de Villiers / Pike The Limits of Resolution

Erscheinungsjahr 2016
ISBN: 978-1-4987-5812-3
Verlag: CRC Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 568 Seiten

Reihe: Series in Optics and Optoelectronics

This book brings together the concept of resolution, which limits what we can determine about our physical world, with linear inverse problems, with an emphasis on showcasing real examples and practical applications. The book focuses on methods for solving illposed problems that do not have unique stable solutions. After introducing basic concepts, the contents address problems with “continuous” data in detail before turning to cases of discrete data sets. As one of the unifying principles of the text, the authors explain how non-uniqueness is a feature of measurement problems in science where precision and resolution is essentially always limited by some kind of noise.

Autoren/Hrsg.

de Villiers, Geoffrey

Pike, E. Roy

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Lasertechnologie, Holographie
• Technische Wissenschaften Technik Allgemein Technische Optik, Lasertechnologie

Inhaltsverzeichnis

Early concepts of resolution. Modern concepts of resolution. Elementary functional analysis. Resolution and ill-posedness.
Optimisation. Deterministic methods for linear inverse problems. Convolution equations and deterministic spectral analysis. Statistical
methods and resolution. Statistical spectral analysis. Resolution in optical microscopy. Some further optical applications. Appendixes.
The origin of spectacles. Set theory and mappings. Methods for finding the eigenvalue and singular-value decompositions. Topological
spaces. Basic probability theory