Titan: High-Resolution Speckle Images from the Keck Telescope

Atmospheric turbulence profoundly limits the angular resolution of astronomical telescopes working at visible and near-infrared wavelengths. In fact, the angular resolution for conventional imaging through turbulence is on the order of 5{endash}20{percent} of the diffraction-limited resolution at the best observatories in the world. The origin of these performance degradations is random turbulence-induced fluctuations in the index of refraction of the atmosphere. Random index-of-refraction fluctuations producing the optical path length of the atmosphere to be random in both space and time, producing random aberrations in the telescope pupil that degrade imaging performance. Over the past several years significant advances have been made in developing both hardware and image-processing-based techniques for improving the resolution of astronomical telescopes. Hardware-oriented correction techniques are based on wave-front sensing and adaptive optics. Image-processing-based methods include speckle-imaging techniques and hybrid imaging techniques that use elements of adaptive-optics systems and image reconstruction. Analysis techniques for predicting the performance of these imaging methods have been developed, and the comparative performance of these imaging techniques has been examined. This paper discusses turbulence and image-detection statistics, describes the fundamentals of methods for overcoming turbulence effects, and provides representative performance results. {copyright} {ital 1997} {ital The American Physical Society}

Improving the resolution of ground-based telescopes

Abstract An analysis of the effects of photon noise on astronomical speckle image reconstruction using the Knox-Thompson algorithm is presented. It is shown that the quantities resulting from the speckle average are biased, but that the biases are easily estimated and compensated. Calculations are also made of the convergence rate for the speckle average as a function of the source brightness. An illustration of the effects of photon noise on the image recovery process is included.

Effects of photon noise on speckle image reconstruction with the Knox-Thompson algorithm. [in astronomy

We present a new speckle camera designed and built at Observatoire Midi-Pyrenees. This focal instrument has been used for four years with the 2-meter Bernard Lyot Telescope of Pic du Midi observatory. It can be set in various operating modes: full pupil imaging, masked-pupil imaging, spectroscopy, wave-front sensor and stellar coronagraphy, hence its name 'PISCO' ('Pupil Interferometry Speckle COronagraph'). Restored images of double and triple stars have demonstrated its capabilities in providing close to diffraction limited images (0.06′′ in V). PISCO has been fully tested and is now ready to be used by the whole astronomical community.

https://hal.archives-ouvertes.fr/hal-00102232/document

The 'Pisco' Speckle Camera at Pic Du Midi Observatory

Long-baseline optical interferometry uses the power spectrum and bispectrum constructs as fundamental observables. Noise arising in the detection of the fringe pattern gives rise to both variance and biases in the power spectrum and bispectrum. Previous work on correcting the biases and estimating the variances for these quantities typically includes restrictive assumptions about the sampling of the interferogram and/or about the relative importance of Poisson and Gaussian noise sources. Until now it has been difficult to accurately compensate for systematic biases in data which violates these assumptions. We seek a formalism to allow the construction of bias-free estimators of the bispectrum and power spectrum, and to estimate their variances, under less restrictive conditions which include both unevenly-sampled data and measurements affected by a combination of noise sources with Poisson and Gaussian statistics. We used a method based on the moments of the noise distributions to derive formulae for the biases introduced to the power spectrum and bispectrum when the complex fringe amplitude is derived from an arbitrary linear combinations of a set of discrete interferogram measurements. We simulated interferograms with different combinations of photon noise and read noise and with different fringe encoding schemes to illustrate the effects of these biases. We have derived formulae for bias-free estimators of the power spectrum and bispectrum which can be used with any linear estimator of the fringe complex amplitude. We have demonstrated the importance of bias-free estimators for the case of the detection of faint companions (for example exoplanets) using closure phase nulling. We have derived formulae for the variance of the power spectrum and have shown how the variance of the bispectrum could be calculated.

/pdf/detection-noise-bias-and-variance-in-the-power-spectrum-and-1o18yj74bo.pdf

Detection noise bias and variance in the power spectrum and bispectrum in optical interferometry

Limits to the recovery of planetary images by speckle imaging were investigated by means of a numerical simulation of the image-forming process. Laboratory measurements established that the numerical model correctly represented the process. With this numerical model we studied the observing conditions required to obtain useful planetary data for Neptune and Io, and we learned which factors are important for the successful recovery of images. We also showed that our methods of amplitude and phase recovery do not contribute to image degradation, which is essentially caused by photon noise alone. From this conclusion we were led to two simple models of speckle imaging that involve neither details of the recovery procedure nor of the atmospheric behavior (except for the size of the seeing disk). Both models are governed by a dimensionless ratio that involves all parameters relevant to the process of image restoration. The models can be used by any observer, and they have been used by us to predict the performance of speckle imaging for T-tauri stars and for a Mars cloud study.

Recovery of planetary images by speckle imaging.

Deterministic photon bias in speckle imaging

This paper is devoted to the development of a two-dimensional computer-simulation model that is based on the rigid constraints of optical diffraction theory with careful attention paid to the generation of sample realizations of Gaussian-distributed, spatially random, isotropic wave fronts that have zero-mean and prescribed-covariance functions. Given a sample realization of the wave front, the corresponding centered point-spread function and optical-transfer function are evaluated. A detailed study is made of the statistics of random wave-front tilt, point-spread function, modulus squared of transfer function, and phase of transfer function.

Influence of atmospherically induced random wave fronts on diffraction imagery : a computer simulation model for testing image reconstruction algorithms

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Recovery of planetary images by speckle imaging.

Deterministic photon bias in speckle imaging

Influence of atmospherically induced random wave fronts on diffraction imagery : a computer simulation model for testing image reconstruction algorithms