#### 1. Introduction

In fiber optic strainmeter the optical scheme of the Mach-Zehnder interferometer [1] providing a possibility of registration of deformations to 10

In the early 1980s the use of 3x3 couplers in the demodulation of interferometric fiber optic sensors was first proposed [2] and demonstrated [3]. This demodulation allows the generation of three outputs separated in phase by 120 degrees. In early methods two of the three outputs are used to obtain the required 90 degrees phase difference from their sum and difference and these form the inputs to a differentiating cross-multiplying demodulator [3], the method needs a dc offset in the circuit to eliminate the dc component resulting from summing up the two inputs, therefore when the light power in the interferometer changes, the circuit will become unbalanced. Further all three outputs are utilized symmetrically in an analog processing algorithm to obtain the demodulated time-changing phase difference [4].

In this paper a strainmeter based on the fiber optic Mach-Zehnder interferometer with 3

#### 2. Materials and Methods

The three outputs of the 3

and can be expressed as:

where subscripts 1, 2 and 3 denote the three outputs of the 3
*t*) is the phase shift between the sensing and reference fibers of the Mach-Zehnder interferometer; *C* is the central value around which the output will vary with amplitude *B*.

To calculate phase shift Δφ(*t*) the algorithm of interferometer signals processing offered in [4] was used.

The DC offset *C* of the output can be obtained by adding the three inputs as follows:

Three new parameters, y

The next step in the processing is to take the difference between each of the three possible pairings of the derivatives and multiply this by the third signal:

Summation of Equations (4a), (4b) and (4c), yields:

Taking the squares of Equations (3a), (3b) and (3c), then adding them, leads to:

Dividing Equation (6) into Equation (5), yields:

We can integrate Equation (7) to obtain the phase shift Δφ(*t*) as follows:

The described algorithm was used for processing of output signals of the fiber optic Mach-Zehnder interferometer in a strainmeter which scheme is shown in fig. 1.

CW optical radiation from laser (7) is coupled by means of fiber-optic Y-splitter (8) into two single-mode optical fibers which work as sensing (10) and reference (11) arms of the interferometer. Sensing optical fiber wound between mobile (4) and fixed (6) half of the cylinder. A mobile half of the cylinder fastens by the end of an extensive rope (2) which second end is fixed on a column (1). Afterword the signal and reference waves are combined at the 3

Experimental setup for testing performance of the fiber-optic strainmeter is shown in fig. 2. Vibrator (3) sustains harmonic oscillations of the end of a strainmeter rope (2). The corresponding signal is registered by means of Michelson's interferometer consisting of He-Ne laser (4), beamsplitter (5), photodetector (6), mirrors (7) and (8). The Mirror (7) is fixed on a mobile part of a vibrator. The dotted line has shown a laser beam.

#### 3. Results

Results of testing of the fiber optic strainmeter with the 3

#### 4. Conclusions

In this paper a strainmeter based on the fiber optic Mach-Zehnder interferometer with 3x3 coupler for a phase shift demodulation is presented. Laboratory experiments on registration of harmonic deformation with the use of strainmeter were carried out. The possibility of use of the splitter 3