This master's thesis is focused on optical methods of measurement of very small dynamic displacements. Principles of interfermeters with picometer resolution including Fabry-Pérot interferometer are discussed and an integration using this interferometer was designed. Parasitic influencers of Fabry-Pérot interferometer were described as well as signal processing methods for interferometer's output signal. An interferometric meter for measurement of dynamic displacement was designed with frequency range of several kHz. These parameters are achieved under condition of photonic crystal layer placed on measured sample.

Wave scattering by arrays of cylinders has received special attention by many authors and analytical solutions have been derived. The investigation of optical and acoustical analogies to the problem of interaction of water waves with rigid and flexible cylinder arrays is the main focus of this thesis. In acoustics, a sound may be attenuated while it propagates through a layer of bubbly liquid. In fact, if the natural frequency of the bubbles is in the range of the wave periods, the attenuation becomes more evident. The ultimate objective of the research described herein is to determine if this phenomenon may also be found in the interaction between water waves and arrays of flexible cylinders. In a first approach, arrays of rigid cylinders are studied in shallow water. The array is treated as an effective medium, which allows for the definition of reflection and transmission coefficients for the array, and theories from Hu and Chan (2005) associated with the Fabry-Perot interferometer are compared against direct computations of wave scattering using the commercial code WAMIT. Reflection and transmission coefficients from WAMIT are evaluated by applying a Maximum Likelihood Method. The results from WAMIT were found to be in good agreement with those obtained from the effective medium theory. Due to observed inconsistencies for short wave periods and small incident angles, the effective width of the medium is defined and corrected. For the case of a flexible cylinder, generalized modes corresponding to deformations of the cylinder's surface are formulated and added to WAMIT's subroutine. Equations of motion are derived from the theory of vibration for thin shells and mass and stiffness matrices are defined. The objective is to maximize wave attenuation from the array of flexible cylinders. Therefore, the natural periods of the "breathing" mode for these cylinders is set in the range of the studied wave periods. Then, material properties, as well as mass and stiffness matrices, are chosen to achieve this effect.

The thesis deals with a design of a comparing interferometer. It concerns a setup of two interferometers, one of them is a Michelson and another a Fabry-Pérot type. This set-up is made to compare results of length measurements simultaneously performed by each of them. In the Theory, basic principles of Michelson and Fabry-Pérot interferometers are described. A special attention is paid to an innovative method of length measurement with tunable lasers and optical frequency comb. In the Practical Part, so-called Pilot Experimental Setup is described. It is a prototype that has been used to perform basic experiments on comparing of the two above mentioned methods. Based on experimental results and practical experience with the Pilot Experimental Setup, a Final Setup is designed. It comes in a form of a stand-alone instrument.

Die vorliegende Arbeit beschreibt die Entwicklung und Herstellung von Fabry-Pérot Interferometern (FPI) für die spektrale Analyse von Gasen und Flüssigkeiten. Die FPI werden miniaturisiert mittels Siliziumtechnologie hergestellt und ermöglichen kleine Mikrospektrometer mit hohem Auflösungsvermögen. Die vorliegende Dissertation untersucht Technologie- und Herstellungskonzepte für den sichtbaren (VIS) und infraroten (IR) Spektralbereich mit jeweils unterschiedlichen Reflektorkonzepten. Im VIS-Spektralbereich erfolgt neben der Entwicklung von Bragg-Reflektoren auch die Betrachtung von strukturierten, dielektrischen Membrangittern und strukturierten Metallgittern auf dielektrischen Membranen für eine Einsatzmöglichkeit im FPI. Dabei wird ebenfalls die Entwicklung einer Herstellungs- und Strukturierungstechnologie für hochbrechendes Titandioxid durchgeführt, um einen Bragg-Reflektor mit höheren Brechzahlkontrast zu realisieren. Im IR-Spektralbereich stellen drei Bragg-Reflektorvarianten aus polykristallinem Silizium und Luft den Inhalt dieser Dissertation dar. Die hergestellten Reflektoren werden hinsichtlich ihrer Funktion messtechnisch charakterisiert und die Strukturintegration in einem FPI und Etalon anhand von ausgewählten Reflektoren vorgestellt.