Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.

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Information Theory, Inference and Learning Algorithms

We describe the design, construction, and performance of the Sloan Digital Sky Survey telescope located at Apache Point Observatory. The telescope is a modified two-corrector Ritchey-Chretien design with a 2.5 m, f/2.25 primary, a 1.08 m secondary, a Gascoigne astigmatism corrector, and one of a pair of interchangeable highly aspheric correctors near the focal plane, one for imaging and the other for spectroscopy. The final focal ratio is f/5. The telescope is instrumented by a wide-area, multiband CCD camera and a pair of fiber-fed double spectrographs. Novel features of the telescope include the following: (1) A 3° diameter (0.65 m) focal plane that has excellent image quality and small geometric distortions over a wide wavelength range (3000-10,600 A) in the imaging mode, and good image quality combined with very small lateral and longitudinal color errors in the spectroscopic mode. The unusual requirement of very low distortion is set by the demands of time-delay-and-integrate (TDI) imaging. (2) Very high precision motion to support open-loop TDI observations. (3) A unique wind baffle/enclosure construction to maximize image quality and minimize construction costs. The telescope had first light in 1998 May and began regular survey operations in 2000.

https://iopscience.iop.org/article/10.1086/500975/pdf

The 2.5 m Telescope of the Sloan Digital Sky Survey

Course Description This is an advanced course in which we explore the field of Statistical Optics. Topics covered include such subjects as the statistical properties of natural (thermal) and laser light, spatial and temporal coherence, effects of partial coherence on optical imaging instruments, effects on imaging due to randomly inhomogeneous media, and a statistical treatment of the detection of light. Development of this more comprehensive model of the behavior of light draws upon the use of tools traditionally available to the electrical engineer, such as linear system theory and the theory of stochastic processes.

http://ieeexplore.ieee.org/iel5/3/23094/01073023.pdf

Statistical optics

The Bayesian framework for model comparison and regularisation is demonstrated by studying interpolation and classification problems modelled with both linear and non-linear models. This framework quantitatively embodies 'Occam's razor'. Over-complex and under-regularised models are automatically inferred to be less probable, even though their flexibility allows them to fit the data better.
When applied to 'neural networks', the Bayesian framework makes possible (1) objective comparison of solutions using alternative network architectures; (2) objective stopping rules for network pruning or growing procedures; (3) objective choice of type of weight decay terms (or regularisers); (4) on-line techniques for optimising weight decay (or regularisation constant) magnitude; (5) a measure of the effective number of well-determined parameters in a model; (6) quantified estimates of the error bars on network parameters and on network output. In the case of classification models, it is shown that the careful incorporation of error bar information into a classifier's predictions yields improved performance.
Comparisons of the inferences of the Bayesian framework with more traditional cross-validation methods help detect poor underlying assumptions in learning models.
The relationship of the Bayesian learning framework to 'active learning' is examined. Objective functions are discussed which measure the expected informativeness of candidate data measurements, in the context of both interpolation and classification problems.
The concepts and methods described in this thesis are quite general and will be applicable to other data modelling problems whether they involve regression, classification or density estimation.

Bayesian methods for adaptive models

1. Introduction 2. Radial velocities 3. Astrometry 4. Timing 5. Microlensing 6. Transits 7. Imaging 8. Host stars 9. Brown dwarfs and free-floating planets 10. Formation and evolution 11. Interiors and atmospheres 12. The Solar System Appendixes References Index.

/pdf/the-exoplanet-handbook-3g3nzlvc20.pdf

The Exoplanet Handbook

IMAGES formed by ground-based telescopes are marred by atmospheric 'seeing9. The plane wavefront from an unresolved star is distorted by continually changing turbulent fluctuations in the air's refractive index. Diffraction-limited performance can in principle be recovered through the methods of adaptive optics, in which the instantaneous wavefront shape is sensed and corrected in real-time by deformable optics that cancel the distortion1,2. The highest resolution will be achieved when this technique is applied to multiple-telescope arrays. For such arrays, the biggest errors caused by seeing at infrared wavelengths are the variations in pathlength and wavefront tilt between array elements. We show here that these errors can be derived by an artificial neural network, given only a pair of simultaneous in-focus and out-of-focus images of a reference star formed at the combined focus of all the array elements. We have optimized a neural network appropriate for 2.2-μm wavelength imaging at the Multiple Mirror Telescope in Arizona. Corrections made by moving the beam-combining mirrors will largely recover the diffraction-limited profile, with a resolution of 0.06 arcsec.

Adaptive optics for array telescopes using neural-network techniques

When equipped with adaptive optics, the coming generation of large 6–10-m telescopes can combine huge light grasp with very sharp images. We describe a specific design concept for recovery of diffraction-limited images in the 1.6- and the 2.2-μm atmospheric windows, yielding 0.05-arcsec resolution for an 8-m telescope. Our goal has been to achieve this performance routinely by not requiring above-average atmospheric conditions or the use of unusually bright nearby stars. Atmospheric blurring is sensed with a sodium laser beacon of a few watts. Image motion is sensed by starlight, with a quadrant detector that is sensitive to the broad infrared band in which photon flux is typically largest and the field star has been sharpened by laser-beacon correction that is shared with the science target. A detailed performance analysis shows that for typical conditions Strehl ratios of >25% are expected at 2.2 μm, with the probability of finding a sufficiently bright field star exceeding 50%.

Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes

We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high-performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramer-Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramer-Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

Using five independent analytic and Monte Carlo simulation codes, we have studied the performance of wide-field ground-layer adaptive optics (GLAO), which can use a single, relatively low order deformable mirror to correct the wave-front errors from the lowest altitude turbulence. GLAO concentrates more light from a point source in a smaller area on the science detector, but unlike with traditional adaptive optics, images do not become diffraction-limited. Rather, the GLAO point-spread function (PSF) has the same functional form as a seeing-limited PSF and can be characterized by familiar performance metrics such as full width at half-maximum (FWHM). The FWHM of a GLAO PSF is reduced by 01 or more for optical and near-infrared wavelengths over different atmospheric conditions. For the Cerro Pachon atmospheric model, this correction is even greater when the image quality is poorest, which effectively eliminates "bad seeing" nights; the best seeing-limited image quality, available only 20% of the time, can be achieved 60%–80% of the time with GLAO. This concentration of energy in the PSF will reduce required exposure times and improve the efficiency of an observatory up to 30%–40%. These performance gains are relatively insensitive to a number of trade-offs, including the exact field of view of a wide-field GLAO system, the conjugate altitude and actuator density of the deformable mirror, and the number and configuration of the guide stars.

/pdf/performance-modeling-of-a-wide-field-ground-layer-adaptive-24gcn385d4.pdf

Performance Modeling of a Wide-Field Ground-Layer Adaptive Optics System

An adaptive optics system is being built for the 6.5 m Multiple Mirror Telescope (MMT) conversion on Mount Hopkins for diffraction-limited observations in the near-infrared. At the heart of the system is a deformable secondary mirror which introduces corrections to the optical wavefront. By compensating these errors at the telescope's secondary, the system has been optimized for low thermal emissivity and high photon throughput. The scientific productivity of the facility will thereby be enhanced in comparison with a telescope equipped with more conventional adaptive optics. The Large Binocular Telescope under construction on Mount Graham will also use adaptive secondary mirrors. This paper explores the benefit to both facilities in terms of the integration time required to achieve a given signal-to-noise ratio. The gain is found to be substantial in the photometric bands K, L, M, and N.

https://www.jstor.org/stable/10.1086/316503

Michael Lloyd-Hart

Papers

Adaptive optics for array telescopes using neural-network techniques

Adaptive optics for diffraction-limited infrared imaging with 8-m telescopes

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

Performance Modeling of a Wide-Field Ground-Layer Adaptive Optics System

Thermal Performance Enhancement of Adaptive Optics by Use of a Deformable Secondary Mirror