrid (AMG) hierarchy or as stand-alone preconditioners. These patch-based relaxation techniques are a form of well-known overlapping Schwarz methods where the computational domain is covered with a series of overlapping sub-domains (or patches). Patch relaxation then corresponds to solving a set of independent linear systems associated with each patch. In the context of GMHD, we also reformulate the underlying discrete representation used to generate a suitable set of matrix equations. In general, deriving a discretization that accurately approximates the curl operator and the Hall term while also producing linear systems with physically meaningful near null space properties can be challenging. Unfortunately, many natural discretization choices lead to a near null space that includes non-physical oscillatory modes and where it is not possible to span the near null space with a minimal set of locally supported basis vectors. Further discretization research is needed to understand the resulting trade-offs between accuracy, stability, and ease in solving the associated linear systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2001

Focal adhesion kinase is involved in mechanosensing during fibroblast migration

Focal adhesion kinase (FAK) is a non-receptor protein tyrosine kinase localized at focal adhesions and is believed to mediate adhesion-stimulated effects. Although ablation of FAK impairs cell movement, it is not clear whether FAK might be involved in the guidance of cell migration, a role consistent with its putative regulatory function. We have transfected FAK-null fibroblasts with FAK gene under the control of the tetracycline repression system. Cells were cultured on flexible polyacrylamide substrates for the detection of traction forces and the application of mechanical stimulation. Compared with control cells expressing wild-type FAK, FAK-null cells showed a decrease in migration speed and directional persistence. In addition, whereas FAK-expressing cells responded to exerted forces by reorienting their movements and forming prominent focal adhesions, FAK-null cells failed to show such responses. Furthermore, FAK-null cells showed impaired responses to decreases in substrate flexibility, which causes control cells to generate weaker traction forces and migrate away from soft substrates. Cells expressing Y397F FAK, which cannot be phosphorylated at a key tyrosine site, showed similar defects in migration pattern and force-induced reorientation as did FAK-null cells. However, other aspects of F397-FAK cells, including the responses to substrate flexibility and the amplification of focal adhesions upon mechanical stimulation, were similar to that of control cells. Our results suggest that FAK plays an important role in the response of migrating cells to mechanical input. In addition, phosphorylation at Tyr-397 is required for some, but not all, of the functions of FAK in cell migration.

NASA Discipline Cell Biology↗

NASA NTRS2010

Interferometry in the Era of Very Large Telescopes

Research in modern stellar interferometry has focused primarily on ground-based observatories, with very long baselines or large apertures, that have benefited from recent advances in fringe tracking, phase reconstruction, adaptive optics, guided optics, and modern detectors. As one example, a great deal of effort has been put into development of ground-based nulling interferometers. The nulling technique is the sparse aperture equivalent of conventional coronography used in filled aperture telescopes. In this mode the stellar light itself is suppressed by a destructive fringe, effectively enhancing the contrast of the circumstellar material located near the star. Nulling interferometry has helped to advance our understanding of the astrophysics of many distant objects by providing the spatial resolution necessary to localize the various faint emission sources near bright objects. We illustrate the current capabilities of this technique by describing the first scientific results from the Keck Interferometer Nuller that combines the light from the two largest optical telescopes in the world including new, unpublished measurements of exozodiacal dust disks. We discuss prospects in the near future for interferometry in general, the capabilities of secondary masking interferometry on very large telescopes, and of nulling interferometry using outriggers on very large telescopes. We discuss future development of a simplified space-borne NIR nulling architecture, the Fourier-Kelvin Stellar Interferometer, capable of detecting and characterizing an Earth twin in the near future and how such a mission would benefit from the optical wavelength coverage offered by large, ground-based instruments.

Barry, Richard K.↗

NASA NTRS2012

The Keck Interferometer Nuller

The Keck Interferometer Nuller (KIN), the first operational separated-aperture infrared nulling interferometer, was designed to null the mid-infrared emission from nearby stars so as to ease the measurement of faint circumstellar emission. This paper describes the basis of the KIN's four-beam, two-stage measurement approach and compares it 10 the simpler case of a two-beam nuller. In the four-beam KIN system, the starlight is first nulled in a pair of nullers operating on parallel 85 m Keck-Keck baselines, after which "cross-combination" on 4 m baselines across the Keck apertures is used to modulate and detect residual coherent off-axis emission. Comparison to the constructive itellar fringe provides calibration. The response to an extended source is similar in the two cases, except that the four-beam response includes a term due to the visibility of the source on the cross-combiner baseline-a small effect for relatively compact sources. The characteristics of the dominant null depth errors are also compared for the two cases. In the two-beam nuller, instrumental imperfections and asymmetries lead to a series of quadratic, positivedefinite null leakage terms. For the four-beam nuller, the leakage is instead a series of correlation cross-tenns combining corresponding errors in each of the two nullers, which contribute offsets only to the extent that these errors are correlated on the timescale of the measurement. This four-beam architecture has allowed a significant (approx. order of magnitude) improvement in mid-infrared long-baseline fringe-visibility accuracies.

Serabyn, E.↗

NASA NTRS2008

Terrestrial Planet Finder, Planet Detection Test-Bed: Latest Results of Planet Light Detection in the Presence of Starlight

The Terrestrial Planet Finder, Planet Detection Test-bed is a lab based simulation of the optics and control systems for the Terrestrial Planet Finder Interferometer mission. The test-bed supports starlight nulling at 10um infrared wavelengths, with fringe tracking at 2um wavelengths and angle and shear tracking at visible wavelengths. It further allows injection of simulated planet light in the presence of the nulled star light, to allow testing of planet detection methods. We will describe the detailed construction and operation of the test-bed from an optical and control system perspective. We will also report the latest results for narrow band nulls, and the detection of broad band planet light in the presence of nulled starlight.

Interferometry↗