Abstract

Two-wavelength interferometry combines measurement at two wavelengths λ1 and λ2 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=λ1λ2|λ1λ2|, 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 17.3μm, much larger than the synthetic wavelength, which is only Λ=2.2μm. Applications to metrology and fringe tracking are discussed.

© 2009 Optical Society of America

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

2006

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]

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]

2004

2003

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]

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

2001

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]

1998

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

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

1997

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]

1996

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).

1995

1994

1988

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).

1984

1983

1973

1971

1898

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

Absil, O.

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]

Ahmed, A.

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]

Amans, J.-P.

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]

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]

Barillot, M.

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]

Beichman, C.

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]

Benoît, M. R.

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

Bönsch, G.

Born, M.

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

Buey, T.

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]

Cassaing, F.

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]

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]

Cheng, Y.-Y.

Clédassou, R.

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]

Colavita, M. M.

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).

Coudé du Foresto, V.

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]

Creath, K.

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

Dändliker, R.

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

de Groot, P. J.

Delpech, M.

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]

Delplancke, F.

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]

Derie, F.

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]

Duchon, P.

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]

Elandaloussi, H.

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]

Eriksson, H.

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]

Escarrat, L.

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]

Falaggis, K.

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

Fleury, B.

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]

Glindemann, A.

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]

Gorius, N.

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]

Guidotti, P.-Y.

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]

Gursel, Y.

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

Henault, F.

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]

Himbert, M. E.

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]

Hines, B. E.

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).

Houairi, K.

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]

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]

Hutter, D. J.

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).

Ishii, Y.

Jacquinod, S.

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]

Johnston, K.

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]

Jones, J. D. C.

Juncar, P.

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]

Kato, M.

Klaver, R. G.

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

Laporte, P.

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]

Lawson, P.

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]

Lawson, P. R.

Lay, O.

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]

Le Duigou, J. M.

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]

Le Duigou, J.-M.

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]

Léger, A.

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).

Lévêque, S.

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]

Lévy, F.

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]

Löfdahl, M. G.

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]

Malbet, F.

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]

Marcotto, A.

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]

Mariotti, J. M.

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).

Ménardi, S.

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]

Mennesson, B.

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).

Meyssignac, B.

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]

Mourard, D.

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]

Ollivier, M.

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]

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).

Paresce, F.

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]

Pinard, J.

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]

Pirson, L.

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]

Polhemus, C.

Puget, J. L.

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).

Rabbia, Y.

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]

Razet, A.

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]

Reess, J.-M.

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]

Rouan, D.

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).

Rousset, G.

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]

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]

Salvadé, Y.

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

Schneider, J.

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).

Schwider, J.

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

Shao, M.

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).

Sorrente, B.

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]

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]

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]

Staelin, D. H.

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).

Towers, C. E.

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]

Towers, D. P.

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]

Unwin, S.

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]

van Brug, H.

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

Wada, A.

Wolf, E.

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

Wyant, J. C.

Zimmermann, E.

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

Appl. Opt.

Astron. Astrophys.

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).

Astrophys. Space Sci.

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]

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).

IEEE Trans. Instrum. Meas.

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]

J. Opt.

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

J. Opt. Soc. Am. A

J. Phys. (France)

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

Opt. Eng.

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]

Opt. Lett.

Proc. SPIE

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]

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]

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

Pure Appl. Opt.

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

Other

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.

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

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Figures (4)

Fig. 1
Fig. 1

Orders of interference measured at λ 1 and λ 2 are plotted as dotted and dashed lines, respectively. The difference m ̂ of the orders of interference is plotted as a solid line. In this simulation, there is no additional measurement error.

Fig. 2
Fig. 2

Analogy of OPD measurements with TWI and a calliper rule. The current OPD is marked with a bold dashed line, and its value can be measured (modulo λ i ) with respect to the closest λ i tick. But the relative position of the closest λ 1 and λ 2 ticks gives an information related to the absolute OPD value.

Fig. 3
Fig. 3

Experimental results obtained with Persee’s cophasing system when an OPD range of ± 11 μ m is applied. Sawtooth lines represent the measured orders of interference m ̇ 1 and m ̇ 2 , plotted as solid and dashed lines, respectively. The steps represent the estimated rounded order of interference m ¯ ̂ 1 .

Fig. 4
Fig. 4

Illustration of the rational approximation error ϵ f of π by a fraction p q for q [ 2 , 3 × 10 5 ] . It also shows the different types of couple according to Eq. (23) (the worst, the good, or the lucky couples).

Tables (2)

Tables Icon

Table 1 Order of Interference Measurement Error and Error Margin for Different Couples ( p , q ) a

Tables Icon

Table 2 Fractional Error and Bound Value of the Total Error for Different Couples ( p , q ) a

Equations (39)

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

Λ = λ 1 λ 2 λ 2 λ 1 with λ 2 > λ 1 .
m i = δ λ i .
δ = ( m ¯ i + m ̇ i ) λ i with { m ¯ i Z m ̇ i [ ] 0.5 , 0.5 [ ] .
δ ̂ Λ = m ̂ Λ with m ̂ = wrap ( m 1 m 2 ) .
X ( δ ) = m ¯ 2 λ 2 m ¯ 1 λ 1 ,
OPD = λ 1 ( m ¯ 1 + m ̇ 1 ) = λ 2 ( m ¯ 2 + m ̇ 2 ) .
r λ m ¯ 1 + r λ m ̇ 1 = m ¯ 2 + m ̇ 2 ,
r λ = λ 1 λ 2 .
r ̂ λ = r λ + ϵ r .
r ̂ λ = p q + ϵ f with | ϵ f | < 1 2 q .
m i = m ̇ i + ϵ i .
q ( m 2 r ̂ λ m 1 ) = p m ¯ 1 q m ¯ 2 + ϵ ,
ϵ = q ( m ¯ 1 ϵ 1 ) ( ϵ f ϵ r ) + q ϵ 2 p ϵ 1 q m 1 ϵ r .
| ϵ | < 1 2 .
q ( m 2 r ̂ λ m 1 ) ¯ p m ¯ 1 ( mod q ) ,
k × p 1 ( mod q ) .
k × q ( m 2 r ̂ λ m 1 ) ¯ m ¯ 1 ( mod q ) .
δ ̂ = λ 1 ( m ¯ ̂ 1 + m 1 ) ,
m ¯ ̂ 1 = q × wrap ( k q × q ( m 2 r ̂ λ m 1 ) ¯ ) .
Λ = q λ 1 ,
2 | ϵ | q 2 | ϵ f | + q 2 | ϵ r | + 2 ( p + q ) | ϵ m | + q | ϵ r | .
q 2 | ϵ f | + q 2 | ϵ r | + 2 ( p + q ) | ϵ m | 1 .
q | ϵ f | 1 2 , the worst couples ;
q | ϵ f | < 1 10 , the good couples ;
q 2 | ϵ f | < 1 3 , the lucky couples .
q 2 | ϵ r | + 2 q ( 1 + r λ ) | ϵ m | 2 3 .
q max ( 1 + r λ ) | ϵ m | | ϵ r | ( 1 + s 2 1 ) ,
s = 2 3 | ϵ r | ( 1 + r λ ) | ϵ m | .
q max { 1 3 ( 1 + r λ ) | ϵ m | if s 1 0.82 | ϵ r | if s 1 1 | ϵ r | ( 0.58 0.24 s ) if s 1 } .
Λ Λ = q λ 1 ( r λ 1 ) 1 λ 2 q p .
δ ̂ = λ 2 ( m ¯ ̂ 2 + m 2 ) ,
m ¯ ̂ 2 = p × wrap ( l p × q ( r ̂ λ m 1 m 2 ) ¯ ) ,
l × q 1 ( mod p ) .
ϵ margin = 1 q 2 ( | ϵ f | + | ϵ r | ) 2 ( p + q ) .
λ 1 = 824 nm ± 3 nm ,
λ 2 = 1332 nm ± 3 nm ,
r λ = 0.6180 with | ϵ r | = 1 × 10 4 .
ϵ m = 0.005 .
λ 1 λ 2 13 21 .

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