Two-wavelength interferometry: extended range and accurate optical path difference analytical estimator

doi:10.1364/JOSAA.26.002503

Two-wavelength interferometry: extended range and accurate optical path difference analytical estimator

Kamel Houairi and Frédéric Cassaing »View Author Affiliations

JOSA A, Vol. 26, Issue 12, pp. 2503-2511 (2009)
http://dx.doi.org/10.1364/JOSAA.26.002503

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Abstract

Two-wavelength interferometry combines measurement at two wavelengths $λ_{1}$ and $λ_{2}$ in order to increase the unambigous range (UR) for the measurement of an optical path difference. With the usual algorithm, the UR is equal to the synthetic wavelength $Λ = λ_{1} λ_{2} ∕ | λ_{1} - λ_{2} |$ , and the accuracy is a fraction of Λ. We propose here a new analytical algorithm based on arithmetic properties, allowing estimation of the absolute fringe order of interference in a noniterative way. This algorithm has nice properties compared with the usual algorithm: it is at least as accurate as the most accurate measurement at one wavelength, whereas the UR is extended to several times the synthetic wavelength. The analysis presented shows how the actual UR depends on the wavelengths and different sources of error. The simulations presented are confirmed by experimental results, showing that the new algorithm has enabled us to reach an UR of $17.3 μ m$ , much larger than the synthetic wavelength, which is only $Λ = 2.2 μ m$ . Applications to metrology and fringe tracking are discussed.

OCIS Codes
(110.5100) Imaging systems : Phased-array imaging systems
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: July 24, 2009
Manuscript Accepted: September 24, 2009
Published: November 4, 2009

Virtual Issues
November 25, 2009 Spotlight on Optics

Citation
Kamel Houairi and Frédéric Cassaing, "Two-wavelength interferometry: extended range and accurate optical path difference analytical estimator," J. Opt. Soc. Am. A 26, 2503-2511 (2009)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-26-12-2503

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References

Y. Gursel, “Picometer-accuracy, laser-metrology gauge for Keck interferometer differential-phase subsystem,” Proc. SPIE 4838, 995-1010 (2003). [CrossRef]
M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, and D. J. Hutter, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357-371 (1988).
P. R. Lawson, “Group-delay tracking in optical stellar interferometry with the fast Fourier transform,” J. Opt. Soc. Am. A 12, 366-374 (1995). [CrossRef]
F. Delplancke, F. Derie, F. Paresce, A. Glindemann, F. Lévy, S. Lévêque, and S. Ménardi, “PRIMA for the VLTI--Science,” Astrophys. Space Sci. 286, 99-104 (2003). [CrossRef]
M. G. Löfdahl and H. Eriksson, “Algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40, 984-990 (2001). [CrossRef]
P. Juncar, H. Elandaloussi, M. E. Himbert, J. Pinard, and A. Razet, “A new optical wavelength ratio measurement apparatus: the fringe counting sigmameter,” IEEE Trans. Instrum. Meas. 46, 690-695 (1997). [CrossRef]
M. R. Benoît, “Application des phénomènes d'interférence à des déterminations métrologiques,” J. Phys. (France) 3, 57-68 (1898).
J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113-2118 (1971). [CrossRef] [PubMed]
C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071-2074 (1973). [CrossRef] [PubMed]
K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), vol. XXVI, chap. V, pp. 349-393. [CrossRef]
J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1990), vol. XXVIII, chap. IV, pp. 371-359.
Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539-4543 (1984). [CrossRef] [PubMed]
R. Dändliker, Y. Salvadé, and E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105-114 (1998). [CrossRef]
A. Wada, M. Kato, and Y. Ishii, “Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes,” J. Opt. Soc. Am. A 25, 3013-3020 (2008). [CrossRef]
P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948-5953 (1994). [CrossRef] [PubMed]
H. van Brug and R. G. Klaver, “On the effective wavelength in two-wavelength interferometry,” Pure Appl. Opt. 7, 1465-1471 (1998). [CrossRef]
K. Falaggis, D. P. Towers, and C. E. Towers, “A hybrid technique for ultra-high dynamic range interferometry,” Proc. SPIE 7063, 70630X (2008). [CrossRef]
C. E. Towers, D. P. Towers, and J. D. C. Jones, “Generalized frequency selection in multifrequencyinterferometry,” Opt. Lett. 29, 1348-1350 (2004). [CrossRef] [PubMed]
M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).
G. Bönsch, “Wavelength ratio of stabilized laser radiation at 3.39 μm and 0.633 μm,” Appl. Opt. 22, 3414-3420 (1983). [CrossRef] [PubMed]
J. M. Le Duigou, M. Ollivier, A. Léger, F. Cassaing, B. Sorrente, B. Fleury, G. Rousset, O. Absil, D. Mourard, Y. Rabbia, L. Escarrat, F. Malbet, D. Rouan, R. Clédassou, M. Delpech, P. Duchon, B. Meyssignac, P.-Y. Guidotti, and N. Gorius, “Pegase: a space-based nulling interferometer,” Proc. SPIE 6265, 62651M (2006). [CrossRef]
A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, and J. Schneider, “The DARWIN project,” Astrophys. Space Sci. 241, 135-146 (1996).
C. Beichman, P. Lawson, O. Lay, A. Ahmed, S. Unwin, and K. Johnston, “Status of the terrestrial planet finder interferometer (TPF-I),” Proc. SPIE 6268, 62680S (2006). [CrossRef]
K. Houairi, F. Cassaing, J.-M. Le Duigou, B. Sorrente, S. Jacquinod, and J.-P. Amans, “PERSEE, the dynamic nulling demonstrator: recent progress on the cophasing system,” Proc. SPIE 7013, 70131W (2008). [CrossRef]
F. Cassaing, J.-M. Le Duigou, J.-P. Amans, M. Barillot, T. Buey, F. Henault, K. Houairi, S. Jacquinod, P. Laporte, A. Marcotto, L. Pirson, J.-M. Reess, B. Sorrente, G. Rousset, V. Coudé du Foresto, and M. Ollivier, “Persee: a nulling demonstrator with real-time correction of external disturbances,” Proc. SPIE 7013, 70131Z (2008). [CrossRef]

Absil, O.
Ahmed, A.
Amans, J.-P.
Barillot, M.
Beichman, C.
Benoît, M. R.
Bönsch, G.
Born, M.
Buey, T.
Cassaing, F.
Cheng, Y.-Y.
Clédassou, R.
Colavita, M. M.
Coudé du Foresto, V.
Creath, K.
Dändliker, R.
de Groot, P. J.
Delpech, M.
Delplancke, F.
Derie, F.
Duchon, P.
Elandaloussi, H.
Eriksson, H.
Escarrat, L.
Falaggis, K.
Fleury, B.
Glindemann, A.
Gorius, N.
Guidotti, P.-Y.
Gursel, Y.
Henault, F.
Himbert, M. E.
Hines, B. E.
Houairi, K.
Hutter, D. J.
Ishii, Y.
Jacquinod, S.
Johnston, K.
Jones, J. D. C.
Juncar, P.
Kato, M.
Klaver, R. G.
Laporte, P.
Lawson, P.
Lawson, P. R.
Lay, O.
Le Duigou, J. M.
Le Duigou, J.-M.
Léger, A.
Lévêque, S.
Lévy, F.
Löfdahl, M. G.
Malbet, F.
Marcotto, A.
Mariotti, J. M.
Ménardi, S.
Mennesson, B.
Meyssignac, B.
Mourard, D.
Ollivier, M.
Paresce, F.
Pinard, J.
Pirson, L.
Polhemus, C.
Puget, J. L.
Rabbia, Y.
Razet, A.
Reess, J.-M.
Rouan, D.
Rousset, G.
Salvadé, Y.
Schneider, J.
Schwider, J.
Shao, M.
Sorrente, B.
Staelin, D. H.
Towers, C. E.
Towers, D. P.
Unwin, S.
van Brug, H.
Wada, A.
Wolf, E.
Wyant, J. C.
Zimmermann, E.

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[1] Y. Gursel, “Picometer-accuracy, laser-metrology gauge for Keck interferometer differential-phase subsystem,” Proc. SPIE 4838, 995-1010 (2003). [CrossRef]

[2] M. Shao, M. M. Colavita, B. E. Hines, D. H. Staelin, and D. J. Hutter, “The Mark III stellar interferometer,” Astron. Astrophys. 193, 357-371 (1988).

[3] P. R. Lawson, “Group-delay tracking in optical stellar interferometry with the fast Fourier transform,” J. Opt. Soc. Am. A 12, 366-374 (1995). [CrossRef]

[4] F. Delplancke, F. Derie, F. Paresce, A. Glindemann, F. Lévy, S. Lévêque, and S. Ménardi, “PRIMA for the VLTI--Science,” Astrophys. Space Sci. 286, 99-104 (2003). [CrossRef]

[5] M. G. Löfdahl and H. Eriksson, “Algorithm for resolving 2π ambiguities in interferometric measurements by use of multiple wavelengths,” Opt. Eng. 40, 984-990 (2001). [CrossRef]

[6] P. Juncar, H. Elandaloussi, M. E. Himbert, J. Pinard, and A. Razet, “A new optical wavelength ratio measurement apparatus: the fringe counting sigmameter,” IEEE Trans. Instrum. Meas. 46, 690-695 (1997). [CrossRef]

[7] M. R. Benoît, “Application des phénomènes d'interférence à des déterminations métrologiques,” J. Phys. (France) 3, 57-68 (1898).

[8] J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113-2118 (1971). [CrossRef] [PubMed]

[9] C. Polhemus, “Two-wavelength interferometry,” Appl. Opt. 12, 2071-2074 (1973). [CrossRef] [PubMed]

[10] K. Creath, “Phase measurement interferometry techniques,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1988), vol. XXVI, chap. V, pp. 349-393. [CrossRef]

[11] J. Schwider, “Advanced evaluation techniques in interferometry,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1990), vol. XXVIII, chap. IV, pp. 371-359.

[12] Y.-Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539-4543 (1984). [CrossRef] [PubMed]

[13] R. Dändliker, Y. Salvadé, and E. Zimmermann, “Distance measurement by multiple-wavelength interferometry,” J. Opt. 29, 105-114 (1998). [CrossRef]

[14] A. Wada, M. Kato, and Y. Ishii, “Large step-height measurements using multiple-wavelength holographic interferometry with tunable laser diodes,” J. Opt. Soc. Am. A 25, 3013-3020 (2008). [CrossRef]

[15] P. J. de Groot, “Extending the unambiguous range of two-color interferometers,” Appl. Opt. 33, 5948-5953 (1994). [CrossRef] [PubMed]

[16] H. van Brug and R. G. Klaver, “On the effective wavelength in two-wavelength interferometry,” Pure Appl. Opt. 7, 1465-1471 (1998). [CrossRef]

[17] K. Falaggis, D. P. Towers, and C. E. Towers, “A hybrid technique for ultra-high dynamic range interferometry,” Proc. SPIE 7063, 70630X (2008). [CrossRef]

[18] C. E. Towers, D. P. Towers, and J. D. C. Jones, “Generalized frequency selection in multifrequencyinterferometry,” Opt. Lett. 29, 1348-1350 (2004). [CrossRef] [PubMed]

[19] M. Born and E. Wolf, Principles of Optics (Pergamon, 1986).

[20] G. Bönsch, “Wavelength ratio of stabilized laser radiation at 3.39 μm and 0.633 μm,” Appl. Opt. 22, 3414-3420 (1983). [CrossRef] [PubMed]

[21] J. M. Le Duigou, M. Ollivier, A. Léger, F. Cassaing, B. Sorrente, B. Fleury, G. Rousset, O. Absil, D. Mourard, Y. Rabbia, L. Escarrat, F. Malbet, D. Rouan, R. Clédassou, M. Delpech, P. Duchon, B. Meyssignac, P.-Y. Guidotti, and N. Gorius, “Pegase: a space-based nulling interferometer,” Proc. SPIE 6265, 62651M (2006). [CrossRef]

[22] A. Léger, J. M. Mariotti, B. Mennesson, M. Ollivier, J. L. Puget, D. Rouan, and J. Schneider, “The DARWIN project,” Astrophys. Space Sci. 241, 135-146 (1996).

[23] C. Beichman, P. Lawson, O. Lay, A. Ahmed, S. Unwin, and K. Johnston, “Status of the terrestrial planet finder interferometer (TPF-I),” Proc. SPIE 6268, 62680S (2006). [CrossRef]

[24] K. Houairi, F. Cassaing, J.-M. Le Duigou, B. Sorrente, S. Jacquinod, and J.-P. Amans, “PERSEE, the dynamic nulling demonstrator: recent progress on the cophasing system,” Proc. SPIE 7013, 70131W (2008). [CrossRef]

[25] F. Cassaing, J.-M. Le Duigou, J.-P. Amans, M. Barillot, T. Buey, F. Henault, K. Houairi, S. Jacquinod, P. Laporte, A. Marcotto, L. Pirson, J.-M. Reess, B. Sorrente, G. Rousset, V. Coudé du Foresto, and M. Ollivier, “Persee: a nulling demonstrator with real-time correction of external disturbances,” Proc. SPIE 7013, 70131Z (2008). [CrossRef]

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Two-wavelength interferometry: extended range and accurate optical path difference analytical estimator