Abstract

A superresolution method for interference fringes obtained by parallel four-step phase-shifting digital holography is proposed. A complex amplitude distribution of an object wave is derived from a recorded hologram by parallel phase-shifting interferometry using two pixels without any interpolation procedures. Multiple distributions are derived by changing one of the two pixels when conducting phase-shifting interferometry. The angular spectrum distribution of the object wave is obtained by both the Fourier transforms and synthesis of the spectrum distribution from the Fourier-transformed images in the spatial frequency domain. Available space bandwidth is extended to half of that of an image sensor.

© 2014 Optical Society of America

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2013 (3)

2012 (1)

2011 (1)

2010 (3)

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Rev. 17, 519 (2010).
[CrossRef]

T. Tahara, K. Ito, M. Fujii, T. Kakue, Y. Shimozato, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Express 18, 18975 (2010).
[CrossRef]

2009 (2)

2008 (2)

2007 (1)

2006 (2)

2005 (1)

2004 (2)

Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
[CrossRef]

A. Stern and B. Javidi, J. Opt. Soc. Am. A 21, 360 (2004).
[CrossRef]

2001 (1)

2000 (1)

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

1997 (1)

1994 (1)

1987 (1)

1982 (1)

1967 (1)

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

1948 (1)

D. Gabor, Nature 161, 777 (1948).
[CrossRef]

Andrés, P.

Araiza-Esquivel, M.

Awatsuji, Y.

Brooker, G.

J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
[CrossRef]

Cai, L. Z.

Climent, V.

Depeursinge, C.

Dong, G. Y.

Fujii, A.

Fujii, M.

Gabor, D.

D. Gabor, Nature 161, 777 (1948).
[CrossRef]

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Greivenkamp, J. E.

Hoshiba, T.

Ina, H.

Ito, K.

Ito, Y.

Javidi, B.

Kakue, T.

Kaneko, A.

Kim, M.

Kobayashi, S.

Komai, K.

Koyama, T.

Kubota, T.

Kühn, J.

Lancis, J.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

Lee, B.

Lee, S.-Y.

Li, H.

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

Lim, Y.

Liu, Z.

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

Lo, C.-M.

Mann, C.

Martínez-León, L.

Matoba, O.

Meng, X. F.

Miao, L.

Murata, S.

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

Nishio, K.

Nitta, K.

Ohtsuka, Y.

Oka, K.

Pavillon, N.

Psaltis, D.

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

Rosen, J.

J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
[CrossRef]

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
[CrossRef]

Seelamantula, C. S.

Shen, X. X.

Shi, K.

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

Shimozato, Y.

Stern, A.

Tahara, T.

Tajahuerce, E.

Takeda, M.

Unser, M.

Ura, S.

Wang, Y. R.

Watanabe, E.

Xia, P.

Xu, Q.

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

Xu, X. F.

Yamagiwa, M.

Yamaguchi, I.

Yang, X. L.

Yasuda, N.

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

Yu, L.

Zhang, T.

Appl. Opt. (7)

Appl. Phys. Express (1)

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, Appl. Phys. Express 6, 022502 (2013).
[CrossRef]

Appl. Phys. Lett. (2)

Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
[CrossRef]

J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Nat. Photonics (1)

J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
[CrossRef]

Nature (1)

D. Gabor, Nature 161, 777 (1948).
[CrossRef]

Opt. Express (5)

Opt. Laser Technol. (1)

S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
[CrossRef]

Opt. Lett. (4)

Opt. Rev. (1)

T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Rev. 17, 519 (2010).
[CrossRef]

Phys. Rev. Lett. (1)

K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Principle of parallel four-step phase-shifting digital holography. (a) Schematic and (b) SBW available for recording an object wave. d is the pixel pitch of the image sensor.

Fig. 2.
Fig. 2.

Basic concept of the proposed technique. Parallel phase-shifting interferometry using two (a) horizontal and (b) vertical pixels, and the obtained SBWs.

Fig. 3.
Fig. 3.

Flow of the proposed image-reconstruction procedure.

Fig. 4.
Fig. 4.

Optical setup for an experiment. (a) Schematic of the constructed system and (b) photographs of the object.

Fig. 5.
Fig. 5.

Experimental results. (a), (c), and (e) show images reconstructed by the conventional method. (b), (d), and (f) show images reconstructed by the proposed method. The scale bar shown in Fig. 5(a) is 5 mm. From (a), (b) to (e), (f), the object was shifted 5.0 mm along the horizontal direction.

Equations (12)

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I(x,y)=I(x,y)Ir(x,y)={|Ao(x,y)|2+2Ao(x,y)Ir(x,y)cosϕ(x,y)when(x,y)=(even,even),|Ao(x,y)|2+2Ao(x,y)Ir(x,y)sinϕ(x,y)when(x,y)=(even,odd),|Ao(x,y)|22Ao(x,y)Ir(x,y)cosϕ(x,y)when(x,y)=(odd,odd),|Ao(x,y)|22Ao(x,y)Ir(x,y)sinϕ(x,y)when(x,y)=(odd,even),
|Ao(x,y)|2=ss22w2,
s=I(x,y)+I(x+1,y)+2Ir(x,y),
w=I(x,y)2+I(x+1,y)2,
Uh(x,y)={12Ir(x,y)[{I(x,y)|Ao(x,y)|2}j{I(x+1,y)|Ao(x,y)|2}]whenxy=even,12Ir(x,y)[{I(x,y)|Ao(x,y)|2}+j{I(x+1,y)|Ao(x,y)|2}]whenxy=odd,
|Ao(x,y)|2=ss22w2,
s=I(x,y)+I(x,y+1)+2Ir(x,y),
w=I(x,y)2+I(x,y+1)2,
Uv(x,y)={12Ir(x,y)[{I(x,y)|Ao(x,y)|2}+j{I(x,y+1)|Ao(x,y)|2}]when xy=even,12Ir(x,y)[{I(x,y)|Ao(x,y)|2}j{I(x,y+1)|Ao(x,y)|2}]whenxy=odd.
U(x,y)=|U(x,y)|exp[jarg{U(x,y)}],
arg{U(x,y)}={arg{U(x,y)}when(x,y)=(even,even),arg{U(x,y)}+π2when(x,y)=(even,odd),arg{U(x,y)}+πwhen(x,y)=(odd,odd),arg{U(x,y)}+3π2when(x,y)=(odd,even).
F[Uo(x,y)]={F[Uh(x,y)]when|kx|<|ky|,F[Uv(x,y)]when|kx||ky|.

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