Four Mt. Wilson measurements ( T> 4 h) of the photospheric motion at one point on the Sun are shown to have the characteristics of a narrow-band random process. The motion is shown to have a characteristic correlation time of 23 rain and a mean power spectrum that is a smooth, single-peaked function centered at 3.4 mHz. In order to make this classification we use the analytic signal to estimate the amplitude, phase, and frequency as functions of time. The power spectrum analysis differs from the common approaches in that it uses the theoretical expression for the mean spectrum for a sequence of random pulses. Because of the random nature of the motion, we doubt the existence of more than one eigenfrequency characteristic of the photosphere as a whole. Likewise, any description of the observed motion in terms of simple deterministic functions will be inadequate for the data used here.
On the basis of diffraction transformations of wave fields, a mathematical model of a speckle interferometer of transverse displacements of a scattering object has been developed and numerical modeling of speckle-modulated interference patterns and signals at the output of the interferometer has been performed. Numerical calculations of the spatial distribution of complex amplitudes of wave fields in an interferometer were used for modeling when the displaced scattering surface was illuminated by two obliquely incident laser Gaussian beams. A statistical numerical experiment was performed to determine the measurement error of the scattering surface displacement caused by the change of realizations of interfering speckle fields. The simulation results are in good agreement with the results of experimental studies of transverse displacements in the range up to 600 micrometers. Keywords: interferometry, diffraction, interference, laser interferometer, speckle interferometry, interference pattern, speckle modulation, computer simulation.
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