Abstract

Wavefront control is a significant parameter in inertial confinement fusion (ICF). The complex transmittance of large optical elements which are often used in ICF is obtained by computing the phase difference of the illuminating and transmitting fields using Ptychographical Iterative Engine (PIE). This can accurately and effectively measure the transmittance of large optical elements with irregular surface profiles, which are otherwise not measurable using commonly used interferometric techniques due to a lack of standard reference plate. Experiments are done with a Continue Phase Plate (CPP) to illustrate the feasibility of this method.

© 2014 Optical Society of America

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    [CrossRef]
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2013 (1)

2010 (1)

2009 (3)

G. R. Brady, M. Guizar-Sicairos, J. R. Fienup, “Optical wavefront measurement using phase retrieval with transverse translation diversity,” Opt. Express 17(2), 624–639 (2009).
[CrossRef] [PubMed]

C. Liu, T. Walther, J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultramicroscopy 109(10), 1263–1275 (2009).
[CrossRef] [PubMed]

X. Liu, Y. Gao, M. Chang, “A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry,” J. Opt. A Pure Appl. Opt. 11(4), 045702 (2009).
[CrossRef]

2007 (1)

2004 (1)

J. M. Rodenburg, H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

2003 (1)

2000 (1)

1996 (1)

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

1995 (1)

J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2(11), 3933–4024 (1995).
[CrossRef]

1994 (1)

G. Cao, X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[CrossRef]

1980 (1)

J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 297–305 (1980).
[CrossRef]

1979 (1)

J. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18(5), 529–534 (1979).
[CrossRef]

1978 (1)

1972 (1)

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

Auerbach, J. M.

Beau, V.

Bowers, M. W.

Brady, G. R.

Cao, G.

G. Cao, X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[CrossRef]

Chang, M.

X. Liu, Y. Gao, M. Chang, “A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry,” J. Opt. A Pure Appl. Opt. 11(4), 045702 (2009).
[CrossRef]

Daurios, J.

Dixit, S. N.

Erbert, G. V.

Faulkner, H. M.

J. M. Rodenburg, H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

Fienup, J.

J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 297–305 (1980).
[CrossRef]

J. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18(5), 529–534 (1979).
[CrossRef]

Fienup, J. R.

Gao, Y.

X. Liu, Y. Gao, M. Chang, “A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry,” J. Opt. A Pure Appl. Opt. 11(4), 045702 (2009).
[CrossRef]

Gerchberg, R.

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

Guizar-Sicairos, M.

Haya, S.

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

Haynam, C. A.

Heestand, G. M.

Henesian, M. A.

Hermann, M. R.

Higashi, Y.

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

Humphry, M. J.

Jancaitis, K. S.

Lavergne, M.

Lin, Q.

Lindl, J.

J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2(11), 3933–4024 (1995).
[CrossRef]

Liu, C.

X. Pan, C. Liu, Q. Lin, J. Zhu, “Ptycholographic iterative engine with self-positioned scanning illumination,” Opt. Express 21(5), 6162–6168 (2013).
[CrossRef] [PubMed]

C. Liu, T. Walther, J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultramicroscopy 109(10), 1263–1275 (2009).
[CrossRef] [PubMed]

Liu, X.

X. Liu, Y. Gao, M. Chang, “A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry,” J. Opt. A Pure Appl. Opt. 11(4), 045702 (2009).
[CrossRef]

Maiden, A. M.

Manes, K. R.

Marshall, C. D.

Matsuoka, S.

Mehta, N. C.

Menapace, J.

Mori, T.

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

Moses, E.

Murray, J. R.

Néauport, J.

Nostrand, M. C.

Orth, C. D.

Otsuka, M.

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

Pan, X.

Patterson, R.

Ribeyre, X.

Rodenburg, J. M.

A. M. Maiden, J. M. Rodenburg, M. J. Humphry, “Optical ptychography: a practical implementation with useful resolution,” Opt. Lett. 35(15), 2585–2587 (2010).
[CrossRef] [PubMed]

C. Liu, T. Walther, J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultramicroscopy 109(10), 1263–1275 (2009).
[CrossRef] [PubMed]

J. M. Rodenburg, H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

Sacks, R. A.

Sato, S.

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

Shaw, M. J.

Spaeth, M.

Sutton, S. B.

Valla, D.

Van Wonterghem, B. M.

Videau, L.

Walther, T.

C. Liu, T. Walther, J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultramicroscopy 109(10), 1263–1275 (2009).
[CrossRef] [PubMed]

Wegner, P. J.

White, R. K.

Widmayer, C. C.

Williams, W. H.

Yamakawa, K.

Yamamoto, H.

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

Yang, S. T.

Yu, X.

G. Cao, X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[CrossRef]

Zhu, J.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. M. Rodenburg, H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[CrossRef]

J. Electron Spectrosc. Relat. Phenom. (1)

S. Sato, T. Mori, Y. Higashi, S. Haya, M. Otsuka, H. Yamamoto, “A profilometer for synchrotron radiation mirrors,” J. Electron Spectrosc. Relat. Phenom. 80, 481–484 (1996).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

X. Liu, Y. Gao, M. Chang, “A partial differential equation algorithm for wavefront reconstruction in lateral shearing interferometry,” J. Opt. A Pure Appl. Opt. 11(4), 045702 (2009).
[CrossRef]

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

Opt. Eng. (3)

G. Cao, X. Yu, “Accuracy analysis of a Hartmann-Shack wavefront sensor operated with a faint object,” Opt. Eng. 33(7), 2331–2335 (1994).
[CrossRef]

J. Fienup, “Space object imaging through the turbulent atmosphere,” Opt. Eng. 18(5), 529–534 (1979).
[CrossRef]

J. Fienup, “Iterative method applied to image reconstruction and to computer-generated holograms,” Opt. Eng. 19(3), 297–305 (1980).
[CrossRef]

Opt. Express (2)

Opt. Lett. (2)

Optik (1)

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

Phys. Plasmas (1)

J. Lindl, “Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain,” Phys. Plasmas 2(11), 3933–4024 (1995).
[CrossRef]

Ultramicroscopy (1)

C. Liu, T. Walther, J. M. Rodenburg, “Influence of thick crystal effects on ptychographic image reconstruction with moveable illumination,” Ultramicroscopy 109(10), 1263–1275 (2009).
[CrossRef] [PubMed]

Other (7)

D. Malacara, Optical Shop Testing (John Wiley, 2007),Chap. 15.

W. Jiang and H. Li, “Hartmann-Shack wavefront sensing and wavefront control algorithm,” in The Hague'90, 12–16 April (International Society for Optics and Photonics, 1990), 82–93.

D. J. Trummer, R. J. Foley, and G. S. Shaw, “Stability of optical elements in the NIF target area building,” in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion (International Society for Optics and Photonics, 1999), 363–371.
[CrossRef]

W. H. Williams, J. M. Auerbach, M. A. Henesian, J. K. Lawson, J. T. Hunt, R. A. Sacks, and C. C. Widmayer, “Modeling characterization of the National Ignition Facility focal spot,” in Optoelectronics and High-Power Lasers and Applications (International Society for Optics and Photonics, 1998), pp. 93–104.

V. Y. Zavalova and A. V. Kudryashov, “Shack-Hartmann wavefront sensor for laser beam analyses,” in International Symposium on Optical Science and Technology (International Society for Optics and Photonics, 2002), 277–284.

G. R. Brady and J. R. Fienup, “Measurement of an optical surface using phase retrieval,” in Optical Fabrication and Testing (Optical Society of America, 2006).

S.-W. Bahk, J. Bromage, J. D. Zuegel, and J. R. Fienup, “Application of Phase Retrieval for Predicting a High-Intensity Focused Laser Field,” in Conference on Lasers and Electro-Optics (Optical Society of America, 2008).

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Figures (6)

Fig. 1
Fig. 1

Schematic of standard PIE method. The specimen is illuminated by a probe beam and the diffraction patterns are recorded in the far field.

Fig. 2
Fig. 2

Experimental setup for measuring the transmission functions with ePIE. A parallel beam focused by a non-spherical lens illuminates an object O(x, y) near the focal plane and the diffraction patterns are recorded by CCD behind the object during the transverse scanning of the object.

Fig. 3
Fig. 3

(a) The CPP used in the experiment. The diameter is 31 cm, shown by the adjacent scale, (b) the designed phase distribution of CPP, and (c) the measurement of CPP by Zygo interferometer

Fig. 4
Fig. 4

The diffraction recorded and reconstructed results without CPP. (a)One of the diffraction patterns recorded by CCD, reconstructed modulus(b) and phase(c) distribution of illumination on scanning object, modulus(d) and phase (e)distribution of emergent light after the condenser lens.

Fig. 5
Fig. 5

The diffraction recorded and reconstructed results with CPP. (a)One of diffraction patterns recorded by CCD, reconstructed amplitude(b) and phase(c) distribution of illumination on scanning object, amplitude(d) and phase(e) distribution of emergent light after the condenser lens.

Fig. 6
Fig. 6

(a) Wrapped phase of the measured modulation function, (b) wrapped phase of the measured modulation function, (c) the measured result and designed value alone the vertical lines of Figs. 3(b) and 6(b); (e) the measured result and designed value alone the horizontal lines of Figs. 3(b) and 6(b).

Equations (6)

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φ n,g ( r, R i )= P n,g ( r ) O n,g ( r R i )
ϕ g,n ( k, R i )=FFT[ φ g,n ( r, R i ) ]=| ϕ g,n ( k, R i ) | e i θ n ( k, R i )
ϕ c,n ( k, R i )= I n e i θ n ( k, R i )
φ c,n ( r, R i )=FF T 1 [ ϕ c,n ( k, R i ) ]
O new ( r, R i )= O g,n ( r, R i )+ | P n ( r ) | | P n ( r ) | max P n * ( r ) [ | P n ( r ) | 2 +α ] [ φ c,n ( r, R i )- P n ( r )O( r, R i ) ]
P new ( r )=P( r )+ | O( r, R i ) | | O( r, R i ) | max O * ( r, R i ) [ | O( r, R i ) | 2 +α ] ×[ φ c,n ( r, R i )- P n ( r )O( r, R i ) ]

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