The dissertation is concerned with the description and utilization of interference of two coherent optical rays. In addition, the conditions of coherence and its connections with the occurance of interference are discussed. Michelson's interferometer is used for the practical utilization of the interference effect. The possibility of measuring relatively small changes is demonstrated - deviation of piezocrystal, measurement of the coherent length of optical source and measurement of the index of refraction of tramsparent materials. The manner of optical coherent detention and its utilization in optical communication systems is indicated. After demonstration of the principle was carried out the measuring of detection of optical signal modified by the external modulator.

This thesis deals with the precise measurement of distances in nanometer range at ultrasonic frequencies for the purposes of vibrometry. The paper is primary focused on~nanometric displacement measurement methods. First the thesis deals with the physical phenomena based on light in the theoretical section. This includes interference of light, index of refraction, polarization, interferometry and more. Understanding of these physical laws is crucial for design and assembling of the interferometer. Subjects of interferometric method for precise and fast measurement of the nanometric displacement and vibration are discussed. Interferometer components such as lasers, photodetectors and optical elements are described are described in the final part of this section. Practical section of thesis can be divided into two parts. The design and assembling issues are discussed in the first section. Many problems which I had to solve are described. Control software and implementation of the signal processing is the subject of the second part. I met with particular problems such as phase unwrapping. I solved this problem of discontinuous phase field with user written algorithm. Finally the graphical user interface was created. Using assembled interferometer and written software application I measured vibration of Langevin transducer on ultrasonic frequencies.