*S. R. Cloude*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199569731
- eISBN:
- 9780191721908
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199569731.003.0006
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, Geophysics, Atmospheric and Environmental Physics

This chapter deals with the formal fusion of polarisation with interferometry. It develops an approach based on a general coherency matrix formulation, which scales naturally to multiple baselines, ...
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This chapter deals with the formal fusion of polarisation with interferometry. It develops an approach based on a general coherency matrix formulation, which scales naturally to multiple baselines, and shows how this may be used to generate interferograms for arbitrary choice of transmit and receive polarisations. It then considers the topic of coherence optimisation: methods for selecting the polarisation combinations that maximise the interferometric coherence and hence minimise the phase error. It is shown that there are two important classes of such optimisation: constrained and unconstrained. This leads to several important new concepts such as the coherence region, and the relationship between singular value decomposition (SVD) and Schur subspace analysis for the interpretation of the shape of this region. It concludes with a brief treatment of the practical issues of coherence bias in multi-channel interferometry.Less

This chapter deals with the formal fusion of polarisation with interferometry. It develops an approach based on a general coherency matrix formulation, which scales naturally to multiple baselines, and shows how this may be used to generate interferograms for arbitrary choice of transmit and receive polarisations. It then considers the topic of coherence optimisation: methods for selecting the polarisation combinations that maximise the interferometric coherence and hence minimise the phase error. It is shown that there are two important classes of such optimisation: constrained and unconstrained. This leads to several important new concepts such as the coherence region, and the relationship between singular value decomposition (SVD) and Schur subspace analysis for the interpretation of the shape of this region. It concludes with a brief treatment of the practical issues of coherence bias in multi-channel interferometry.

*Jennifer Coopersmith*

- Published in print:
- 2017
- Published Online:
- June 2017
- ISBN:
- 9780198743040
- eISBN:
- 9780191802966
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198743040.003.0002
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology, History of Physics

Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the ...
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Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the Bernoullis, Leibniz, Maupertuis, Euler, and d’Alembert. Also, Stevin was the first to invoke the impossibility of perpetual motion in a proof, and Huygens was the first to put Galilean Relativity to a quantitative test. The Swiss family of mathematical geniuses, the Bernoullis, tackled isoperimetric problems, such as the brachystochrone, and Johann Bernoulli discovered the Principle of Virtual Velocities. The flavour of the eighteenth century is shown in the evocative tale of the König affair, and the correspondence between Daniel Bernoulli and Euler. It is shown how symmetry arguments, leading ultimately to an energy-analysis, were competing with Newton’s force-analysis. The Principle of Least Action and Variational Mechanics, proper, were developed by Lagrange, Hamilton, and Jacobi.Less

Early ideas about optimization principles were brought in by an eclectic group of extraordinary thinkers: the Ancients (Hero, and Princess Dido), Fermat with his Principle of Least Time, the Bernoullis, Leibniz, Maupertuis, Euler, and d’Alembert. Also, Stevin was the first to invoke the impossibility of perpetual motion in a proof, and Huygens was the first to put Galilean Relativity to a quantitative test. The Swiss family of mathematical geniuses, the Bernoullis, tackled isoperimetric problems, such as the brachystochrone, and Johann Bernoulli discovered the Principle of Virtual Velocities. The flavour of the eighteenth century is shown in the evocative tale of the König affair, and the correspondence between Daniel Bernoulli and Euler. It is shown how symmetry arguments, leading ultimately to an energy-analysis, were competing with Newton’s force-analysis. The Principle of Least Action and Variational Mechanics, proper, were developed by Lagrange, Hamilton, and Jacobi.