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

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

Confidence Level and Sensitivity Limits in High Contrast Imaging

In long adaptive optics corrected exposures, exoplanet detections are currently limited by speckle noise originating from the telescope and instrument optics, and it is expected that such noise will also limit future high-contrast imaging instruments for both ground and space-based telescopes. Previous theoretical analysis have shown that the time intensity variations of a single speckle follows a modified Rician. It is first demonstrated here that for a circular pupil this temporal intensity distribution also represents the speckle spatial intensity distribution at a fix separation from the point spread function center; this fact is demonstrated using numerical simulations for coronagraphic and non-coronagraphic data. The real statistical distribution of the noise needs to be taken into account explicitly when selecting a detection threshold appropriate for some desired confidence level. In this paper, a technique is described to obtain the pixel intensity distribution of an image and its corresponding confidence level as a function of the detection threshold. Using numerical simulations, it is shown that in the presence of speckles noise, a detection threshold up to three times higher is required to obtain a confidence level equivalent to that at 5sigma for Gaussian noise. The technique is then tested using TRIDENT CFHT and angular differential imaging NIRI Gemini adaptive optics data. It is found that the angular differential imaging technique produces quasi-Gaussian residuals, a remarkable result compared to classical adaptive optic imaging. A power-law is finally derived to predict the 1-3*10^-7 confidence level detection threshold when averaging a partially correlated non-Gaussian noise.Comment: 29 pages, 13 figures, accepted to Ap

An Analysis of Fundamental Waffle Mode in Early AEOS Adaptive Optics Images

Adaptive optics (AO) systems have significantly improved astronomical imaging capabilities over the last decade, and are revolutionizing the kinds of science possible with 4-5m class ground-based telescopes. A thorough understanding of AO system performance at the telescope can enable new frontiers of science as observations push AO systems to their performance limits. We look at recent advances with wave front reconstruction (WFR) on the Advanced Electro-Optical System (AEOS) 3.6 m telescope to show how progress made in improving WFR can be measured directly in improved science images. We describe how a "waffle mode" wave front error (which is not sensed by a Fried geometry Shack-Hartmann wave front sensor) affects the AO point-spread function (PSF). We model details of AEOS AO to simulate a PSF which matches the actual AO PSF in the I-band, and show that while the older observed AEOS PSF contained several times more waffle error than expected, improved WFR techniques noticeably improve AEOS AO performance. We estimate the impact of these improved WFRs on H-band imaging at AEOS, chosen based on the optimization of the Lyot Project near-infrared coronagraph at this bandpass.Comment: 15 pages, 11 figures, 1 table; to appear in PASP, August 200

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

The statistics of the photometric accuracy based on MASS data and the evaluation of high-altitude wind

The effect of stellar scintillation on the accuracy of photometric measurements is analyzed. We obtain a convenient form of estimaton of this effect in the long exposure regime, when the turbulence shift produced by the wind is much larger than the aperture of the telescope. A simple method is proposed to determine index $S_3$ introduced by perture of the Kenyon et al. (2006), directly from the measurements with the Multi Aperture Scintillation Sensor (MASS) without information on vertical profile of the wind. The statistics $S_3$ resulting from our campaign of 2005 -- 2007 at Maidanak observatory is presented. It is shown that these data can be used to estimate high-altitude winds at pressure level 70 -- 100 mbar. Comparison with the wind speed retrieved from the NCEP/NCAR global models shows a good agreement. Some prospects for retrieval of the wind speed profile from the MASS measurements are outlined.Comment: 11 pages, 9 figures, accepted for publication in Astronomy Letter

Michelson Interferometry with the Keck I Telescope

We report the first use of Michelson interferometry on the Keck I telescope for diffraction-limited imaging in the near infrared JHK and L bands. By using an aperture mask located close to the f/25 secondary, the 10 m Keck primary mirror was transformed into a separate-element, multiple aperture interferometer. This has allowed diffraction-limited imaging of a large number of bright astrophysical targets, including the geometrically complex dust envelopes around a number of evolved stars. The successful restoration of these images, with dynamic ranges in excess of 200:1, highlights the significant capabilities of sparse aperture imaging as compared with more conventional filled-pupil speckle imaging for the class of bright targets considered here. In particular the enhancement of the signal-to-noise ratio of the Fourier data, precipitated by the reduction in atmospheric noise, allows high fidelity imaging of complex sources with small numbers of short-exposure images relative to speckle. Multi-epoch measurements confirm the reliability of this imaging technique and our whole dataset provides a powerful demonstration of the capabilities of aperture masking methods when utilized with the current generation of large-aperture telescopes. The relationship between these new results and recent advances in interferometry and adaptive optics is briefly discussed.Comment: Accepted into Publications of the Astronomical Society of the Pacific. To appear in vol. 112. Paper contains 10 pages, 8 figure