13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- ) ( 0 1 1 t i kx E E e , (8) ) ( 0 2 2 t i kx E E e , (9) where – E0 amplitude of electric intensity of an electromagnetic field (we assume for simplification of calculations that it is identical in both optical fibers); k=2π/λ – wave number; ω– circular frequency of laser radiation; φ– an initial phase which also is considered identical to both optical fibers; x1 – distance from beam splitter BS1 to the photodetector PD on optical fiber OF1; x2 – distance from beam splitter BS1 to the photodetector on optical fiber OF2. Distance from beam splitter BS1 to the photodetector on an optical fiber OF2 recorded in the following kind: r x r r 2 2 0 , (9) where r0 – distance from beam splitter BS1 to a research object O; r – distance from a research object O to the photodetector PD on optical fiber OF2; ±Δr – the value of displacement of a research surface. As the photodetector registers intensity, than the distribution of the intensity in an interference pattern of the single speckle will record in the following kind: r k x r r I x t E E E E E 2 ) 2 1 cos ( , 1 0 2 0 2 2 1 2 1 , (10) where the top index (+) means that vector value of electric intensity of an electromagnetic field is transposed and in a complex interfaced. As appears from Eq. (10), and as it was noted above, intensity of a speckle changes from minimum to maximum values (or on the contrary) at change of value of a phase baked on ±π (2n+1), (where n=0,1,2…) which is connected by dynamics of a research surface, that is with change Δr in time. Change of intensity of the single speckle on an entrance of the photodetector it will be transformed to change of output signal of the photodetector which (see Eq. 10) can be expressed as follows: (0) ( )] cos[ ( ) t u t A B , (11) where u(t) – the output voltage of the electrical scheme of the photodetector; A – the output bias voltage which is related to the average intensity of the single speckle; B – amplitude of useful output voltage which is defined by parameters of the optoelectronic scheme which related to a displacement of a research surface and kind of the optical scheme; φ(0) = k(x1-r0-r) – initial value of a phase difference between the reference beam and the object beam forming speckle pattern in plane of a optical image. This phase difference can change but remains to constants in the time of measurements; φ(t) = ±2kΔr is the change of a phase in single speckle related with change of the optical path in the object arm of a optical scheme at dynamic displacements of a research surface. From the analysis of a Eq. (10) and (11) follows that change of output voltage of the photodetector depends on phase change φ(t) characterizing dynamics single speckle related with movement of a research surface. As intensity single speckle changes from minimum to maximum or on the contrary, respectively and output voltage from the photodetector changes from the minimum value – u(t)min to the maximum value – u(t)max or on the contrary. The theoretical results of behavior of the output voltage u(t) in respect of vibrating displacements of the investigation surface are demonstrates in Fig. 4. The dashed curve represents the vibrations of
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