Abstract

When the topography of a rough surface is measured with a double-wavelength interferometer, the phase error of the signal corresponding to the synthetic wavelength increases in the vicinity of dark speckles. To overcome this problem we perform an amplitude-dependent averaging of the synthetic phase over independent speckles (diversity detection). We either use spatially neighboring speckles or in the case of depolarizing surfaces, we use speckles of the same spatial mode, but with orthogonal polarizations. For the latter case the lateral resolution stays unaffected. The reduction of the speckle noise is demonstrated experimentally for a laterally scanning double-wavelength interferometer with superheterodyne detection of the synthetic phase.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  12. J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
    [CrossRef]
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  16. J. Trautner, G. Leuchs, “Interferometrische Einrichtung zur Messung der Lage eines reflektierenden Objektes,” Patentschrift DE100 38 346 A1 (2000).
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2000 (1)

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

1998 (1)

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

1997 (2)

1996 (1)

1995 (1)

1991 (1)

1988 (1)

1986 (1)

1985 (1)

1979 (1)

1973 (1)

1971 (1)

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, Wiley series in microwave and optical engineering, K. Chang, ed. (Wiley, New York, 1992).

Bodermann, B.

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

Brozeit, A.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Burke, J.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Dändliker, R.

Donati, S.

Fercher, A. F.

Fischer, E.

Geiser, M.

Giunti, C.

Goodman, J. W.

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer, Berlin, 1984), pp. 9–75.

Helmers, H.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Hu, H. Z.

Ittner, T.

Leuchs, G.

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

J. Trautner, G. Leuchs, “Interferometrische Einrichtung zur Messung der Lage eines reflektierenden Objektes,” Patentschrift DE100 38 346 A1 (2000).

Maier, N.

Manhart, S.

Margheri, G.

Martini, G.

Maurer, R.

Polhemus, C.

Prongué, D.

Rothe, A.

Sagehorn, H.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Salvade, Y.

R. Dändliker, Y. Salvade, “Multiple-wavelength interferometry for absolute distance measurement,” in International Trends in Optics and Photonics, T. Asakura, ed. (Springer, Berlin, 1999), pp. 294–317.
[CrossRef]

Schmitt, J. M.

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42, 1427–1439 (1997).
[CrossRef] [PubMed]

Schuh, R.

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Sodnik, Z.

Telle, H. R.

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

Thalmann, R.

Tiziani, H. J.

Trautner, J.

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

J. Trautner, G. Leuchs, “Interferometrische Einrichtung zur Messung der Lage eines reflektierenden Objektes,” Patentschrift DE100 38 346 A1 (2000).

Vry, U.

Walcher, K.

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

Wyant, J. C.

Zatti, S.

Appl. Opt. (7)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Laser Technol. (1)

A. Brozeit, J. Burke, H. Helmers, H. Sagehorn, R. Schuh, “Noise reduction in electronic speckle pattern interferometry fringes by merging orthogonally polarised speckle fields,” Opt. Laser Technol. 30, 325–329 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Med. Biol. (1)

J. M. Schmitt, “Array detection for speckle reduction in optical coherence microscopy,” Phys. Med. Biol. 42, 1427–1439 (1997).
[CrossRef] [PubMed]

Technisches Messen (1)

J. Trautner, K. Walcher, G. Leuchs, B. Bodermann, H. R. Telle, “Mehrwellenlängen-Interferometrie zur absoluten Abstandsmessung und 3D-Bildgebung,” Technisches Messen 67, 406–409 (2000).
[CrossRef]

Other (4)

J. W. Goodman, “Statistical properties of laser speckle patterns,” in Laser Speckle and Related Phenomena, J. C. Dainty, ed. (Springer, Berlin, 1984), pp. 9–75.

J. Trautner, G. Leuchs, “Interferometrische Einrichtung zur Messung der Lage eines reflektierenden Objektes,” Patentschrift DE100 38 346 A1 (2000).

R. Dändliker, Y. Salvade, “Multiple-wavelength interferometry for absolute distance measurement,” in International Trends in Optics and Photonics, T. Asakura, ed. (Springer, Berlin, 1999), pp. 294–317.
[CrossRef]

G. P. Agrawal, Fiber-Optic Communication Systems, Wiley series in microwave and optical engineering, K. Chang, ed. (Wiley, New York, 1992).

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Figures (15)

Fig. 1
Fig. 1

Speckle detection schemes.

Fig. 2
Fig. 2

Parallel speckle processing (for the detection schemes A, C, or D).

Fig. 3
Fig. 3

Serial speckle processing (for the detection scheme B): Trace of the synthetic pointer p ij (t) ∈ ℂ for a lateral scan (t 1 < t 2 < t 3 … ).

Fig. 4
Fig. 4

Double-wavelength source.

Fig. 5
Fig. 5

Multichannel diversity detector (scheme C).

Fig. 6
Fig. 6

Electronic circuit of the four-channel detector.

Fig. 7
Fig. 7

Probability density functions for the one-channel detector and for the four-channel detector.

Fig. 8
Fig. 8

Polarization-diversity detector (scheme D).

Fig. 9
Fig. 9

Probability density functions for the detection of a single polarization (s or p) and for polarization-diversity detection (scheme D).

Fig. 10
Fig. 10

Demodulation and time integration of the synthetic signal for serial diversity detection (scheme B).

Fig. 11
Fig. 11

Probability density functions for a serial speckle detection with and without lateral averaging.

Fig. 12
Fig. 12

One-dimensional lateral averaging for two different lateral scan velocities of 2 ms and 4 ms per speckle.

Fig. 13
Fig. 13

Phase resolution for a two-dimensional lateral averaging within a quadratic integration cell.

Fig. 14
Fig. 14

Synthetic phase map and profile cut of a wooden knob on a metal surface measured without diversity detection.

Fig. 15
Fig. 15

Knob from Fig. 14 measured with serial diversity detection. The integration cell contains 16 speckles.

Tables (2)

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Table 1 Speckle Detection Schemes

Tables Icon

Table 2 Comparison of the diversity detection schemes

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

z=m+ φ2πλ2.
φij=φi-φj=2π zλi2- zλj2- mi-mj=2πzΛij2-mij.
pˆij=1nc=1npijc.
pˆijt=1τ- pijtw t-tdt,
wt= 0fort>τ21fortτ2.
ΔxΔxsp,
Δx  Δxsp.
pˆijx, y= 1ΔxΔy-- pijx, ywxx-xwyy-ydxdy.
I12t=A12tsinφ12t,
Q12t=A12tcosφ12t.
Iˆ12t= 1τ- I12twt-tdt,
Qˆ12t= 1τ- Q12twt-tdt.
Aˆ12= Iˆ122+Qˆ1221/2,
φˆ12=arctanIˆ12Qˆ12.

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