## 1 Introduction
Of course, the spatial resolution may be improved by shortening the propagation path of the ultrasonic wave, for example, reducing the distance between the ultrasonic transmitter and receiver, but it unavoidably increases the measurement errors. The objective of this work was development of measurement methods and corresponding signal processing procedures enabling to obtain spatial distributions of non-uniform elastic properties of a thin films and plates. Those methods are based on excitation of a slow sub-sonic A\({}_{0}\) mode in a plate, measurement of normal displacements of the plate, formation of the B-scan and processing the collected signals. For a signal processing two different methods were proposed and investigated. In the first method the all zero-crossing instants of the recorded ultrasonic signals at different distances are found and from them the delay time B-scan is formed. This B-scan is used to obtain spatial distributions of the A\({}_{0}\) mode velocity in different parts of the plate or film under investigation. The second method is based on calculation of the two-dimensional spatial-temporal spectrum of the primary B-scan of normal displacements. From this spectrum is possible to identify A\({}_{0}\) modes propagating with different velocities. Strictly speaking this method does not provide a spatial distribution of ultrasound velocity in plates, but enables to measure velocities of different guided waves modes, for example A\({}_{0}\) Lamb wave modes, which are caused by spatially non-uniform areas of the plate with different elastic properties and/or thickness. As it will be shown in this paper, some information about spatial distributions can be obtained by selecting a window in the spatial domain in which the 2D Fourier transform is performed. Efficiency of the proposed methods was investigated on mica paper samples. Mica is a naturally occurring mineral, consisting of aluminium, potassium, magnesium, iron, water, and possessing a thin plate-like structure. The tensile strength of the mica is very low; therefore, it is reinforced according to the product with some backing, like glass cloth or polyethylene film. Mica is widely used in the electrical industry as an insulating material because it possesses a high dielectric strength. In the aerospace industry mica, due to its resistance to high compression at very high temperatures, is used for insulation of aircraft thrust reversal systems, where thermal protection is critical. According to manufacturers the most important parameters of the mica paper are density, tensile strength, porosity, and uniformity of elastic properties. On-line measurement of those parameters, especially of the elastic properties and thickness during a manufacturing process, have not been solved up to now. The paper consists of five sections. A numerical modelling of propagation of the slow A\({}_{0}\) mode in a thin mica paper is discussed in Section 2, the B-scan zero-crossing reconstruction method enabling spatial reconstruction of non-uniform elastic properties is described in Section 3, the 2D spatial-temporal spectrum method in Section 4, and the theoretical results are verified by measurements performed by a laser interferometer in Section 5.