**4. Conclusion**

In this chapter, we have reviewed digital demodulation algorithms for interferometric metrology systems. Digital demodulation has the potential for producing a more robust and less costly sensor system. In general, the savings in optical and electronic hardware is traded-off with complex software algorithms. Consider the information shown in Table 1 of the specific digital demodulation techniques presented in this chapter.

Note that each of the digital demodulation methods presented in Table 1 is based on a homodyne approach. The heterodyne techniques require additional optical and electronic hardware to shift the frequency of one of the interfering optical beams. A key advantage of digital demodulation is a significant reduction in cost and hardware system complexity.

We have also presented a new demodulation algorithm for the well-known phase-generated carrier modulation scheme. Our algorithm is based on a frequency domain approach and requires both the magnitude and phase information present in the signal. This demodulation scheme suffers from the need for active feedback control. One possible approach to ameliorate this limitation is to investigate the use of a more sophisticated modulation signal. In the demodulation algorithm presented in Section 3, the carrier signal is a pure sinusoid and the desired output is the fixed phase *R* . We have studied interferometers, which use the phase-generated carrier modulation scheme and detect the amplitude of a *sinusoidally* varying phase *R t*( ) . These systems produce harmonics, which we detect and then compute their ratio to remove the dependence on unknown quantities.


Table 1. Comparison of digital demodulation techniques presented in this chapter.

It may be possible to design a carrier signal, which produces an appropriate set of harmonics that can be mathematically manipulated to cancel out any variations in *M* and *W* , yet still be solvable for the fixed phase *R* . The trade-off would be a true open-loop system, which would not require stringent initialization procedures, at the expense of a sophisticated carrier modulation signal. Further investigation into the viability of this approach is suggested.

#### **5. Acknowledgment**

The authors would like to recognize funding support from Weatherford International, Inc. for research related to the phase-generated carrier demodulation scheme presented in Sec. 3.

#### **6. References**


**Homodyne/Heterodyne** Homodyne Homodyne Homodyne Homodyne **Passive/Active** Active Active Passive Passive

It may be possible to design a carrier signal, which produces an appropriate set of harmonics that can be mathematically manipulated to cancel out any variations in *M* and *W* , yet still be solvable for the fixed phase *R* . The trade-off would be a true open-loop system, which would not require stringent initialization procedures, at the expense of a sophisticated carrier modulation signal. Further investigation into the viability of this

The authors would like to recognize funding support from Weatherford International, Inc. for research related to the phase-generated carrier demodulation scheme presented in Sec. 3.

Barbour, N. & Schmidt, G., Inertial sensor technology trends. *IEEE Sensors Journal*, vol. 1, no.

Bush, J., Davis, C. A., McNair, F., Cekorich, A., & Bostick, J., Low cost fiber optic

Cekorich, A., Bush, J., & Kirkendall, C., Multi-channel interferometric demodulator. *Proceed.* 

Cekorich, A., Demodulator for interferometric sensors.*Proceed. of the SPIE*, vol. 3860,

Cole, J. H., Danver, B. A., & Bucaro, J. A., Synthetic-heterodyne interferometric

Culshaw, B. & Giles, I. P., Frequency modulated heterdyne optical fiber Sagnac

interferometric sensors.*Proceed. of the SPIE – Second Pacific Northwest Fiber Optic* 

*of the SPIE – Third Pacific Northwest Fiber Optic Sensor Workshop*, vol. 3180, (May

demodulation. *IEEE J. Quantum Electron.*, vol. QE-18, no. 4, (April 1982), pp. 694-

interferometer. *IEEE J. Quantum Electron.*, vol. QE-18, no. 4, (April 1982), pp. 690-

Table 1. Comparison of digital demodulation techniques presented in this chapter.

**Phasegenerated carrier (frequency domain)** 

Down-hole oil well drilling bit parameter measurement

> Real-time processing

**J1 ... J4 3x3 fiber** 

MEMS vibrating amplitude measurement

> Real-time processing

**coupler** 

Ballistic shock (velocity) measurement

> Postprocessing

**Phasegenerated carrier (time domain)** 

Biological cell contraction measurement

> Real-time processing

**Demodulation Technique** 

**Application** 

**Real-time/Postprocessing** 

approach is suggested.

**5. Acknowledgment** 

4, (December 2001), pp. 332-339

(December 1999), pp. 338-347.

1997), pp. 1-11.

697.

693).

*Sensor Workshop*, vol. 2872, (May 1996), pp. 1-12.

**6. References** 

