# Mainz 2017 – wissenschaftliches Programm

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# Q: Fachverband Quantenoptik und Photonik

## Q 31: Poster: Quantum Optics and Photonics I

### Q 31.79: Poster

### Dienstag, 7. März 2017, 17:00–19:00, P OG1+2

**The Gauss-Newton algorithm for light scattering on transparent cylinders** — •Gunnar Claussen^{1,2}, Werner Blohm^{1}, and Armin Lechleiter^{2} — ^{1}Fachbereich Ingenieurwissenschaften, Jade Hochschule Wilhelmshaven Oldenburg Elsfleth — ^{2}Zentrum für Technomathematik, Universität Bremen

We aim to determine the diameter of a glass fiber under perpendicular incidence of plane-wave light and treat this question as an inverse scattering problem, which is solvable through an iteratively regularized Gauss-Newton algorithm. Within each step of the algorithm, the expression ||*F*′[*q*_{n}^{δ}]*h*_{n} + *F*(*q*_{n}^{δ}) − *u*_{∞}^{δ}||_{L2}^{2} + α_{n}||*h*_{n} + *q*_{n}^{δ}− *q*_{0}||_{s}^{2} is minimized. This term includes the measured far-field pattern *u*_{∞}^{δ}, the data-to-pattern operator *F*(·), i.e. the formalism given by the Mie theory for cylinder scattering, and its Fréchet derivate *F*′(·), the parameter vector *q*_{n}^{δ} and its alteration *h*_{n} within the current step of the iteration. The algorithm terminates once the residual ||*F*(*q*_{n}^{δ})−*u*_{∞}^{δ}|| becomes sufficiently small. However, it turns out that for transparent cylinders the residual forms a complex “landscape” in the parameter-space that is characterized by a number of false minima, thereby hindering the correct execution of the algorithm. We introduce a novel variation of the Gauss-Newton algorithm which allows to skip these minima in order to reach the global minimum, allowing us to determine the cylinder diameter with a precision several magnitudes smaller than the incident wavelength λ. We will present the performance of this algorithm in terms of precision, running time, experimental applicability and tolerance towards variations of fixed parameters.