Abstract

For digital phase detection, the characteristic polynomial method permits algorithms that are insensitive to the harmonic content of the signal and insensitive to miscalibration to be designed easily. It is shown here that this method can also be used to design algorithms that are insensitive to a possible bias modulation of the intensity.

© 1997 Optical Society of America

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References

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  1. Y. Surrel, “Design of algorithms for phase measurements by the use of phase-shifting,” Appl. Opt. 35, 51–60 (1996).
    [Crossref] [PubMed]
  2. R. Onodera, Y. Ishii, “Phase-extraction analysis of laser-diode phase-shifting interferometry that is insensitive to changes in laser power,” J. Opt. Soc. Am. A 13, 139–146 (1996).
    [Crossref]
  3. Y. Surrel, “Additive noise effect in digital phase detection,” Appl. Opt. 36, 271–276 (1997).
    [Crossref] [PubMed]

1997 (1)

1996 (2)

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Figures (2)

Fig. 1
Fig. 1

Characteristic diagram of the six-sample algorithm described by Eq. (5), indicating the location of the characteristic polynomial roots on the complex unit circle. Multiple roots are indicated by multiple circles with the same multiplicity. The double root located at 1 ensures that the algorithm is insensitive to a linear bias modulation. This algorithm detects -φ because the double root is located at i rather than at - i.

Fig. 2
Fig. 2

Characteristic diagram of the five-sample algorithm described by Eq. (6). It has the same properties as the one illustrated by the characteristic diagram shown in Fig. 1; apart from that it detects +ϕ.

Equations (10)

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Ik=A1+γ frngφ+kδ,
φ*=arctank=0M-1 bkIkk=0M-1akIk,
Sφ=k=0M-1ckIk,
Px=k=0M-1ckxk.
expimφk=0M-1ckexpimδk=expimφPexpimδ.
k=0M-1ck=0,
k=0M-1ckk=P1.
φ*=arctan3I0-5I1+5I4-3I5-I0-3I1+4I2+4I3-3I4-I5
φ*=arctan-I0+2I1-2I3+I4-2I1+4I2-2I3.
k=0M-1ckks=DsP1,

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