274 f CLEO/PACIFIC RIM f FRIDAY MORNING

I " ' " " "

Distance (gndpoinln)

FJ4 Fig. 3. Line marked "gradient" shows estimated (solid) and fitted (dashed) surface gradient. Lines marked "profile" show surface profile obtained by phase-stepping (solid) and by wavelet transform (dashed). Note that they have been offset slightly for clarity.

tively from isolated peaks due to the noise. The absolute value of the gradient is determined from the estimated local fringe frequency whereas the sign of the gradient is obtained from the direction of the fringe shift between the data sets as the laser frequency is altered. This shift may be estimated from the analytic sig- nals of the detrended interference patterns.

The surface profile may be deter- mined (up to an additive constant) by in- tegrating the gradient in those regions where the fringe frequency is sufficiently large that the wavelet transform gives a good estimate. These regions are shown by the solid sections of the line labelled 'gradient" in Fig. 3. These are joined by the dashed line which is obtained by a smoothness-constrained algorithm which minimizes the misfit to the observed data. The estimated profile shape com- puted from only two interference pat- terns is shown as the dashed curve in Fig. 3. For comparison, the profile recon- structed from four patterns using the four phase-step algorithm is shown as the solid curve, slightly offset for clarity. The method affords considerable simpli- fication of the measurement apparatus and yields accurate profiles even in the presence of noise. 1. K. Creath, "Phase measurement in-

terferometry and techniques," Pro- gress in Optics 26, E. Wolf, ed., El- sevier, Amsterdam, 384-393 (1988). Y. Ishii, "Recent developments in la- ser diode interferometry," Opt. La- sers. Eng. 14, 293-309 (1991). I. Daubechies, "The wavelet trans- form: a method for time-frequency localisation," Advances in Spectrum Analysis and Array Processing, S. Haykin, ed., Prentice Hall, 366-417 (1991).

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FJ5 1200

Digital demodulation technique for wide- dynamic-range with an optical fiber strain sensor

Lih-Horng Shyu, Yeh-Feu Fu,* National Yunlin Polytechnic Institute, Department of Electro-optzcs Enpeering, 64 Wunhua Road, Huwel, Yunlin, Taiwan, CHINA The conventional fiber optic interferom- eter IS commonly based on a PZT to mod- ulate and demodulate,'-3 therefore, it

needs the optical fiber wound and glued on a PZT, and this will increase the com- plexity of the system structure.

The signal intensity distribution of a conventional Mach-Zehnder interferom- eter can be expressed as

I = A + BcosQ (1)

where A is the DC term, B is the ampli- tude of the interference signal, and @ i s the phrase, which includes the measured strain signal.

Since the wavelength and the ampli- tude of the laser beam, B, changes line- arly with the injection current, therefore, both of the detected signal and the injec- tion current should be normalized so that the amplitude, E , can retain a constant. Therefore, only if an equal-time-interval sampling being taken within a period, a four-set normalized signal of equal phase spacing, A+, can be obtained.

rl = A + B COS(@ - 3 ~ + / 2 ) (2)

l2 = A + B COS(@ - A+/2)

I3 = A + B COS(@ + A+/2)

I4 = A + B COS(@ + 3A+/2)

(3)

(4)

(5)

By using Carre' demodulation formula' and simultaneously solving Eqs. (2-5), the phase @ can be obtained as

@ = tan-'

d[3(r2 - I J - (1' - r4m + r2 - - r4) r2 + r3 - r, - r,,

(6)

The phase of 0 - 360" can be solved by using a computer. Moreover, a processing of unwrapping is executed, and a very large dynamic range is obtained.

In order to accomplish the phase modulation job, a 100 kHz sawtooth wave is injected into the laser diode. Then adjusting the amplitude of the saw- wave will produce about a 2 n phase- shift of the interference signal. If Cane's method is adopted during the demodu- lation processing, then only a four-set signal is required within a period of 2n, and no exact 90" phase-shift' is required. Since this method is insensitive to the shift of the modulated signal and the drift of the frequency, therefore, it has a better system reliability.

For considering the signal-to-noise ra- tio and the processing speed, a DSP chip is used to do the digital processing job. Each time, as the middle value and the mean value are calculated per 100 strokes (400 data), the actual processing speed is only 1 kHz.

In this paper, an optical fiber strain sensor, which is combined with the con- ventional phase shifting interferometry and the DSP technology, is proposed. Since it adopts the Carre' demodulation formula, therefore, it is insensitive to the variations of the frequency and the am- plitude of the modulation signal, and its reliability is also high. In addition, with the processing of unwrapping, an ex- tremely large dynamic range can be ob- tained, and also with the adoption of the DSP technology, the system can have very high compatibility and expandabil- ity. The experimental result shows that

El E2

U T D .+::::

F15 Fig. 1. System structure MS: modulation source; PC: photocoupler; SG: signal generator; TG: time generator; B/A: normalized circuit, S/H: sampling & hold; D: PIN photodiode; DSP: digital signal processing; FC: fiber coupler; T test arm; R reference arm; El: fixed end; E2: free end; Al, A2: amplifier; ESPU: electrical signal processing unit; and UTD: under test device.

Norma 1 i za t ion Phase

Fikr St,.l" ca.+?

12 -

9 -.

00 1 0 2 0 30 40 5 0 Displacement (mm)

00 1 0 2 0 30 40 5 0 Displacement (mm)

FJ5 Fig. 2. Plot of the measured strain.

the relation of the strain and the mea- surement data is linear, and the linearity is better than 37%. *China Junior College Industrial b Commercial Management, Department of Management lnformation Science, No. 56, Section 3 ShingLung Road, Taipei, Taiwan, CHlNA 1. K. Creath, "Phase-measurement in-

terferometer techniques," Prog. Op- tics 26, 349 (1988). 0. Sasaki, H. Okazaki, M. Sakai, "Sinusoidal phase modulating inter- ferometer using the integrating- bucket method," Appl. Opt. 26, 1089 (1987). Y. Ishii, J. Chen, K. Murata, "Digital phase-measuring interferometry with a tunable laser diode," Opt. Lett. 12, 233 (1987). L. H. Shyu, Y. F. Fu, J. Y. Shieh, "Fi- ber optic strain sensing with phase- shifting interferometric techniques,"

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