Abstract

Wavefront sensing with numerical phase-error correction system is carried out using a random phase plate and phase retrieval using multiple intensity measurements of axially-displaced speckle patterns and the wave propagation equation. Various wavefronts with smooth curvatures incident on the developed phase plate (DPP) are examined: planar, spherical, cylindrical, and a wavefront passing through the side of a bare optical fiber. Spurious fringe pattern in the wavefront reconstructions due to a small tilt (Δθ=0.212°) in the plane illumination wave is detected and numerically corrected for. Fringe pattern of the illumination wave obtained for the setup without the phase object being investigated is used as reference fringe pattern. Fringe compensation yields wavefronts with the correct shape and numerical value based on the specifications of the setup. The numerical phase-error correction system described in this study can be extended to other types of phase errors such as those due to aberrations if optical elements are present in the setup or due to perturbations in the environment.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2008 (1)

2007 (6)

2006 (4)

2005 (4)

2002 (1)

2000 (2)

A. Nemeth, J. Kornis, and Z. Fuzessy, "Fringe compensation in holographic interferometry using phase-shifted interferograms," Opt. Eng. 39, 3196-3200 (2000).
[CrossRef]

P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
[CrossRef]

1999 (1)

1998 (1)

1997 (1)

1996 (1)

1995 (1)

P. Rastogi, "Interferometric comparison of diffuse objects using comparative holography," Opt. Eng. 34, 1923-1929 (1995).
[CrossRef]

1994 (2)

1992 (1)

1990 (1)

1988 (1)

1987 (1)

1986 (1)

1979 (1)

N. Abramson and H. Bjelkhagen, "Sandwich hologram interferometry 5: Measurement of in-plane displacement and compensation for rigid body motion," Appl. Opt. 18, 2872-2882 (1979).
[CrossRef]

1972 (1)

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

Abramson, N.

N. Abramson and H. Bjelkhagen, "Sandwich hologram interferometry 5: Measurement of in-plane displacement and compensation for rigid body motion," Appl. Opt. 18, 2872-2882 (1979).
[CrossRef]

Alfieri, D.

Almoro, P.

Anand, A.

Andersen, G. P.

Ares, M.

Aspert, N.

Barbero, S.

S. Barbero and L. N. Thibos, "Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation," Opt. Eng. 45, 094001 (2006).
[CrossRef]

Bille, J. F.

Bjelkhagen, H.

N. Abramson and H. Bjelkhagen, "Sandwich hologram interferometry 5: Measurement of in-plane displacement and compensation for rigid body motion," Appl. Opt. 18, 2872-2882 (1979).
[CrossRef]

Blanchard, P. M.

Bourquin, S.

Caum, J.

Cervino, A.

A. Cervino, S. Hosking, and M. Dunne, "Operator-induced errors in Hartmann-Shack wavefront sensing: Model eye study," J. Cataract Refract. Surg. 33, 115-121 (2007).
[CrossRef]

Charrière, F.

Colomb, T.

Colton, I.

Cuche, E.

Dainty, J. C.

De Nicola, S.

Depeursinge, C.

Duan, Z.

Dunne, M.

A. Cervino, S. Hosking, and M. Dunne, "Operator-induced errors in Hartmann-Shack wavefront sensing: Model eye study," J. Cataract Refract. Surg. 33, 115-121 (2007).
[CrossRef]

Esposito, S.

Ferraro, P.

Finizio, A.

Fisher, D. J.

Fontanella, J. C.

Fox, P.

Fuzessy, Z.

A. Nemeth, J. Kornis, and Z. Fuzessy, "Fringe compensation in holographic interferometry using phase-shifted interferograms," Opt. Eng. 39, 3196-3200 (2000).
[CrossRef]

Ganesan, A. R.

Gerchberg, R. W.

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

Ghebremichael, F.

Goelz, S.

Goncharov, A. V.

Greenaway, A. H.

Grilli, S.

Grimm, B.

Gurley, K. S.

Hanson, S. G.

Hosking, S.

A. Cervino, S. Hosking, and M. Dunne, "Operator-induced errors in Hartmann-Shack wavefront sensing: Model eye study," J. Cataract Refract. Surg. 33, 115-121 (2007).
[CrossRef]

Jitsuno, T.

Joenathan, C.

Juptner, W.

Jüptner, W.

Kornis, J.

A. Nemeth, J. Kornis, and Z. Fuzessy, "Fringe compensation in holographic interferometry using phase-shifted interferograms," Opt. Eng. 39, 3196-3200 (2000).
[CrossRef]

Kühn, J.

Lane, R.

Liang, J.

Lindlein, N.

Mackin, T.

Marian, A.

Marquet, P.

Miyamoto, Y.

Montfort, F.

Nakai, S.

Nakatsuka, M.

Nemeth, A.

A. Nemeth, J. Kornis, and Z. Fuzessy, "Fringe compensation in holographic interferometry using phase-shifted interferograms," Opt. Eng. 39, 3196-3200 (2000).
[CrossRef]

Nugent, K.

Osten, W.

Pedrini, G.

Pfund, J.

Pierattini, G.

Primot, J.

Rastogi, P.

P. Rastogi, "Interferometric comparison of diffuse objects using comparative holography," Opt. Eng. 34, 1923-1929 (1995).
[CrossRef]

Roddier, F.

Rousset, G.

Royo, S.

Sansone, L.

Saxton, W. O.

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

Schnars, U.

Scholten, R.

Schwider, J.

Seebacher, S.

Seifert, L.

L. Seifert, H. J. Tiziani, and W. Osten, "Wavefront reconstruction with the adaptive Shack-Hartmann sensor," Opt. Commun. 245, 255-269 (2005).
[CrossRef]

Sirohi, R. S.

Takeda, M.

Tallon, M.

Thibos, L. N.

S. Barbero and L. N. Thibos, "Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation," Opt. Eng. 45, 094001 (2006).
[CrossRef]

Tiziani, H. J.

L. Seifert, H. J. Tiziani, and W. Osten, "Wavefront reconstruction with the adaptive Shack-Hartmann sensor," Opt. Commun. 245, 255-269 (2005).
[CrossRef]

Turner, L.

Wagner, C.

Wang, W.

Woods, S. C.

Yamaguchi, I.

Yoon, G. Y.

Yura, H. T.

Zhang, F.

G. Pedrini, F. Zhang, and W. Osten, "Deterministic phase retrieval from diffracted intensities speckle fields," Opt. Commun. 277, 50-56 (2007).
[CrossRef]

G. Pedrini, F. Zhang, and W. Osten, "Digital holographic microscopy in the deep (193 nm) ultraviolet," Appl. Opt. 46, 7829-7835 (2007).
[CrossRef] [PubMed]

Zhang, T.

Appl. Opt. (12)

N. Abramson and H. Bjelkhagen, "Sandwich hologram interferometry 5: Measurement of in-plane displacement and compensation for rigid body motion," Appl. Opt. 18, 2872-2882 (1979).
[CrossRef]

R. Lane and M. Tallon, "Wave-front reconstruction using a Shack-Hartmann sensor," Appl. Opt. 31, 6902-6908 (1992).
[CrossRef] [PubMed]

U. Schnars and W. Juptner, "Direct recording of holograms by a CCD target and numerical reconstruction," Appl. Opt. 33, 179- (1994).
[CrossRef] [PubMed]

C. Wagner, S. Seebacher, W. Osten, and W. Jüptner, "Digital Recording and Numerical Reconstruction of Lensless Fourier Holograms in Optical Metrology," Appl. Opt. 38, 4812-4820 (1999).
[CrossRef]

G. Y. Yoon, T. Jitsuno, M. Nakatsuka, and S. Nakai, "Shack Hartmann wave-front measurement with a large F-number plastic microlens array," Appl. Opt. 35, 188- (1996).
[CrossRef] [PubMed]

P. M. Blanchard, D. J. Fisher, S. C. Woods, and A. H. Greenaway, "Phase-diversity wave-front sensing with a distorted diffraction grating," Appl. Opt. 39, 6649-6655 (2000).
[CrossRef]

J. Pfund, N. Lindlein, and J. Schwider, "Misalignment effects of the Shack-Hartmann sensor," Appl. Opt. 37, 22-27 (1998).
[CrossRef]

C. Joenathan, A. R. Ganesan, and R. S. Sirohi, "Fringe compensation in speckle interferometry: application to nondestructive testing," Appl. Opt. 25, 3781-3784 (1986).
[CrossRef] [PubMed]

P. Almoro, G. Pedrini, and W. Osten, "Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field," Appl. Opt. 45, 8596-8605 (2006).
[CrossRef] [PubMed]

F. Ghebremichael, G. P. Andersen, and K. S. Gurley, "Holography-based wavefront sensing," Appl. Opt. 47, A62-A69 (2008).
[CrossRef] [PubMed]

G. Pedrini, F. Zhang, and W. Osten, "Digital holographic microscopy in the deep (193 nm) ultraviolet," Appl. Opt. 46, 7829-7835 (2007).
[CrossRef] [PubMed]

F. Roddier, "Curvature sensing and compensation: a new concept in adaptive optics," Appl. Opt. 27, 1223-1225 (1988).
[CrossRef] [PubMed]

J. Cataract Refract. Surg. (1)

A. Cervino, S. Hosking, and M. Dunne, "Operator-induced errors in Hartmann-Shack wavefront sensing: Model eye study," J. Cataract Refract. Surg. 33, 115-121 (2007).
[CrossRef]

J. Opt. Soc. Am. A (5)

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

Opt. Commun. (2)

L. Seifert, H. J. Tiziani, and W. Osten, "Wavefront reconstruction with the adaptive Shack-Hartmann sensor," Opt. Commun. 245, 255-269 (2005).
[CrossRef]

G. Pedrini, F. Zhang, and W. Osten, "Deterministic phase retrieval from diffracted intensities speckle fields," Opt. Commun. 277, 50-56 (2007).
[CrossRef]

Opt. Eng. (3)

P. Rastogi, "Interferometric comparison of diffuse objects using comparative holography," Opt. Eng. 34, 1923-1929 (1995).
[CrossRef]

A. Nemeth, J. Kornis, and Z. Fuzessy, "Fringe compensation in holographic interferometry using phase-shifted interferograms," Opt. Eng. 39, 3196-3200 (2000).
[CrossRef]

S. Barbero and L. N. Thibos, "Error analysis and correction in wavefront reconstruction from the transport-of-intensity equation," Opt. Eng. 45, 094001 (2006).
[CrossRef]

Opt. Express (1)

Opt. Lett. (6)

Optik (Stuttgart) (1)

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

Other (1)

P. F. Almoro, DTU Fotonik, Department of Photonics Engineering, and S. G. Hanson are preparing a manuscript to be called "Random phase plate for wavefront sensing via phase retrieval and a volume speckle field."

Supplementary Material (3)

» Media 1: MOV (729 KB)     
» Media 2: MOV (848 KB)     
» Media 3: MOV (883 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Experimental setup for wavefront sensing using speckles

Fig. 2.
Fig. 2.

Schematic diagram for phase retrieval using multiple speckle intensity measurements and simulated wave propagations between measurement planes

Fig. 3.
Fig. 3.

Fringe patterns of plane illumination wave at a) normal, and b) tilted incidence at the plane of DPP. c) Spurious fringe pattern resulting from a tilted illumination of the test phase object

Fig. 4.
Fig. 4.

Phase-error correction system: subtraction of the reference fringes from the spurious fringes to obtain the desired fringe pattern

Fig. 5.
Fig. 5.

Numerical simulations of wavefronts with varying curvatures, before and after fringe compensation. a) Plane wave (PW), b) converging spherical wave (CSW), c) diverging cylindrical wave (DCW), and d) wavefront through cylindrical glass rod (CGR). (730 kB) Movie of propagating simulated wavefronts. [Media 1]

Fig. 6.
Fig. 6.

Experimental fringe patterns with varying curvatures, before and after fringe compensation. a) Plane wave, b) converging spherical wave, c) diverging cylindrical wave, and d) wavefront through the side of a bare optical fiber tip. (848 kB) Movie of propagating reconstructed wavefronts. (884 kB) Movie of numerical and experimental results. [Media 2][Media 3]

Equations (2)

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U ( x , y , d ) = C u ( f x , f y ) exp [ ( i 2 π d λ ) ( 1 λ 2 f x 2 λ 2 f y 2 ) 1 2 ] ×
exp [ i 2 π ( f x x + f y y ) ] d f x d f y

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