A New Shear Estimator for Weak Lensing Observations

We present a new shear estimator for weak lensing observations which properly accounts for the effects of a realistic point spread function (PSF). Images of faint galaxies are subject to gravitational shearing followed by smearing with the instrumental and/or atmospheric PSF. We construct a `finite resolution shear operator' which when applied to an observed image has the same effect as a gravitational shear applied prior to smearing. This operator allows one to calibrate essentially any shear estimator. We then specialize to the case of weighted second moment shear estimators. We compute the shear polarizability which gives the response of an individual galaxy's polarization to a gravitational shear. We then compute the response of the population of galaxies, and thereby construct an optimal weighting scheme for combining shear estimates from galaxies of various shapes, luminosities and sizes. We define a figure of merit --- an inverse shear variance per unit solid angle --- which characterizes the quality of image data for shear measurement. The new method is tested with simulated image data. We discuss the correction for anisotropy of the PSF and propose a new technique involving measuring shapes from images which have been convolved with a re-circularizing PSF. We draw attention to a hitherto ignored noise related bias and show how this can be analyzed and corrected for. The analysis here draws heavily on the properties of real PSF's and we include as an appendix a brief review, highlighting those aspects which are relevant for weak lensing.Comment: 39 pages, 9 figure

Detection of arcs in Saturn's F ring during the 1995 Sun ring-plane crossing

Observations of the November 1995 Sun crossing of the Saturn's ring-plane made with the 3.6m CFH telescope, using the UHAO adaptive optics system, are presented here. We report the detection of four arcs located in the vicinity of the F ring. They can be seen one day later in HST images. The combination of both data sets gives accurate determinations of their orbits. Semi-major axes range from 140020 km to 140080 km, with a mean of 140060 +- 60 km. This is about 150 km smaller than previous estimates of the F ring radius from Voyager 1 and 2 data, but close to the orbit of another arc observed at the same epoch in HST images.Comment: 8 pages, 3 figures, 1 table, To appear in A&A, for comments : [email protected]

A New Strategy for Deep Wide-Field High Resolution Optical Imaging

We propose a new strategy for obtaining enhanced resolution (FWHM = 0.12 arcsec) deep optical images over a wide field of view. As is well known, this type of image quality can be obtained in principle simply by fast guiding on a small (D = 1.5m) telescope at a good site, but only for target objects which lie within a limited angular distance of a suitably bright guide star. For high altitude turbulence this 'isokinetic angle' is approximately 1 arcminute. With a 1 degree field say one would need to track and correct the motions of thousands of isokinetic patches, yet there are typically too few sufficiently bright guide stars to provide the necessary guiding information. Our proposed solution to these problems has two novel features. The first is to use orthogonal transfer charge-coupled device (OTCCD) technology to effectively implement a wide field 'rubber focal plane' detector composed of an array of cells which can be guided independently. The second is to combine measured motions of a set of guide stars made with an array of telescopes to provide the extra information needed to fully determine the deflection field. We discuss the performance, feasibility and design constraints on a system which would provide the collecting area equivalent to a single 9m telescope, a 1 degree square field and 0.12 arcsec FWHM image quality.Comment: 46 pages, 22 figures, submitted to PASP, a version with higher resolution images and other supplementary material can be found at http://www.ifa.hawaii.edu/~kaiser/wfhr

Speckle Statistics in Adaptively Corrected Images

(abridged) Imaging observations are generally affected by a fluctuating background of speckles, a particular problem when detecting faint stellar companions at small angular separations. Knowing the distribution of the speckle intensities at a given location in the image plane is important for understanding the noise limits of companion detection. The speckle noise limit in a long-exposure image is characterized by the intensity variance and the speckle lifetime. In this paper we address the former quantity through the distribution function of speckle intensity. Previous theoretical work has predicted a form for this distribution function at a single location in the image plane. We developed a fast readout mode to take short exposures of stellar images corrected by adaptive optics at the ground-based UCO/Lick Observatory, with integration times of 5 ms and a time between successive frames of 14.5 ms ($\lambda=2.2$ $\mu$m). These observations temporally oversample and spatially Nyquist sample the observed speckle patterns. We show, for various locations in the image plane, the observed distribution of speckle intensities is consistent with the predicted form. Additionally, we demonstrate a method by which $I_c$ and $I_s$ can be mapped over the image plane. As the quantity $I_c$ is proportional to the PSF of the telescope free of random atmospheric aberrations, this method can be used for PSF calibration and reconstruction.Comment: 7 pages, 4 figures, ApJ accepte

Improving Interferometric Null Depth Measurements using Statistical Distributions: Theory and First Results with the Palomar Fiber Nuller

A new "self-calibrated" statistical analysis method has been developed for the reduction of nulling interferometry data. The idea is to use the statistical distributions of the fluctuating null depth and beam intensities to retrieve the astrophysical null depth (or equivalently the object's visibility) in the presence of fast atmospheric fluctuations. The approach yields an accuracy much better (about an order of magnitude) than is presently possible with standard data reduction methods, because the astrophysical null depth accuracy is no longer limited by the magnitude of the instrumental phase and intensity errors but by uncertainties on their probability distributions. This approach was tested on the sky with the two-aperture fiber nulling instrument mounted on the Palomar Hale telescope. Using our new data analysis approach alone-and no observations of calibrators-we find that error bars on the astrophysical null depth as low as a few 10-4 can be obtained in the near-infrared, which means that null depths lower than 10-3 can be reliably measured. This statistical analysis is not specific to our instrument and may be applicable to other interferometers

Optimization of Apodized Pupil Lyot Coronagraph for ELTs

We study the optimization of the Apodized Pupil Lyot Coronagraph (APLC) in the context of exoplanet imaging with ground-based telescopes. The APLC combines an apodization in the pupil plane with a small Lyot mask in the focal plane of the instrument. It has been intensively studied in the literature from a theoretical point of view, and prototypes are currently being manufactured for several projects. This analysis is focused on the case of Extremely Large Telescopes, but is also relevant for other telescope designs. We define a criterion to optimize the APLC with respect to telescope characteristics like central obscuration, pupil shape, low order segment aberrations and reflectivity as function of the APLC apodizer function and mask diameter. Specifically, the method was applied to two possible designs of the future European-Extremely Large Telescope (E-ELT). Optimum configurations of the APLC were derived for different telescope characteristics. We show that the optimum configuration is a stronger function of central obscuration size than of other telescope parameters. We also show that APLC performance is quite insensitive to the central obscuration ratio when the APLC is operated in its optimum configuration, and demonstrate that APLC optimization based on throughput alone is not appropriate.Comment: 9 pages, 17 figures, accepted for publication in Astronomy & Astrophysic

Characterizing the Adaptive Optics Off-Axis Point-Spread Function - I: A Semi-Empirical Method for Use in Natural-Guide-Star Observations

Even though the technology of adaptive optics (AO) is rapidly maturing, calibration of the resulting images remains a major challenge. The AO point-spread function (PSF) changes quickly both in time and position on the sky. In a typical observation the star used for guiding will be separated from the scientific target by 10" to 30". This is sufficient separation to render images of the guide star by themselves nearly useless in characterizing the PSF at the off-axis target position. A semi-empirical technique is described that improves the determination of the AO off-axis PSF. The method uses calibration images of dense star fields to determine the change in PSF with field position. It then uses this information to correct contemporaneous images of the guide star to produce a PSF that is more accurate for both the target position and the time of a scientific observation. We report on tests of the method using natural-guide-star AO systems on the Canada-France-Hawaii Telescope and Lick Observatory Shane Telescope, augmented by simple atmospheric computer simulations. At 25" off-axis, predicting the PSF full width at half maximum using only information about the guide star results in an error of 60%. Using an image of a dense star field lowers this error to 33%, and our method, which also folds in information about the on-axis PSF, further decreases the error to 19%.Comment: 29 pages, 9 figures, accepted for publication in the PAS

Imaging extrasolar planets by stellar halo suppression in separately-corrected color bands

Extra-solar planets have not been imaged directly with existing ground or space telescopes because they are too faint to be seen against the halo of the nearby bright star. Most techniques being explored to suppress the halo are achromatic, with separate correction of diffraction and wavefront errors. Residual speckle structure may be subtracted by differencing images taken through narrowband filters, but photon noise remains and ultimately limits sensitivity. Here we describe two ways to take advantage of narrow bands to reduce speckle photon flux and to obtain better control of systematic errors. Multiple images are formed in separate color bands of 5-10% bandwidth, and recorded by coronagraphic interferometers equipped with active control of wavefront phase and/or amplitude. In one method, a single deformable pupil mirror is used to actively correct both diffraction and wavefront components of the halo. This yields good diffraction suppression for complex pupil obscuration, with high throughput over half the focal plane. In a second method, the coronagraphic interferometer is used as a second stage after conventional apodization. The halo from uncontrollable residual errors in the pupil mask or wavefront is removed by destructive interference made directly at the detector focal plane with an "anti-halo", synthesized by spatial light modulators in the reference arm of the interferometer. In this way very deep suppression may be achieved by control elements with greatly relaxed, and thus achievable, tolerances. In both examples, systematic errors are minimized because the planet imaging cameras themselves also provide the error sensing data.Comment: Accepted by ApJ

Adaptive optics in high-contrast imaging

The development of adaptive optics (AO) played a major role in modern astronomy over the last three decades. By compensating for the atmospheric turbulence, these systems enable to reach the diffraction limit on large telescopes. In this review, we will focus on high contrast applications of adaptive optics, namely, imaging the close vicinity of bright stellar objects and revealing regions otherwise hidden within the turbulent halo of the atmosphere to look for objects with a contrast ratio lower than 10^-4 with respect to the central star. Such high-contrast AO-corrected observations have led to fundamental results in our current understanding of planetary formation and evolution as well as stellar evolution. AO systems equipped three generations of instruments, from the first pioneering experiments in the nineties, to the first wave of instruments on 8m-class telescopes in the years 2000, and finally to the extreme AO systems that have recently started operations. Along with high-contrast techniques, AO enables to reveal the circumstellar environment: massive protoplanetary disks featuring spiral arms, gaps or other asymmetries hinting at on-going planet formation, young giant planets shining in thermal emission, or tenuous debris disks and micron-sized dust leftover from collisions in massive asteroid-belt analogs. After introducing the science case and technical requirements, we will review the architecture of standard and extreme AO systems, before presenting a few selected science highlights obtained with recent AO instruments.Comment: 24 pages, 14 figure