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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Gabor, Nature 161, 777 (1948).
    [CrossRef]
  2. T. Kubota, K. Komai, M. Yamagiwa, and Y. Awatsuji, Opt. Express 15, 14348 (2007).
    [CrossRef]
  3. J. W. Goodman and R. W. Lawrence, Appl. Phys. Lett. 11, 77 (1967).
    [CrossRef]
  4. C. Mann, L. Yu, C.-M. Lo, and M. Kim, Opt. Express 13, 8693 (2005).
    [CrossRef]
  5. J. Rosen and G. Brooker, Nat. Photonics 2, 190 (2008).
    [CrossRef]
  6. E. Watanabe, T. Hoshiba, and B. Javidi, Opt. Lett. 38, 1319 (2013).
    [CrossRef]
  7. S. Murata and N. Yasuda, Opt. Laser Technol. 32, 567 (2000).
    [CrossRef]
  8. Y. Ohtsuka and K. Oka, Appl. Opt. 33, 2633 (1994).
    [CrossRef]
  9. E. Tajahuerce, O. Matoba, and B. Javidi, Appl. Opt. 40, 3877 (2001).
    [CrossRef]
  10. K. Shi, H. Li, Q. Xu, D. Psaltis, and Z. Liu, Phys. Rev. Lett. 104, 093902 (2010).
    [CrossRef]
  11. Y. Lim, S.-Y. Lee, and B. Lee, Opt. Express 19, 5202 (2011).
    [CrossRef]
  12. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156 (1982).
    [CrossRef]
  13. I. Yamaguchi and T. Zhang, Opt. Lett. 22, 1268 (1997).
    [CrossRef]
  14. N. Pavillon, C. S. Seelamantula, J. Kühn, M. Unser, and C. Depeursinge, Appl. Opt. 48, H186 (2009).
    [CrossRef]
  15. T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, O. Matoba, and T. Kubota, Appl. Phys. Express 6, 022502 (2013).
    [CrossRef]
  16. Y. Awatsuji, M. Sasada, and T. Kubota, Appl. Phys. Lett. 85, 1069 (2004).
    [CrossRef]
  17. Y. Awatsuji, T. Tahara, A. Kaneko, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Appl. Opt. 47, D183 (2008).
    [CrossRef]
  18. L. Miao, K. Nitta, O. Matoba, and Y. Awatsuji, Appl. Opt. 51, 2633 (2012).
    [CrossRef]
  19. T. Tahara, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Rev. 17, 519 (2010).
    [CrossRef]
  20. 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]
  21. T. Tahara, Y. Ito, P. Xia, Y. Awatsuji, K. Nishio, S. Ura, T. Kubota, and O. Matoba, Opt. Lett. 38, 2463 (2013).
    [CrossRef]
  22. J. E. Greivenkamp, Appl. Opt. 26, 5245 (1987).
    [CrossRef]
  23. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, Opt. Lett. 31, 1414 (2006).
    [CrossRef]
  24. A. Stern and B. Javidi, J. Opt. Soc. Am. A 21, 360 (2004).
    [CrossRef]
  25. Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, Appl. Opt. 45, 2995 (2006).
    [CrossRef]
  26. L. Martínez-León, M. Araiza-Esquivel, B. Javidi, P. Andrés, V. Climent, J. Lancis, and E. Tajahuerce, Opt. Express 17, 12900 (2009).
    [CrossRef]

2013

2012

2011

2010

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]

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

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

2009

2008

2007

2006

2005

2004

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

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

2001

2000

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

1997

1994

1987

1982

1967

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

1948

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.

Appl. Phys. Express

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

Appl. Phys. Lett.

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.

J. Opt. Soc. Am. A

Nat. Photonics

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

Nature

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

Opt. Express

Opt. Laser Technol.

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

Opt. Lett.

Opt. Rev.

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

Phys. Rev. Lett.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

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

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|.

Metrics