Optical transfer functions of Kerr nonlinear cavities and interferometers

We present the optical transfer functions for third-order nonlinear cavities that involve an optical carrier frequency and its modulation sideband fields. Our approach is based on linearized transformations and provides a convenient tool to calculate squeezed light sources as well as complex interferometer topologies, containing subsystems that involve intensity dependent phase shifts, i.e., optical Kerr media. As the result we present the noise spectral density of a Michelson interferometer with Kerr nonlinear arm cavities and resonant sideband extraction and find that quantum noise can be squeezed by arbitrary amounts even outside the cavity linewidth. Such a system might apply for future gravitational wave detectors or simply for a continuous wave source of squeezed states.     

Sound source reconstruction using inverse boundary element calculations

Whereas standard boundary element calculations focus on the forward problem of computing the radiated acoustic field from a vibrating structure, the aim in this work is to reverse the process, i.e., to determine vibration from acoustic field data. This inverse problem is brought on a form suited for solution by means of an inverse boundary element method. Since the numerical treatment of the inverse source reconstruction results in a discrete ill-posed problem, regularization is imposed to avoid unstable solutions dominated by errors. In the present work the emphasis is on Tikhonov regularization and parameter-choice methods not requiring an error-norm estimate for choosing the right amount of regularization. Several parameter-choice strategies have been presented lately, but it still remains to be seen how well these can handle industrial applications with real measurement data. In the present work it is demonstrated that the L-curve criterion is robust with respect to the errors in a real measurement situation. In particular, it is shown that the L-curve criterion is superior to the more conventional generalized cross-validation (GCV) approach for the present tire noise studies.     

Non-Equispaced Fast Fourier Transforms with Applications to Tomography

In this article we describe a non-equispaced fast Fourier transform. It is similar to the algorithms of Dutt and Rokhlin and Beylkin but is based on an exact Fourier series representation. This results in a greatly simplified analysis and increased flexibility. The latter can be used to achieve more efficiency. Accuracy and efficiency of the resulting algorithm are illustrated by numerical examples. In the second part of the article the non-equispaced FFT is applied to the reconstruction problem in Computerized Tomography. This results in a different view of the gridding method of OSullivan and in a new ultra fast reconstruction algorithm. The new reconstruction algorithm outperforms the filtered backprojection by a speedup factor of up to 100 on standard hardware while still producing excellent reconstruction quality.     

Structure of the set of annihilators

We investigate the right annihilator lattice of a^*-ring and ask whether it is orthomodular with respect to a naturally given involution. In particular, we introduce a new class of^*-rings with orthomodular right annihilator lattice.