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NASA NTRS2009

NASA Tech Briefs, October 2009

Topics covered include: Light-Driven Polymeric Bimorph Actuators; Guaranteeing Failsafe Operation of Extended-Scene Shack-Hartmann Wavefront Sensor Algorithm; Cloud Water Content Sensor for Sounding Balloons and Small UAVs; Pixelized Device Control Actuators for Large Adaptive Optics; T-Slide Linear Actuators; G4FET Implementations of Some Logic Circuits; Electrically Variable or Programmable Nonvolatile Capacitors; System for Automated Calibration of Vector Modulators; Complementary Paired G4FETs as Voltage-Controlled NDR Device; Three MMIC Amplifiers for the 120-to-200 GHz Frequency Band; Low-Noise MMIC Amplifiers for 120 to 180 GHz; Using Ozone To Clean and Passivate Oxygen-Handling Hardware; Metal Standards for Waveguide Characterization of Materials; Two-Piece Screens for Decontaminating Granular Material; Mercuric Iodide Anticoincidence Shield for Gamma-Ray Spectrometer; Improved Method of Design for Folding Inflatable Shells; Ultra-Large Solar Sail; Cooperative Three-Robot System for Traversing Steep Slopes; Assemblies of Conformal Tanks; Microfluidic Pumps Containing Teflon[Trademark] AF Diaphragms; Transparent Conveyor of Dielectric Liquids or Particles; Multi-Cone Model for Estimating GPS Ionospheric Delays; High-Sensitivity GaN Microchemical Sensors; On the Divergence of the Velocity Vector in Real-Gas Flow; Progress Toward a Compact, Highly Stable Ion Clock; Instruments for Imaging from Far to Near; Reflectors Made from Membranes Stretched Between Beams; Integrated Risk and Knowledge Management Program -- IRKM-P; LDPC Codes with Minimum Distance Proportional to Block Size; Constructing LDPC Codes from Loop-Free Encoding Modules; MMICs with Radial Probe Transitions to Waveguides; Tests of Low-Noise MMIC Amplifier Module at 290 to 340 GHz; and Extending Newtonian Dynamics to Include Stochastic Processes.

Source record↗
NASA NTRS2005

Actuation of Deformable Mirrors Using Laser Controlled Pistons

Current deformable mirrors used for adaptive optics employ many actuators to adjust the mirror in order to compensate for optical irregularities. These mechanical actuators, which can number in the hundreds for a given mirror, require a significant amount of electrical wires in order to be controlled. The objective of this research is to implement a different type of actuator that can be controlled without the use of wires. The actuator developed employs a laser to quickly heat and expand the air in a closed 'cell'. When the air expands, it pushes a membrane that causes the mirror to move. Creating an array of these cells, and scanning them with a laser can control a deformable mirror. Testing showed that a single cell with a 5 mm diameter and 10 mm in length can deflect a membrane of aluminized Mylar in excess of our minimum requirement of 20 microns. These cells can now be assembled in a 5 x 5 matrix and attached to many small mirrors. An electro-mechanical scanning assembly can be used to aim the laser directly onto individual cells causing the mirror at that location to move.

deformable mirrors↗
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 NTRS2005

Controlling Laser Spot Size in Outer Space

Three documents discuss a method of controlling the diameter of a laser beam projected from Earth to any altitude ranging from low orbit around the Earth to geosynchronous orbit. Such laser beams are under consideration as means of supplying power to orbiting spacecraft at levels of the order of tens of kilowatts apiece. Each such beam would be projected by use of a special purpose telescope having an aperture diameter of 15 m or more. Expanding the laser beam to such a large diameter at low altitude would prevent air breakdown and render the laser beam eyesafe. Typically, the telescope would include an adaptive-optics concave primary mirror and a convex secondary mirror. The laser beam transmitted out to the satellite would remain in the near field on the telescope side of the beam waist, so that the telescope focal point would remain effective in controlling the beam width. By use of positioning stages having submicron resolution and repeatability, the relative positions of the primary and secondary mirrors would be adjusted to change the nominal telescope object and image distances to obtain the desired beam diameter (typically about 6 m) at the altitude of the satellite. The limiting distance D(sub L) at which a constant beam diameter can be maintained is determined by the focal range of the telescope 4 lambda f(sup 2) where lambda is the wavelength and f the f/number of the primary mirror. The shorter the wavelength and the faster the mirror, the longer D(sub L) becomes.

Bennett, Harold E.↗
NASA NTRS2003

Nanolaminate Mirrors With "Piston" Figure-Control Actuators

Efforts are under way to develop a special class of thin-shell curved mirrors for high-resolution imaging in visible and infrared light in a variety of terrestrial or extraterrestrial applications. These mirrors can have diameters of the order of a meter and include metallic film reflectors on nanolaminate substrates supported by multiple distributed piezoceramic gpiston h-type actuators for micron-level figure control. Whereas conventional glass mirrors of equivalent size and precision have areal mass densities between 50 and 150 kg/sq m, the nanolaminate mirrors, including not only the reflector/ shell portions but also the actuators and the backing structures needed to react the actuation forces, would have areal mass densities that may approach .5 kg/m2. Moreover, whereas fabrication of a conventional glass mirror of equivalent precision takes several years, the reflector/shell portion of a nanolaminate mirror can be fabricated in less than a week, and its actuation system can be fabricated in 1 to 2 months. The engineering of these mirrors involves a fusion of the technological heritage of multisegmented adaptive optics and deformable mirrors with more recent advances in metallic nanolaminates and in mathematical modeling of the deflections of thin, curved shells in response to displacements by multiple, distributed actuators. Because a nanolaminate shell is of the order of 10 times as strong as an otherwise identical shell made of a single, high-strength, non-nanolaminate metal suitable for mirror use, a nanolaminate mirror can be made very thin (typically between 100 and 150 m from the back of the nanolaminate substrate to the front reflecting surface). The thinness and strength of the nanolaminate are what make it possible to use distributed gpiston h-type actuators for surface figure control with minimal local concentrated distortion (called print-through in the art) at the actuation points.

Lowman, Andrew↗
NASA NTRS2011

Exoplanetary Science: Instrumentation, Observations, and Expectations

More than 700 exoplanets have been discovered and studied using indirect techniques, leading our field into the exciting new era of comparative exoplanetology. However, the direct detection of exoplanetary systems still remains at the sensitivity limits of both ground- and space-based observatories. The development of new technologies for adaptive optics systems and high contrast instruments continues to increase the ability to directly study exoplanets. The scientific impact of these developments has promising prospects for both short and long timescales. In my talk, I will discuss recent highlights from the SEEDS survey and the current instrumentation in use at the Subaru telescope. SEEDS is a high contrast imaging strategic observing program with 120 nights of time allocated at the NAOJ's flagship optical and infrared telescope. I will also describe new instrumentation I designed to improve the SEEDS capabilities and efficiency. Finally, I will briefly discuss the conceptual design of a transiting planet camera to fly as a potential second generation instrument on-board NASA's SOFIA observatory.

McElwain, Michael↗
NASA NTRS2011

NASA Tech Briefs, November 2011

The topics include: 1) Flight Test Results from the Rake Airflow Gage Experiment on the F-15B; 2) Telemetry and Science Data Software System; 3) CropEx Web-Based Agricultural Monitoring and Decision Support; 4) High-Performance Data Analysis Tools for Sun-Earth Connection Missions; 5) Experiment in Onboard Synthetic Aperture Radar Data Processing; 6) Microfabrication of a High-Throughput Nanochannel Delivery/Filtration System; 7) Improved Design and Fabrication of Hydrated-Salt Pills; 8) Monolithic Flexure Pre-Stressed Ultrasonic Horns; 9) Cryogenic Quenching Process for Electronic Part Screening; 10) Broadband Via-Less Microwave Crossover Using Microstrip-CPW Transitions; 11) Wheel-Based Ice Sensors for Road Vehicles; 12) G-DYN Multibody Dynamics Engine; 13) Multibody Simulation Software Testbed for Small-Body Exploration and Sampling; 14) Propulsive Reaction Control System Model; 15) Licklider Transmission Protocol Implementation; 16) Core Recursive Hierarchical Image Segmentation; 17) Two-Stage Centrifugal Fan; 18) Combined Structural and Trajectory Control of Variable-Geometry Planetary Entry Systems; 19) Pressure Regulator With Internal Ejector Circulation Pump, Flow and Pressure Measurement Porting, and Fuel Cell System Integration Options; 20) Temperature-Sensitive Coating Sensor Based on Hematite; 21) Standardization of a Volumetric Displacement Measurement for Two-Body Abrasion Scratch Test Data Analysis; 22) Detection of Carbon Monoxide Using Polymer-Carbon Composite Films; 23) Substituted Quaternary Ammonium Salts Improve Low-Temperature Performance of Double-Layer Capacitors; 24) Sustainably Sourced, Thermally Resistant, Radiation Hard Biopolymer; 25) Integrated Lens Antennas for Multi-Pixel Receivers; 26) 180-GHz Interferometric Imager; 27) Maturation of Structural Health Management Systems for Solid Rocket Motors; 28) Validating Phasing and Geometry of Large Focal Plane Arrays; 29) Transverse Pupil Shifts for Adaptive Optics Non-Common Path Calibration; 30) Qualification of Fiber Optic Cables for Martian Extreme Temperature Environments; 31) Solid-State Spectral Light Source System; 32) Multiple-Event, Single-Photon Counting Imaging Sensor; 33) Surface Modeling to Support Small-Body Spacecraft Exploration and Proximity Operations; and 34) Achieving Exact and Constant Turnaround Ratio in a DDS-Based Coherent Transponder.

Source record↗
NASA NTRS2011

Sodium Velocity Maps on Mercury

The objective of the current work was to measure two-dimensional maps of sodium velocities on the Mercury surface and examine the maps for evidence of sources or sinks of sodium on the surface. The McMath-Pierce Solar Telescope and the Stellar Spectrograph were used to measure Mercury spectra that were sampled at 7 milliAngstrom intervals. Observations were made each day during the period October 5-9, 2010. The dawn terminator was in view during that time. The velocity shift of the centroid of the Mercury emission line was measured relative to the solar sodium Fraunhofer line corrected for radial velocity of the Earth. The difference between the observed and calculated velocity shift was taken to be the velocity vector of the sodium relative to Earth. For each position of the spectrograph slit, a line of velocities across the planet was measured. Then, the spectrograph slit was stepped over the surface of Mercury at 1 arc second intervals. The position of Mercury was stabilized by an adaptive optics system. The collection of lines were assembled into an images of surface reflection, sodium emission intensities, and Earthward velocities over the surface of Mercury. The velocity map shows patches of higher velocity in the southern hemisphere, suggesting the existence of sodium sources there. The peak earthward velocity occurs in the equatorial region, and extends to the terminator. Since this was a dawn terminator, this might be an indication of dawn evaporation of sodium. Leblanc et al. (2008) have published a velocity map that is similar.

Potter, A. E.↗
NASA NTRS2012

High Energy Laser Beam Propagation in the Atmosphere: The Integral Invariants of the Nonlinear Parabolic Equation and the Method of Moments

The method of moments is used to define and derive expressions for laser beam deflection and beam radius broadening for high-energy propagation through the Earth s atmosphere. These expressions are augmented with the integral invariants of the corresponding nonlinear parabolic equation that describes the electric field of high-energy laser beam to propagation to yield universal equations for the aforementioned quantities; the beam deflection is a linear function of the propagation distance whereas the beam broadening is a quadratic function of distance. The coefficients of these expressions are then derived from a thin screen approximation solution of the nonlinear parabolic equation to give corresponding analytical expressions for a target located outside the Earth s atmospheric layer. These equations, which are graphically presented for a host of propagation scenarios, as well as the thin screen model, are easily amenable to the phase expansions of the wave front for the specification and design of adaptive optics algorithms to correct for the inherent phase aberrations. This work finds application in, for example, the analysis of beamed energy propulsion for space-based vehicles.

Manning, Robert M.↗
NASA NTRS2012

SEEDS Moving Groups and CHARIS Status Updates

We present the status update for the SEEDS Moving Groups category. To date, we have observed 59 targets and currently have more than 20 candidates. We also present the expected scientific capabilities of CHARIS, the Coronagraphic High Angular Resolution Imaging Spectrograph, which is being built for the Subaru 8.2 m telescope of the National Astronomical Observatory of Japan. CHARIS will be implemented behind the new extreme adaptive optics system at Subaru, SCExAO, and the existing 188-actuator system AO188. CHARIS will offer three observing modes over near~infrared wavelengths from 0.9 to 2.4 microns (the y-, J-, H-, and K-bands), including a low-spectral-resolution mode covering this entire wavelength range and a high-resolution mode within a single band. With these capabilities, CHARIS will offer exceptional sensitivity for discovering giant exoplanets, and will enable detailed characterization of their atmospheres, CHARIS, the only planned high-contrast integral field spectrograph on an 8m-class telescope in the Northern Hemisphere, will complement the similar instruments such as Project 1640 at Palomar, and GPI and SPHERE in Chile.

McElwain, Michael↗
NASA NTRS2012

Conceptual Design of the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS) for the Subaru Telescope

Recent developments in high-contrast imaging techniques now make possible both imaging and spectroscopy of planets around nearby stars. We present the conceptual design of the Coronagraphic High Angular Resolution Imaging Spectrograph (CHARIS), a lenslet-based, cryogenic integral field spectrograph (IFS) for imaging exoplanets on the Subaru telescope. The IFS will provide spectral information for 140 x 140 spatial elements over a 1.75 arcsecs x 1.75 arcsecs field of view (FOV). CHARIS will operate in the near infrared (lambda = 0.9 - 2.5 micron) and provide a spectral resolution of R = 14, 33, and 65 in three separate observing modes. Taking advantage of the adaptive optics systems and advanced coronagraphs (AO188 and SCExAO) on the Subaru telescope, CHARIS will provide sufficient contrast to obtain spectra of young self-luminous Jupiter-mass exoplanets. CHARIS is in the early design phases and is projected to have first light by the end of 2015. We report here on the current conceptual design of CHARIS and the design challenges.

Peters, Mary Anne↗
NASA NTRS2012

LightForce: An Update on Orbital Collision Avoidance Using Photon Pressure

We present an update on our research on collision avoidance using photon-pressure induced by ground-based lasers. In the past, we have shown the general feasibility of employing small orbit perturbations, induced by photon pressure from ground-based laser illumination, for collision avoidance in space. Possible applications would be protecting space assets from impacts with debris and stabilizing the orbital debris environment. Focusing on collision avoidance rather than de-orbit, the scheme avoids some of the security and liability implications of active debris removal, and requires less sophisticated hardware than laser ablation. In earlier research we concluded that one ground based system consisting of a 10 kW class laser, directed by a 1.5 m telescope with adaptive optics, could avoid a significant fraction of debris-debris collisions in low Earth orbit. This paper describes our recent efforts, which include refining our original analysis, employing higher fidelity simulations and performing experimental tracking tests. We investigate the efficacy of one or more laser ground stations for debris-debris collision avoidance and satellite protection using simulations to investigate multiple case studies. The approach includes modeling of laser beam propagation through the atmosphere, the debris environment (including actual trajectories and physical parameters), laser facility operations, and simulations of the resulting photon pressure. We also present the results of experimental laser debris tracking tests. These tests track potential targets of a first technical demonstration and quantify the achievable tracking performance.

Stupl, Jan↗
NASA NTRS2012

A First Order Wavefront Estimation Algorithm for P1640 Calibrator

P1640 calibrator is a wavefront sensor working with the P1640 coronagraph and the Palomar 3000 actuator adaptive optics system (P3K) at the Palomar 200 inch Hale telescope. It measures the wavefront by interfering post-coronagraph light with a reference beam formed by low-pass filtering the blocked light from the coronagraph focal plane mask. The P1640 instrument has a similar architecture to the Gemini Planet Imager (GPI) and its performance is currently limited by the quasi-static speckles due to non-common path wavefront errors, which comes from the non-common path for the light to arrive at the AO wavefront sensor and the coronagraph mask. By measuring the wavefront after the coronagraph mask, the non-common path wavefront error can be estimated and corrected by feeding back the error signal to the deformable mirror (DM) of the P3K AO system. Here, we present a first order wavefront estimation algorithm and an instrument calibration scheme used in experiments done recently at Palomar observatory. We calibrate the P1640 calibrator by measuring its responses to poking DM actuators with a sparse checkerboard pattern at different amplitudes. The calibration yields a complex normalization factor for wavefront estimation and establishes the registration of the DM actuators at the pupil camera of the P1640 calibrator, necessary for wavefront correction. Improvement of imaging quality after feeding back the wavefront correction to the AO system demonstrated the efficacy of the algorithm.

Wavefront sensing↗
NASA NTRS2013

Three-Axis Attitude Estimation With a High-Bandwidth Angular Rate Sensor

A continuing challenge for modern instrument pointing control systems is to meet the increasingly stringent pointing performance requirements imposed by emerging advanced scientific, defense, and civilian payloads. Instruments such as adaptive optics telescopes, space interferometers, and optical communications make unprecedented demands on precision pointing capabilities. A cost-effective method was developed for increasing the pointing performance for this class of NASA applications. The solution was to develop an attitude estimator that fuses star tracker and gyro measurements with a high-bandwidth angular rotation sensor (ARS). An ARS is a rate sensor whose bandwidth extends well beyond that of the gyro, typically up to 1,000 Hz or higher. The most promising ARS sensor technology is based on a magnetohydrodynamic concept, and has recently become available commercially. The key idea is that the sensor fusion of the star tracker, gyro, and ARS provides a high-bandwidth attitude estimate suitable for supporting pointing control with a fast-steering mirror or other type of tip/tilt correction for increased performance. The ARS is relatively inexpensive and can be bolted directly next to the gyro and star tracker on the spacecraft bus. The high-bandwidth attitude estimator fuses an ARS sensor with a standard three-axis suite comprised of a gyro and star tracker. The estimation architecture is based on a dual-complementary filter (DCF) structure. The DCF takes a frequency- weighted combination of the sensors such that each sensor is most heavily weighted in a frequency region where it has the lowest noise. An important property of the DCF is that it avoids the need to model disturbance torques in the filter mechanization. This is important because the disturbance torques are generally not known in applications. This property represents an advantage over the prior art because it overcomes a weakness of the Kalman filter that arises when fusing more than one rate measurement. An additional advantage over prior art is that, computationally, the DCF requires significantly fewer real-time calculations than a Kalman filter formulation. There are essentially two reasons for this: the DCF state is not augmented with angular rate, and measurement updates occur at the slower gyro rate instead of the faster ARS sampling rate. Finally, the DCF has a simple and compelling architecture. The DCF is exactly equivalent to flying two identical attitude observers, one at low rate and one at high rate. These attitude observers are exactly of the form currently flown on typical three-axis spacecraft.

Bayard, David S.↗
NASA NTRS2012

Direct Imaging of Extra-Solar Planets in Star Forming Regions: Lessons Learned from a False Positive Around IM Lup

Context. Most exoplanet imagers consist of ground-based adaptive optics coronagraphic cameras which are currently limited in contrast, sensitivity and astrometric precision, but advantageously observe in the near-infrared window (1 5 m). Because of these practical limitations, our current observational aim at detecting and characterizing planets puts heavy constraints on target selection, observing strategies, data reduction, and follow-up. Most surveys so far have thus targeted young systems (1 100 Myr) to catch the putative remnant thermal radiation of giant planets, which peaks in the near-infrared. They also favor systems in the solar neighborhood (d less than 80 pc), which eases angular resolution requirements but also ensures a good knowledge of the distance and proper motion, which are critical to secure the planet status, and enable subsequent characterization. Aims. Because of their youth, it is very tempting to target the nearby star forming regions, which are typically twice as far as the bulk of objects usually combed for planets by direct imaging. Probing these interesting reservoirs sets additional constraints that we review in this paper by presenting the planet search that we initiated in 2008 around the disk-bearing T Tauri star IM Lup, which is part of the Lupus star forming region (140-190 pc). Methods. We show and discuss why age determination, the choice of evolutionary model for both the central star and the planet, precise knowledge of the host star proper motion, relative or absolute (between different instruments) astrometric accuracy (including plate scale calibration), and patience are the key ingredients for exoplanet searches around more distant young stars. Results. Unfortunately, most of the time, precision and perseverance are not paying off: we discovered a candidate companion around IM Lup in 2008, which we report here to be an unbound background object. We nevertheless review in details the lessons learned from our endeavor, and additionally present the best detection limits ever calculated for IM Lup. We also accessorily report on the successful use of innovative data reduction techniques, such as the damped-LOCI and iterative roll subtraction.

D Mawet↗
NASA NTRS2012

A Precise Physical Orbit For The M-Dwarf Binary Gliese 268

We report high-precision interferometric and radial velocity (RV) observations of the M-dwarf binary Gl 268. Combining measurements conducted using the IOTA interferometer and the ELODIE and Harvard Center for Astrophysics RV instruments leads to a mass of 0.22596 plus-minus 0.00084 Mass compared to the sun for component A and 0.19230 plus-minus 0.00071 Mass compared to the sun for component B. The system parallax as determined by these observations is 0.1560 plus-minus 0.0030 arcsec - a measurement with 1.9% uncertainty in excellent agreement with Hipparcos (0.1572 plus-minus 0.0033). The absolute H-band magnitudes of the component stars are not well constrained by these measurements; however, we can place an approximate upper limit of 7.95 and 8.1 for Gl 268A and B, respectively.We test these physical parameters against the predictions of theoretical models that combine stellar evolution with high fidelity, non-gray atmospheric models. Measured and predicted values are compatible within 2sigma. These results are among the most precise masses measured for visual binaries and compete with the best adaptive optics and eclipsing binary results.

Barry, R. K.↗
NASA NTRS2014

Near Infrared Activity Close to the Crab Pulsar Correlated with Giant Gamma-ray Flares

We describe activity observed in the near-infrared correlated with a giant gamma-ray flare in the Crab Pulsar. The Crab Pulsar has been observed by the Fermi and AGILE satellites to flare for a period of 3 to 7 days, once every 1-1.5 years, increasing in brightness by a factor of 3-10 between 100MeV and 1GeV. We used Keck NIRC2 laser guide star adaptive optics imaging to observe the Crab Pulsar and environs before and during the March 2013 flare. We discuss the evidence for the knot as the location of the flares, and the theoretical implications of these observations. Ongoing target-of-opportunity programs hope to confirm this correlation for future flares.

Rudy, Alexander R.↗
NASA NTRS2013

Direct Imaging Search for Extrasolar Planets in the Pleiades

We carried out an imaging survey for extrasolar planets around stars in the Pleiades (125 Myr, 135 pc) in the H and K(sub S) bands using HiCIAO combined with adaptive optics, AO188, on the Subaru telescope. We found 13 companion candidates fainter than 14.5 mag in the H band around 9 stars. Five of these 13 were confirmed to be background stars by measurement of their proper motion. One was not found in the second epoch observation, and thus was not a background or companion object. One had multi-epoch images, but the precision of its proper motion was not sufficient to conclude whether it was a background object. Four other candidates are waiting for second-epoch observations to determine their proper motion. Finally, the remaining two were confirmed to be 60 M(sub J) brown dwarf companions orbiting around HD 23514 (G0) and HII 1348 (K5), respectively, as had been reported in previous studies. In our observations, the average detection limit for a point source was 20.3 mag in the H band beyond 1.′′ 5 from the central star. On the basis of this detection limit, we calculated the detection efficiency to be 90% for a planet with 6 to 12 Jovian masses and a semi-major axis of 50–1000 AU. For this reason we extrapolated the distribution of the planet mass and the semi-major axis derived from radial velocity observations, and adopted the planet evolution model Baraffe et al. (2003, A&A, 402, 701). Since there was no detection of a planet, we estimated the frequency of such planets to be less than 17.9% (2 sigma) around one star of the Pleiades cluster.

extrasolar planets↗