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OPD Demodulation Based on Interferometric Scanning in WLI

Besides the above-mentioned OPD demodulation method, an interferometric scanning “WLI” combining with a broadband light source could also be applied to determine the optical path lengths of FFP sensors. The implication of the term “white light” is that the spectrum is sufficiently broad that the coherence length of the light source is much less than the round-trip optical path length of the FFP. Suitable light sources for WLI include SLDs, ASE source, and tungsten lamps. These sources typically have spectral widths of several tens of nanometers.

A WLI system for reading out an FFP sensor is illustrated schematically in Figure 5.14a, while the optical monitoring

Measurement of interferometer phase shift using low-coherence (white light) interferometry

Figure 5.14 Measurement of interferometer phase shift using low-coherence (white light) interferometry: (a) optical configuration and (b) fringe pattern.

signal is shown in Figure 5.14b. Light from the broadband source is transmitted or reflected by both the sensing and reference interferometers before reaching the photodetector [29]. When the optical path length of the reference interferometer is scanned, the photodetector output is a fringe (interference) pattern that has its maximum amplitude (peak of central fringe) where the OPD of the reference interferometer and that of the sensor interferometer are equal. The width of the pattern is proportional to the coherence length of the light source. The most common reference interferometer is the Michelson, although the Mach-Zehnder [30] and the FP [31] have also been used.

The fringe data as shown in Figure 5.14 are processed electronically to determine the exact OPD of the scanned reference interferometer corresponding to the central fringe peak. Identification of the central fringe is a key issue. A mistaken central fringe identification leads to an error in round-trip optical path length of at least one wavelength. An approach that greatly reduces the chance of central fringe error by

Table 5.2 Methods for Demodulation of Optical Path Difference (OPD)

METHOD

RESOLUTION

REFERENCES

Fringe counting

Depends on fringe 3 dB bandwidth and numbers

[16,18]

Combined one- and two-peak fringe counting

1.5 nm

[17]

Fringe counting and spectrum matching

<1 nm

[19]

Spectrum fitting

0.288 nm; errors will be increased by imperfections of sensors and model

[20]

FFT peak search

1-50 nm; depends on spectrum wavelength range and resolution

[21,22,25]

FFT peak estimation

1 nm

[24,26,27]

FFT WLI

±10 nm

[28]

Interferometric scanning WLI

Depends on scanning wavelength range

[29-31]

improving the fringe amplitude contrast uses two broadband sources with a wide wavelength separation [32]. The drawback of this method is that the OPD demodulation speed is relatively slow, limited by the scanning speed of the mirror.

Comparison of OPD Demodulation Methods

Comparison of OPD demodulation methods is given in Table 5.2. FFT-based demodulation method is helpful to obtain good demodulation performance.

 
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