**3.4 Summary**

328 Modern Metrology Concerns

Fig. 10. Reconstructed amplitudes of the fundamental and second harmonic frequencies as a

A key to reconstructing the amplitudes of the fundamental and second harmonic frequencies is to utilize both the magnitude and phase information provided by the signal's frequency spectrum. This information shown in Figs. 8 and 9 may be used to determine the amplitudes of Eqns. (8) and (9). Fig. 10 shows the amplitudes of the fundamental and second harmonics reconstructed from the data of Figs. 8 and 9. Notice that the amplitude of the fundamental harmonic varies sinusoidally as a function of *R* and the second harmonic varies cosinusoidally as a function of *R* . This data applied to Eqn. (10) may be used with an

interval. This forms the kernel of the frequency domain demodulation algorithm. We have incorporated a fringe counting routine and verified the frequency domain demodulation

In this section, we have verified the theoretical development of the previous section through computer simulation and described how to implement the algorithm in practice. A key step in the kernel of the frequency domain algorithm is use of both the magnitude and phase

We have presented a frequency domain approach to the demodulation of an interferometer, which uses a phased-generated carrier modulation scheme. Through simulation analysis, we have shown that the frequency domain algorithm produces correct demodulation results

operating conditions as used in commercially-available time-domain demodulators.

and *W* 0 ). These are the same

phase

inverse tangent approximation to determine the desired phase *R* over a full 2

function of the phase *R* .

algorithm through computer simulation.

components of the frequency spectrum.

by assuming fixed operating parameters (i.e., *M*

**3.3 Discussion** 

We have presented the kernel of an algorithm for the digital demodulation of an interferometer based on the phase-generated carrier modulation scheme. This algorithm exploits both the magnitude and phase information in its frequency domain manipulation of the signal. The algorithm suffers from requirement that active feedback control is needed.
