Abstract

Multiple-wave achromatic interferometric techniques are used to measure, with high accuracy and high transverse resolution, wave fronts of polychromatic light sources. The wave fronts to be measured are replicated by a diffraction grating into several copies interfering together, leading to an interference pattern. A CCD detector located in the vicinity of the grating records this interference pattern. Some of these wave-front sensors are able to resolve wave-front spatial frequencies 3 to 4 times higher than a conventional Shack–Hartmann technique using an equivalent CCD detector. Its dynamic is also much higher, 2 to 3 orders of magnitude.

© 2005 Optical Society of America

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2003 (1)

2002 (1)

2000 (2)

V. I. Sokolov, M. I. Pergament, A. M. Nugumanov, R. V. Smirnov, “Phase measurements under three wave mixing in a nonlinear crystal,” Opt. Commun. 183, 515–522 (2000).
[CrossRef]

J. Primot, N. Guerineau, “Extended Hartmann test based on the pseudoguiding property of a Hartmann mask completed by a phase chessboard,” Appl. Opt. 39, 5715–5720 (2000).
[CrossRef]

1998 (3)

1995 (1)

1993 (1)

1984 (1)

1979 (1)

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–307 (1979).
[CrossRef]

1972 (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

1971 (1)

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

1904 (1)

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenkd 24, 1–21 (1904).

1835 (1)

G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc. 5, 283–291 (1835).

Airy, G. B.

G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc. 5, 283–291 (1835).

Aleksandrov, A.

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Baldis, H.

J.-C. Chanteloup, H. Baldis, A. Migus, G. Mourou, B. Loiseaux, J.-P. Huignard, “Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop,” Opt. Lett. 23, 475–477 (1998).
[CrossRef]

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, G. Mourou, H. Baldis, “Wave-front detection and correction for ultra-intense laser systems,” Solid State Lasers for Application to Inertial Confinement Fusion, M. L. André, ed., Proc. SPIE3047, 227–338 (1997).
[CrossRef]

Bandulet, H.

B. Wattellier, J. Fuchs, J.-P. Zou, J.-C. Chanteloup, H. Bandulet, P. Michel, C. Labaune, “Generation of a single hot spot by use of a deformable mirror and study of its propagation in an underdense plasma,” J. Opt. Soc. Am. B 20, 1632–1642 (2003).
[CrossRef]

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1989), pp. 395–398.

Bruck, Y. M.

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–307 (1979).
[CrossRef]

Chanteloup, J.-C.

B. Wattellier, J. Fuchs, J.-P. Zou, J.-C. Chanteloup, H. Bandulet, P. Michel, C. Labaune, “Generation of a single hot spot by use of a deformable mirror and study of its propagation in an underdense plasma,” J. Opt. Soc. Am. B 20, 1632–1642 (2003).
[CrossRef]

B. Wattellier, C. Sauteret, J.-C. Chanteloup, A. Migus, “Beam-focus shaping by use of programmable phase-only filters: application to an ultralong focal line,” Opt. Lett. 27, 213–215 (2002).
[CrossRef]

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

J.-C. Chanteloup, H. Baldis, A. Migus, G. Mourou, B. Loiseaux, J.-P. Huignard, “Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop,” Opt. Lett. 23, 475–477 (1998).
[CrossRef]

J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23, 621–623 (1998).
[CrossRef]

B. Wattellier, J.-C. Chanteloup, J. P. Zou, C. Sauteret, A. Migus, “Adaptive optics technique for wave front correction of multi-terawatt Nd:glass laser chain,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Md., 23–28 May 1999.

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, A. Migus, “Liquid crystal based adaptive optics setup for laser wave front correction,” in Laser Technology for Laser Guide Star Adaptive Optics Astronomy, N. Hubin, ed., ESO Proc.55, 23–26 (1997).

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, G. Mourou, H. Baldis, “Wave-front detection and correction for ultra-intense laser systems,” Solid State Lasers for Application to Inertial Confinement Fusion, M. L. André, ed., Proc. SPIE3047, 227–338 (1997).
[CrossRef]

J.-C. Chanteloup, “Contrôle et mise en forme des fronts de phase et d’énergie d’impulsions lasers brèves ultra-intenses,” Ph.D. thesis (Ecole Polytechnique, Palaiseau, France, 1998).

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Chériaux, G.

Collier, J.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Danson, C.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Depierreux, S.

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Druon, F.

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23, 621–623 (1998).
[CrossRef]

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Edwards, C.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Faure, J.

Fuchs, J.

B. Wattellier, J. Fuchs, J.-P. Zou, J.-C. Chanteloup, H. Bandulet, P. Michel, C. Labaune, “Generation of a single hot spot by use of a deformable mirror and study of its propagation in an underdense plasma,” J. Opt. Soc. Am. B 20, 1632–1642 (2003).
[CrossRef]

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Guerineau, N.

Hartmann, J.

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenkd 24, 1–21 (1904).

Hawkes, S.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Hernandez-Gomez, C.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Hooker, C.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Huignard, J.-P.

J.-C. Chanteloup, H. Baldis, A. Migus, G. Mourou, B. Loiseaux, J.-P. Huignard, “Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop,” Opt. Lett. 23, 475–477 (1998).
[CrossRef]

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, A. Migus, “Liquid crystal based adaptive optics setup for laser wave front correction,” in Laser Technology for Laser Guide Star Adaptive Optics Astronomy, N. Hubin, ed., ESO Proc.55, 23–26 (1997).

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, G. Mourou, H. Baldis, “Wave-front detection and correction for ultra-intense laser systems,” Solid State Lasers for Application to Inertial Confinement Fusion, M. L. André, ed., Proc. SPIE3047, 227–338 (1997).
[CrossRef]

Kudryashov, A.

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Labaune, C.

B. Wattellier, J. Fuchs, J.-P. Zou, J.-C. Chanteloup, H. Bandulet, P. Michel, C. Labaune, “Generation of a single hot spot by use of a deformable mirror and study of its propagation in an underdense plasma,” J. Opt. Soc. Am. B 20, 1632–1642 (2003).
[CrossRef]

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Le Garrec, B.

B. Le Garrec, “Adaptive optics operation for lasers: second meeting report,” (Commissariat à l’Energie Atomique, Paris, 2000).

Loiseaux, B.

J.-C. Chanteloup, H. Baldis, A. Migus, G. Mourou, B. Loiseaux, J.-P. Huignard, “Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop,” Opt. Lett. 23, 475–477 (1998).
[CrossRef]

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, A. Migus, “Liquid crystal based adaptive optics setup for laser wave front correction,” in Laser Technology for Laser Guide Star Adaptive Optics Astronomy, N. Hubin, ed., ESO Proc.55, 23–26 (1997).

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, G. Mourou, H. Baldis, “Wave-front detection and correction for ultra-intense laser systems,” Solid State Lasers for Application to Inertial Confinement Fusion, M. L. André, ed., Proc. SPIE3047, 227–338 (1997).
[CrossRef]

Maksimchuk, A.

J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23, 621–623 (1998).
[CrossRef]

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Michard, A.

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Michel, P.

B. Wattellier, J. Fuchs, J.-P. Zou, J.-C. Chanteloup, H. Bandulet, P. Michel, C. Labaune, “Generation of a single hot spot by use of a deformable mirror and study of its propagation in an underdense plasma,” J. Opt. Soc. Am. B 20, 1632–1642 (2003).
[CrossRef]

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Migus, A.

B. Wattellier, C. Sauteret, J.-C. Chanteloup, A. Migus, “Beam-focus shaping by use of programmable phase-only filters: application to an ultralong focal line,” Opt. Lett. 27, 213–215 (2002).
[CrossRef]

J.-C. Chanteloup, H. Baldis, A. Migus, G. Mourou, B. Loiseaux, J.-P. Huignard, “Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop,” Opt. Lett. 23, 475–477 (1998).
[CrossRef]

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, A. Migus, “Liquid crystal based adaptive optics setup for laser wave front correction,” in Laser Technology for Laser Guide Star Adaptive Optics Astronomy, N. Hubin, ed., ESO Proc.55, 23–26 (1997).

B. Wattellier, J.-C. Chanteloup, J. P. Zou, C. Sauteret, A. Migus, “Adaptive optics technique for wave front correction of multi-terawatt Nd:glass laser chain,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Md., 23–28 May 1999.

Mourou, G.

J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23, 621–623 (1998).
[CrossRef]

J.-C. Chanteloup, H. Baldis, A. Migus, G. Mourou, B. Loiseaux, J.-P. Huignard, “Nearly diffraction-limited laser focal spot obtained by use of an optically addressed light valve in an adaptive-optics loop,” Opt. Lett. 23, 475–477 (1998).
[CrossRef]

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, G. Mourou, H. Baldis, “Wave-front detection and correction for ultra-intense laser systems,” Solid State Lasers for Application to Inertial Confinement Fusion, M. L. André, ed., Proc. SPIE3047, 227–338 (1997).
[CrossRef]

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Nantel, M.

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

J.-C. Chanteloup, F. Druon, M. Nantel, A. Maksimchuk, G. Mourou, “Single-shot wave-front measurements of high-intensity ultrashort laser pulses with a three-wave interferometer,” Opt. Lett. 23, 621–623 (1998).
[CrossRef]

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Nees, J.

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Nugumanov, A. M.

V. I. Sokolov, M. I. Pergament, A. M. Nugumanov, R. V. Smirnov, “Phase measurements under three wave mixing in a nonlinear crystal,” Opt. Commun. 183, 515–522 (2000).
[CrossRef]

Pergament, M. I.

V. I. Sokolov, M. I. Pergament, A. M. Nugumanov, R. V. Smirnov, “Phase measurements under three wave mixing in a nonlinear crystal,” Opt. Commun. 183, 515–522 (2000).
[CrossRef]

Platt, B. C.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Primot, J.

Reason, C.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Ross, I.

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

Sauteret, C.

B. Wattellier, C. Sauteret, J.-C. Chanteloup, A. Migus, “Beam-focus shaping by use of programmable phase-only filters: application to an ultralong focal line,” Opt. Lett. 27, 213–215 (2002).
[CrossRef]

B. Wattellier, J.-C. Chanteloup, J. P. Zou, C. Sauteret, A. Migus, “Adaptive optics technique for wave front correction of multi-terawatt Nd:glass laser chain,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Md., 23–28 May 1999.

J. P. Zou, C. Sauteret, “The LULI 100-TW Ti:sapphire/Nd: Glass laser: a first step towards a high performance petawatt facility,” Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 94–97 (1998).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Scheiner, C.

C. Scheiner, Sive fundamentum opticum (Oculus, Innsbruck, Germany, 1619).

Shack, R. V.

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Smirnov, R. V.

V. I. Sokolov, M. I. Pergament, A. M. Nugumanov, R. V. Smirnov, “Phase measurements under three wave mixing in a nonlinear crystal,” Opt. Commun. 183, 515–522 (2000).
[CrossRef]

Sodin, L. G.

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–307 (1979).
[CrossRef]

Sogno, L.

J. Primot, L. Sogno, “Achromatic three-wave (or more) lateral shearing interferometer,” J. Opt. Soc. Am. A 12, 2679–2685 (1995).
[CrossRef]

L. Sogno, “L’interféromètre à décalage Tri-latéral: une nou-velle technique d’analyse de surface d’onde,” Ph.D. thesis (Université Paris XI, Orsay, France, 1996).

Sokolov, V. I.

V. I. Sokolov, M. I. Pergament, A. M. Nugumanov, R. V. Smirnov, “Phase measurements under three wave mixing in a nonlinear crystal,” Opt. Commun. 183, 515–522 (2000).
[CrossRef]

Swanson, G. J.

Vdovin, G.

F. Druon, G. Chériaux, J. Faure, J. Nees, M. Nantel, A. Maksimchuk, G. Mourou, J.-C. Chanteloup, G. Vdovin, “Wave front correction of femtosecond terawatt lasers using deformable mirrors,” Opt. Lett. 23, 1043–1045 (1998).
[CrossRef]

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

Wattellier, B.

B. Wattellier, J. Fuchs, J.-P. Zou, J.-C. Chanteloup, H. Bandulet, P. Michel, C. Labaune, “Generation of a single hot spot by use of a deformable mirror and study of its propagation in an underdense plasma,” J. Opt. Soc. Am. B 20, 1632–1642 (2003).
[CrossRef]

B. Wattellier, C. Sauteret, J.-C. Chanteloup, A. Migus, “Beam-focus shaping by use of programmable phase-only filters: application to an ultralong focal line,” Opt. Lett. 27, 213–215 (2002).
[CrossRef]

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

B. Wattellier, J.-C. Chanteloup, J. P. Zou, C. Sauteret, A. Migus, “Adaptive optics technique for wave front correction of multi-terawatt Nd:glass laser chain,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Md., 23–28 May 1999.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1989), pp. 395–398.

Zou, J. P.

J. P. Zou, C. Sauteret, “The LULI 100-TW Ti:sapphire/Nd: Glass laser: a first step towards a high performance petawatt facility,” Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 94–97 (1998).
[CrossRef]

B. Wattellier, J.-C. Chanteloup, J. P. Zou, C. Sauteret, A. Migus, “Adaptive optics technique for wave front correction of multi-terawatt Nd:glass laser chain,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Md., 23–28 May 1999.

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

Zou, J.-P.

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

R. V. Shack, B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

J. Opt. Soc. Am. A (2)

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

Opt. Commun. (2)

V. I. Sokolov, M. I. Pergament, A. M. Nugumanov, R. V. Smirnov, “Phase measurements under three wave mixing in a nonlinear crystal,” Opt. Commun. 183, 515–522 (2000).
[CrossRef]

Y. M. Bruck, L. G. Sodin, “On the ambiguity of the image reconstruction problem,” Opt. Commun. 30, 304–307 (1979).
[CrossRef]

Opt. Lett. (4)

Optik (Stuttgart) (1)

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttgart) 35, 237–246 (1972).

Trans. Cambridge Philos. Soc. (1)

G. B. Airy, “On the diffraction of an object-glass with circular aperture,” Trans. Cambridge Philos. Soc. 5, 283–291 (1835).

Z. Instrumentenkd (1)

J. Hartmann, “Objektivuntersuchungen,” Z. Instrumentenkd 24, 1–21 (1904).

Other (12)

S. Hawkes, J. Collier, C. Hooker, C. Reason, C. Edwards, C. Hernandez-Gomez, C. Danson, I. Ross, “Adaptive optics trials on Vulcan,” (Rutherford Appleton Laboratory, Didcot, UK, 2001), p. 153.

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, G. Mourou, H. Baldis, “Wave-front detection and correction for ultra-intense laser systems,” Solid State Lasers for Application to Inertial Confinement Fusion, M. L. André, ed., Proc. SPIE3047, 227–338 (1997).
[CrossRef]

J.-C. Chanteloup, B. Loiseaux, J.-P. Huignard, A. Migus, “Liquid crystal based adaptive optics setup for laser wave front correction,” in Laser Technology for Laser Guide Star Adaptive Optics Astronomy, N. Hubin, ed., ESO Proc.55, 23–26 (1997).

L. Sogno, “L’interféromètre à décalage Tri-latéral: une nou-velle technique d’analyse de surface d’onde,” Ph.D. thesis (Université Paris XI, Orsay, France, 1996).

J.-C. Chanteloup, “Contrôle et mise en forme des fronts de phase et d’énergie d’impulsions lasers brèves ultra-intenses,” Ph.D. thesis (Ecole Polytechnique, Palaiseau, France, 1998).

J. Fuchs, B. Wattellier, H. Bandulet, P. Michel, J. P. Zou, J.-C. Chanteloup, C. Labaune, A. Michard, S. Depierreux, A. Kudryashov, A. Aleksandrov, “Wave front correction for diffraction-limited focal spot on 80 J/1 ns laser facility,” presented at International Quantum Electronics Conference/Conference on Lasers, Applications, and Technologies, Moscow, Russia, 27–28 June 2002.

B. Wattellier, J.-C. Chanteloup, J. P. Zou, C. Sauteret, A. Migus, “Adaptive optics technique for wave front correction of multi-terawatt Nd:glass laser chain,” presented at the Conference on Lasers and Electro-Optics, Baltimore, Md., 23–28 May 1999.

F. Druon, M. Nantel, G. Vdovin, A. Maksimchuk, J.-C. Chanteloup, J. Nees, G. Mourou, “Single-shot B-integral wave-front correction of femtosecond laser pulses,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), pp. 279–280.

B. Le Garrec, “Adaptive optics operation for lasers: second meeting report,” (Commissariat à l’Energie Atomique, Paris, 2000).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1989), pp. 395–398.

J. P. Zou, C. Sauteret, “The LULI 100-TW Ti:sapphire/Nd: Glass laser: a first step towards a high performance petawatt facility,” Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 94–97 (1998).
[CrossRef]

C. Scheiner, Sive fundamentum opticum (Oculus, Innsbruck, Germany, 1619).

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Figures (20)

Fig. 1
Fig. 1

Top view (upper-right insert) and lineout profile (thin curve) of the phase term of the Fourier transform of the ideal energy distribution needed in the far field. The bottom-left insert is a three-dimensional view of the real design of the grating, i.e., hexagon-shaped mesas located either at an altitude of λ/3 or 2λ/3 above the silica substrate. The associated profile is represented by the bold square line.

Fig. 2
Fig. 2

Top view of the grating. White hexagons have an altitude of 0, whereas respective altitudes of gray and black hexagons are λ0/3 and 2λ0/3. The distance pas is the pitch between grooves of a one-dimensional grating.

Fig. 3
Fig. 3

Structuring the plate by lithography.

Fig. 4
Fig. 4

Far-field distribution Texp(μ, ν) of diffracted energy by the grating used in the ATWLSI. Although most of the energy can be found in the three first orders, a nonnegligible amount of energy is still diffracted elsewhere.

Fig. 5
Fig. 5

Schematic view of a complete ATWLSI system. An order-selective plate (labeled zero-order beam stop) is inserted in the middle of a telescope relaying the replication plane (i.e., the grating) onto the CCD. Then only the three useful m = +1 orders are selected.

Fig. 6
Fig. 6

Shape of LD(λ)/LD0 in the case where the central wavelength is equal to 1 μm.

Fig. 7
Fig. 7

Picture of an ATWLSI. Scale is given by the 25-mm pitch of the breadboard holes.

Fig. 8
Fig. 8

Description of the phase-recovering algorithm used for analysis of ATWLSI interferograms.

Fig. 9
Fig. 9

Spectral windowing operation for recovering the amplitude.

Fig. 10
Fig. 10

Upper figure shows (in the plane xOz) both replicas φ1 and φ2 (thin curves) of the phase φ in their replication plane PR = xOy (i.e., the grating plane). After being replicated, they propagate along the direction of the mean wave vectors k1 and k2 (bold curves). While doing so, they transversally shear from each other. The middle part of this figure shows a schematic view of the interference pattern IR(x, y) obtained in PR, a regular alignment of dark and bright fringes; information about the phase is lost. In a plane of observation PZ parallel to PR, the interference pattern IZ(x, y) (lower part of the figure) shows then distortions linked to the derivative of φ(x, y) along x.

Fig. 11
Fig. 11

Wave-front distributions (pupil = 5 mm) of a laser beam going through a binary Fresnel-zone plate. Each image is associated with a increasing distance z between PR and PZ. The enclosed graph on the bottom right is a histogram of one of the image (the horizontal axis is graduated up to 256, i.e., the pixel value, while the vertical axis is the count of the pixel having a such value). The contrast of the image is defined by (BA)/C.

Fig. 12
Fig. 12

Contrast evolution between PR(z/hex = 0) and PZ(z/hex = 60). z/hex is the distance to the replication grating normalized to grating characteristic dimension hex = 100 μm.

Fig. 13
Fig. 13

Top-right sketch is the phase part of the AQWLSI grating, i.e., a phase chessboard equivalent to sign[tid(x, y)]. The top-left sketch is the amplitude part, i.e., an approximation of abs[tid(x, y)]. This part appears to be a simple Hartmann plate with holes of square aperture a distributed over a Cartesian grid of period p. The bottom curves show the lineout of abs[tid(x, y)] (semisinusoid arches curve) and its approximation (rectangular curve).

Fig. 14
Fig. 14

Energy distribution t ˜ abs approx(ν) given by a Hartmann plate of aperture a and period p is shown in this graph: The energy is located at the summit of each bold arrow (five of them are represented here with numbers in square boxes). The energy distribution t ˜ approx(ν) given by the same Hartmann plate combined with a phase chessboard of period p is also shown: The effect of the phase chessboard is to translate the previous set of arrows (i.e., energy) by 1/2p to give the dashed arrows (the new positions are labeled ➀ to ➄). Arrows ➀ and ➃ are replaced by two stars at the place where they should be located. There is in fact no energy at these positions owing to the presence of the zeros (± 1/a) of the sin(πνa)/(πνa) envelope. In order to achieve the cancellation of this two orders, the condition a = 2p/3 must be satisfied.

Fig. 15
Fig. 15

Looking in the far field (for instance, in the focal plane of a lens located after the grating), we have access to the energy distribution in different orders of diffraction. In the left and right images, we see that there is no energy in the zero order (thanks to the phase chessboard). Let us call the four first orders the four peaks located the closest to the center of the field of this spectrum (all four belong to the same ring centered in the center of the field; ring one is in the middle image). In the left image, we can see eight peaks located in a second ring surrounding these four peaks (a ≠ 2p/3). These orders of diffraction vanish in the right picture (a = 2p/3).

Fig. 16
Fig. 16

Insert shows an AQWLSI grating, a Hartmann mask modified by the adjunction of a phase chessboard; this is why this wave-front sensor is also called modified Hartmann mask.32 The main picture is an interference pattern obtained with an AQWLSI based on a grating characterized by a = 26 μm and p = 39 μm.

Fig. 17
Fig. 17

Energy distribution recorded in the focal plane of a lens located right after the grating. More than 87% of the incident energy is distributed in the four first orders. Less than a percent is present in the zero order, while no energy can be recorded in ring 2. The remaining energy distributed over a large number of higher orders does not affect the measure.

Fig. 18
Fig. 18

Interferograms and (inserts) recovered laser phase obtained with an AQWLSI. The laser wave front was modulated using a liquid-crystal optical valve.5 The pupil is ~5 mm and distortions amplitude is ~1 wave.

Fig. 19
Fig. 19

Angle between the incident wave vector and any of the four replicas’ wave vectors is α/2. At a distance z from the replicating grating, the distance between two identical structures of the phase observed in two separate replicas is D2. This distance D2(z) defines the z dependence of the transverse resolution.

Fig. 20
Fig. 20

Experimental observation of the variation of D2 with z (dots). The bold line represents the linear regression of the 12 experimental points obtained with z varying from 4 to 45 mm. The resulting slope (mrad) is an almost perfect adequacy with the expected value 25.62 versus 25.64 [Eq. (49)]. Nevertheless the retrieved step width is 10 to 20 times larger than for the real object. The object under study is indeed a 150-nm phase step shown in the insert (interferometric microscope image) at the bottom right. The width of this step is equal to ~30 μm.

Tables (1)

Tables Icon

Table 1 Respectives Performances of SH, ATWLSI, and AQWLSI Wave-Front Sensors

Equations (51)

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pas = 3 hex 2 ,
pas [ sin ( 0 ) + sin ( β ) ] = m λ .
sin ( β ) = 2 λ 3 hex .
i f = 2 λ 3 tan β .
i f = hex cos ( β ) .
i f = hex ( 1 + β 2 2 + ) .
i f = hex ( 1 + 2.5 10 - 5 + ) .
i f = hex .
pas sin     β m ( λ ) = m λ ,
[ sin β m ( λ max ) = sin β n ( λ min ) ] [ m λ max = n λ min ] .
λ max = 2 λ min .
λ 0 = λ min + λ max 2 .
Δ λ ATWLSI = [ 2 λ 0 / 3 , 4 λ 0 / 3 ] .
tan β ( λ ) = 2 λ 3 hex .
r ( λ ) = f 1 tan β ( λ ) .
r ( λ ) = 2 3 λ hex f 1 .
r min = r ( λ min ) = 2 r 0 / 3 , r max = r ( λ max ) = 4 r 0 / 3 ,
r foc ( λ 0 ) < r min , r foc ( λ 0 ) < r max - r min 2 = r min 2 .
r Airy ( λ 0 ) = 1.22 λ 0 f 1 2 .
LD 0 = r min / 2 r Airy ( λ 0 ) = 4 9 1.22 hex .
LD 1 = r ( λ 1 ) - r min r Airy ( λ 1 ) = LD 0 ( 2 λ 0 - 3 Δ λ ) ( 2 λ 0 - Δ λ ) ,
LD 2 = r max - r ( λ 2 ) r Airy ( λ 2 ) = LD 0 ( 2 λ 0 - 3 Δ λ ) ( 2 λ 0 - Δ λ ) .
S ( r ) = φ ( r ) · ( U 0 ° + U 120 ° + U - 120 ° ) = 0 ,
S ( r ) 2 = 3 σ 2 .
φ 1 , R ( x , y ) = φ ( x , y ) + π a λ x , φ 2 , R ( x , y ) = φ ( x , y ) - π a λ x ,
I R ( x , y ) = 2 I 0 ( x , y ) { 1 + cos [ φ 1 , R ( x , y ) - φ 2 , R ( x , y ) ] } .
I R ( x , y ) = 2 I 0 ( x , y ) [ 1 + cos ( 2 π λ a x ) ] .
d x = a z 2 ,
I Z ( x , y ) = 2 I 0 ( x , y ) { 1 + cos [ φ 1 , z ( x , y ) - φ 2 , z ( x , y ) ] } ,
φ 1 , z ( x , y ) = φ ( x + d x 2 , y ) + π a λ ( x + d x 2 ) , φ 2 , z ( x , y ) = φ ( x - d x 2 , y ) - π a λ ( x - d x 2 ) .
M ( x , y ) = cos [ φ 1 , z ( x , y ) - φ 2 , z ( x , y ) ] .
M ( x , y ) = cos [ 2 π λ a x + φ ( x + d x 2 , y ) - φ ( x - d x 2 , y ) ] .
M ( x , y ) = cos [ 2 π λ a x + φ ( x + a 4 z , y ) - φ ( x - a 4 z , y ) ] .
M ( x ) = cos [ 2 π x i + φ ( x + λ z / 4 i ) - φ ( x - λ z / 4 i ) ] .
φ x ( x i , z ) = φ ( x i + λ z / 4 i ) - φ ( x i - λ z / 4 i ) λ z / 2 i for z 0.
φ max ( x i , z ) = 4 π λ i z .
contrast = ( B - A ) C .
t ˜ id ( ν , μ ) = δ ( v - 1 a 0 , μ - 1 a 0 ) + δ ( ν - 1 a 0 , μ + 1 a 0 ) + δ ( ν + 1 a 0 , μ - 1 a 0 ) + δ ( ν + 1 a 0 , μ + 1 a 0 ) ,
t id ( x , y ) = 1 2 { cos [ 2 π ( x + y ) a 0 ] + cos [ 2 π ( x - y ) a 0 ] } .
t id ( x , y ) = sign [ t id ( x , y ) ] abs [ t id ( x , y ) ] ,
t abs approx ( x , y ) = Π a , a ( x , y ) ш a 0 / 2 ( x ) ш a 0 / 2 ( y ) ,
t abs approx ( x ) = Π a ( x ) ш p ( x )
t ˜ abs approx ( ν ) = sin ( π ν a ) π ν a ш 1 / p ( ν ) .
t approx ( x ) = Π a ( x ) [ ш p ( x ) exp ( i π x / p ) ]
t ˜ approx ( ν ) = sin ( π ν a ) π ν a [ ш 1 / p ( ν ) δ ( ν - 1 2 p ) ] .
a = 2 p / 3.
2 p     sin ( α 2 ) = λ .
D 2 ( z ) = α 2 z = α z .
α = 25.64     mrad .
φ max ( x i , f ) = 2 π λ μ / 2 f .
φ max ( x i , z ) = 4 π λ i z .

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