Applications of the speckle pattern techniques to the visualization of modulation transfer functions and quantitative study of vibrations of mechanical structures.

Some statistical properties of a speckle pattern can be characterized by its autocorrelation function and the intensity distribution in its Fraunhofer diffraction pattern, which depends on the granularity of the diffused wave and the contour of the pupil that limits the diffusing surface. It is shown that this property can apply to the visualization of modulation transfer functions, namely, those of synthetic apertures. A method for measurement of tilt angle for diffusing elementary surfaces is also derived. The information that can be extracted from a time-average photographic record of the intensity distribution scattered from a vibrating rough surface is discussed. It is shown that a complete mapping of the surface can be carried out by a suitable spatial filtering of the speckle pattern. As an example, in vibration mode analysis areas of singularity are displayed on the filtered image of a plate.