The fiber sensor displacement measuring system is calibrated by a modified Beck version of the Michelson interferometer [10]. We consider the Michelson set-up adjusted for the observation of fringes of equal thickness at the air wedge located between two mirrors. As shown in Fig.3, a modified Michelson set-up is introduced here to obtain a precise displacement data below 0.1 m . The sensor head is mounted toward the target mirror to obtain the variation of the intensity data. We can modulate He-Ne laser to continuous wave or 1-2 Hz pulse, then from the measuring value isolate D.C. term and obtain A.C. term which represent leaving out the light intensity of the background field.

Errors in measuring the fringe variation and in reading the displacement of the fiber sensor head may account for the slight discrepancies between theory and experiment shown in Fig.4-6. The units of signal V_1/V_2 are arbitrary and we can see the ratio of reflected versus reference light is about 0.1 to 0.09 in the first 10 m distance variations. When a divergent angle of the beam theta is increasing or the w_f is decreasing, the sensitivity is higher but the measuring range is shorter. When theta = 45 and w_f= 1 mm every 1 m distance variation induces a frac11000 intensity variation at the close target measurement. We can see the distance data obtain different sensitivities within different measuring distances and integrate with changes in reflectivity of the target and angularity of the target. Furthermore, in Fig.6 the response curve of the total measuring stroke is presented, and compared to the response curve in other types of fiber sensors the apex effect disappears.

A major advantage of our reflective fiber sensor is that contact is not required for measurement. In other words, it can replace a mechanical linear voltage displacement transformer. The experiment was done using a vibrating circular plate; and a piece of shim brass clamped to an aluminum frame which was excited by a vibrator with various amplitudes and frequencies , the vibration data were computed from a Fast Fourier transform ( FFT) software of a PC 486 personal computer.

The experimental impulse and reading of the displacement of vibration amplitude was transmitted by a RS-232C card and recorded in the computer automatically. Random noise exists so we can't distinguish the signal in the picture of the measuring data for the amplitude vs. time of a mechanical vibration. After FFT we can obtain the spectral analyzing results of the vibration signal. However, high frequency independent information about the vibration motion must be available because the distribution of an excitation spectrum depends not only on the magnitude of the displacement, but also the form of the displacement as a function of time.

From the 'sampling theorem in the frequency domain', we set the sampling rate at 10000 Hz, and the frequency of the vibration excitation devices from 150 Hz to 4000 Hz with a 60 Hz AC line ripple for testing. The amplitude modulation of the vibrator is from 1 m to 2000 m. Fig.7 to Fig.8 are the experimental results of the fiber displacement sensor, and the parameters are listed as follows:

Fig.7 : vibration frequency is 150 Hz and amplitude is 1m.

Fig.8 : vibration frequency is 1500 Hz and amplitude is 1000m.

The results show the straightforward and reliable corresponding vibration displacement measurement. It is very important for different measuring range and sensitivity vibration testing that we calibrate our device once. Although the calculation errors of this fiber sensor system without a modified Michelson interferometer are relatively small, such correction is necessary to maintain a range accuracy in the order of 0.2 m.

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