Abstract

We describe a novel technique for measurement of absolute order of interference in multifrequency interferometry. An optimization criterion is introduced that leads to frequency selection formulations that are optimized with respect to the minimum number of frequencies required for achieving the maximum target dynamic range. The method is generalized to N frequencies and gives a definition of measurement reliability. We demonstrate the technique by means of coherent fringe projection for nonintrusive, full-field profilometry. Experimental data for three frequencies are presented.

© 2003 Optical Society of America

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  1. A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
    [CrossRef]
  2. R. Gens and J. L. van Genderen, Intl. J. Remote Sens. 17, 1803 (1996).
    [CrossRef]
  3. J. M. Huntley and H. O. Saldner, Meas. Sci. Technol. 8, 986 (1997).
    [CrossRef]
  4. M. Kujawinska and J. Wojciak, Opt. Lasers Eng. 14, 325 (1991).
    [CrossRef]
  5. S. Kuwamura and I. Yamaguchi, Appl. Opt. 36, 4473 (1997).
    [CrossRef] [PubMed]
  6. J. M. Huntley, Opt. Lasers Eng. 26, 131 (1997).
    [CrossRef]
  7. D. P. Towers, J. D. C. Jones, and C. E. Towers, in Applied Optics and Opto-Electronics (Institute of Physics, London, 2002), p. 85.
  8. D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
    [CrossRef]
  9. A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
    [CrossRef]

2000

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
[CrossRef]

1997

S. Kuwamura and I. Yamaguchi, Appl. Opt. 36, 4473 (1997).
[CrossRef] [PubMed]

J. M. Huntley, Opt. Lasers Eng. 26, 131 (1997).
[CrossRef]

J. M. Huntley and H. O. Saldner, Meas. Sci. Technol. 8, 986 (1997).
[CrossRef]

1996

R. Gens and J. L. van Genderen, Intl. J. Remote Sens. 17, 1803 (1996).
[CrossRef]

1995

D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
[CrossRef]

1994

A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
[CrossRef]

1991

M. Kujawinska and J. Wojciak, Opt. Lasers Eng. 14, 325 (1991).
[CrossRef]

Barton, J. S.

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
[CrossRef]

Buckberry, C. H.

D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
[CrossRef]

Gens, R.

R. Gens and J. L. van Genderen, Intl. J. Remote Sens. 17, 1803 (1996).
[CrossRef]

Huntley, J. M.

J. M. Huntley and H. O. Saldner, Meas. Sci. Technol. 8, 986 (1997).
[CrossRef]

J. M. Huntley, Opt. Lasers Eng. 26, 131 (1997).
[CrossRef]

Jones, J. D. C.

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
[CrossRef]

D. P. Towers, J. D. C. Jones, and C. E. Towers, in Applied Optics and Opto-Electronics (Institute of Physics, London, 2002), p. 85.

Jones, M. P.

D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
[CrossRef]

Kujawinska, M.

M. Kujawinska and J. Wojciak, Opt. Lasers Eng. 14, 325 (1991).
[CrossRef]

Kuwamura, S.

Lewis, A.

A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
[CrossRef]

McBride, R.

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
[CrossRef]

Moore, A. J.

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
[CrossRef]

Saldner, H. O.

J. M. Huntley and H. O. Saldner, Meas. Sci. Technol. 8, 986 (1997).
[CrossRef]

Stockley, B. C.

D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
[CrossRef]

Towers, C. E.

D. P. Towers, J. D. C. Jones, and C. E. Towers, in Applied Optics and Opto-Electronics (Institute of Physics, London, 2002), p. 85.

Towers, D. P.

D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
[CrossRef]

D. P. Towers, J. D. C. Jones, and C. E. Towers, in Applied Optics and Opto-Electronics (Institute of Physics, London, 2002), p. 85.

van Genderen, J. L.

R. Gens and J. L. van Genderen, Intl. J. Remote Sens. 17, 1803 (1996).
[CrossRef]

Wojciak, J.

M. Kujawinska and J. Wojciak, Opt. Lasers Eng. 14, 325 (1991).
[CrossRef]

Yamaguchi, I.

Appl. Opt.

Intl. J. Remote Sens.

R. Gens and J. L. van Genderen, Intl. J. Remote Sens. 17, 1803 (1996).
[CrossRef]

Meas. Sci. Technol.

J. M. Huntley and H. O. Saldner, Meas. Sci. Technol. 8, 986 (1997).
[CrossRef]

D. P. Towers, C. H. Buckberry, B. C. Stockley, and M. P. Jones, Meas. Sci. Technol. 6, 1242 (1995).
[CrossRef]

A. Lewis, Meas. Sci. Technol. 5, 694 (1994).
[CrossRef]

Opt. Lasers Eng.

M. Kujawinska and J. Wojciak, Opt. Lasers Eng. 14, 325 (1991).
[CrossRef]

J. M. Huntley, Opt. Lasers Eng. 26, 131 (1997).
[CrossRef]

Proc. SPIE

A. J. Moore, R. McBride, J. S. Barton, and J. D. C. Jones, Proc. SPIE 4076, 174 (2000).
[CrossRef]

Other

D. P. Towers, J. D. C. Jones, and C. E. Towers, in Applied Optics and Opto-Electronics (Institute of Physics, London, 2002), p. 85.

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Figures (3)

Fig. 1
Fig. 1

Calculated phases for an optimum four-frequency process.

Fig. 2
Fig. 2

Fiber fringe projector for optical profilometry.

Fig. 3
Fig. 3

Experimental interference-order map for optimum 3-λ heterodyne processing (repeating gray-scale representation).

Tables (1)

Tables Icon

Table 1 Normalized Unambiguous Measurement Range (NUMR) and Dynamic Range with 99.73% Reliability for Optimum Three- and Four-Frequency Interferometry

Equations (6)

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Δϕ01=Δϕ0-Δϕ1=2πLλ1-λ2λ0λ1=2πLΛ01,
Λ01λ02π62σϕ.
Lλ02π62σϕ.
Λ01/Λ02=Λ02/Λ03==Λ0,N-1/λ0.
1λ1=1λ0-1λ0i-1/N-11LN-i/N-1, i=1,,N,
Lλ0N-12π62σϕ.

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