Abstract

We demonstrate a method for single-shot quantitative phase imaging based on the transport of intensity equation (TIE) in a volume holographic microscope (VHM). The VHM system uses a multiplexed volume hologram to laterally separate images from different focal planes. This axial intensity information is then used to solve the TIE and recover object phase quantitatively. Further, we show improved phase recovery by using five multiplexed gratings in one hologram.

© 2010 Optical Society of America

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  1. W. Liu, D. Psaltis, and G. Barbastathis, Opt. Lett. 27, 854 (2002).
    [CrossRef]
  2. Y. Luo, P. Gelsinger-Austin, J. Watson, G. Barbastathis, J. Barton, and R. Kostuk, Opt. Lett. 33, 2098 (2008).
    [CrossRef] [PubMed]
  3. Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.
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    [CrossRef]
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    [CrossRef]
  6. L. Waller, Y. Luo, and G. Barbastathis, in AIP Conf. Proc. 1236, 76 (2010).
    [CrossRef]
  7. P. van Heerden, in Vol. MS 171 of SPIE Milestone Series (2001), p. 427.
  8. Y. Luo, S. B. Oh, and G. Barbastathis, Opt. Lett. 35, 781 (2010).
    [PubMed]
  9. A. Sinha, G. Barbastathis, W. Liu, and D. Psaltis, Opt. Eng. 43, 1959 (2004).
    [CrossRef]
  10. G. Barbastathis, in Photorefractive Materials and Their Applications 3 (Springer, 2007), pp. 51–76.
    [CrossRef]
  11. M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
    [CrossRef]
  12. D. Paganin and K. Nugent, Phys. Rev. Lett. 80, 2586 (1995).
    [CrossRef]
  13. E. Barone-Nugent, A. Barty, and K. Nugent, J. Microsc. 206, 194 (2002).
    [CrossRef] [PubMed]
  14. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
    [CrossRef]
  15. S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
    [CrossRef]
  16. T. Gureyev and S. Wilkins, Opt. Commun. 147, 229 (1998).
    [CrossRef]
  17. S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, Opt. Lett. 35, 447 (2010).
    [CrossRef] [PubMed]
  18. P. Blanchard and A. Greenaway, Appl. Opt. 38, 6692 (1999).
    [CrossRef]
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    [CrossRef]
  20. X. Fengjie, J. Zongfu, X. Xiaojun, and G. Yifeng. J. Opt. Soc. Am. A 24, 3444 (2007).
    [CrossRef]
  21. P. Blanchard and A. Greenaway, Opt. Commun. 183, 29 (2000).
    [CrossRef]
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    [CrossRef]
  24. L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010).
    [CrossRef] [PubMed]
  25. K. Nugent, D. Paganin, and T. Gureyev, Phys. Today 54, 27 (2001).
    [CrossRef]
  26. N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography, OSA Technical Digest Series (Optical Society of America2010), paper JMA7.
  27. C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
    [CrossRef] [PubMed]
  28. C. Sheppard, Appl. Opt. 41, 5951 (2002).
    [CrossRef] [PubMed]

2010

2008

2007

2004

A. Sinha, G. Barbastathis, W. Liu, and D. Psaltis, Opt. Eng. 43, 1959 (2004).
[CrossRef]

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

2002

M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
[CrossRef]

E. Barone-Nugent, A. Barty, and K. Nugent, J. Microsc. 206, 194 (2002).
[CrossRef] [PubMed]

W. Liu, D. Psaltis, and G. Barbastathis, Opt. Lett. 27, 854 (2002).
[CrossRef]

C. Sheppard, Appl. Opt. 41, 5951 (2002).
[CrossRef] [PubMed]

2001

K. Nugent, D. Paganin, and T. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

2000

P. Blanchard, D. Fisher, S. Woods, and A. Greenaway, Appl. Opt. 39, 6649 (2000).
[CrossRef]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

P. Blanchard and A. Greenaway, Opt. Commun. 183, 29 (2000).
[CrossRef]

1999

1998

1995

D. Paganin and K. Nugent, Phys. Rev. Lett. 80, 2586 (1995).
[CrossRef]

1993

1984

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

1983

1969

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Allman, B. E.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

Bajt, S.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

Barbastathis, G.

L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010).
[CrossRef] [PubMed]

Y. Luo, S. B. Oh, and G. Barbastathis, Opt. Lett. 35, 781 (2010).
[PubMed]

L. Waller, Y. Luo, and G. Barbastathis, in AIP Conf. Proc. 1236, 76 (2010).
[CrossRef]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, Opt. Lett. 35, 447 (2010).
[CrossRef] [PubMed]

Y. Luo, P. Gelsinger-Austin, J. Watson, G. Barbastathis, J. Barton, and R. Kostuk, Opt. Lett. 33, 2098 (2008).
[CrossRef] [PubMed]

A. Sinha, G. Barbastathis, W. Liu, and D. Psaltis, Opt. Eng. 43, 1959 (2004).
[CrossRef]

W. Liu, D. Psaltis, and G. Barbastathis, Opt. Lett. 27, 854 (2002).
[CrossRef]

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography, OSA Technical Digest Series (Optical Society of America2010), paper JMA7.

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

G. Barbastathis, in Photorefractive Materials and Their Applications 3 (Springer, 2007), pp. 51–76.
[CrossRef]

Barone-Nugent, E.

E. Barone-Nugent, A. Barty, and K. Nugent, J. Microsc. 206, 194 (2002).
[CrossRef] [PubMed]

Barton, J.

Barton, J. K.

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

Barty, A.

E. Barone-Nugent, A. Barty, and K. Nugent, J. Microsc. 206, 194 (2002).
[CrossRef] [PubMed]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

Beleggia, M.

M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
[CrossRef]

Bellair, C. J.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

Blanchard, P.

Curl, C. L.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

Curtis, K.

De Leon, E.

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

Delbridge, L. M. D.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

Fengjie, X.

Fisher, D.

Gelsinger, P. J.

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

Gelsinger-Austin, P.

Greenaway, A.

Gureyev, T.

K. Nugent, D. Paganin, and T. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

T. Gureyev and S. Wilkins, Opt. Commun. 147, 229 (1998).
[CrossRef]

Harris, P. J.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

Harwell, J.

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

Kostuk, R.

Kostuk, R. K.

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

Kou, S. S.

Liu, W.

A. Sinha, G. Barbastathis, W. Liu, and D. Psaltis, Opt. Eng. 43, 1959 (2004).
[CrossRef]

W. Liu, D. Psaltis, and G. Barbastathis, Opt. Lett. 27, 854 (2002).
[CrossRef]

Loomis, N.

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography, OSA Technical Digest Series (Optical Society of America2010), paper JMA7.

Luo, Y.

Y. Luo, S. B. Oh, and G. Barbastathis, Opt. Lett. 35, 781 (2010).
[PubMed]

L. Waller, Y. Luo, and G. Barbastathis, in AIP Conf. Proc. 1236, 76 (2010).
[CrossRef]

Y. Luo, P. Gelsinger-Austin, J. Watson, G. Barbastathis, J. Barton, and R. Kostuk, Opt. Lett. 33, 2098 (2008).
[CrossRef] [PubMed]

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

McCartney, M.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

Nugent, K.

E. Barone-Nugent, A. Barty, and K. Nugent, J. Microsc. 206, 194 (2002).
[CrossRef] [PubMed]

K. Nugent, D. Paganin, and T. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

D. Paganin and K. Nugent, Phys. Rev. Lett. 80, 2586 (1995).
[CrossRef]

Nugent, K. A.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

Oh, S. B.

Paganin, D.

K. Nugent, D. Paganin, and T. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

D. Paganin and K. Nugent, Phys. Rev. Lett. 80, 2586 (1995).
[CrossRef]

Psaltis, D.

Roberts, A.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, Opt. Lett. 23, 817 (1998).
[CrossRef]

Schofield, M.

M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
[CrossRef]

Sheppard, C.

Sheppard, C. J. R.

Sinha, A.

A. Sinha, G. Barbastathis, W. Liu, and D. Psaltis, Opt. Eng. 43, 1959 (2004).
[CrossRef]

Streibl, N.

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Teague, M.

Tian, L.

van Heerden, P.

P. van Heerden, in Vol. MS 171 of SPIE Milestone Series (2001), p. 427.

Volkov, V.

M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
[CrossRef]

Wall, M.

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

Waller, L.

L. Waller, L. Tian, and G. Barbastathis, Opt. Express 18, 12552 (2010).
[CrossRef] [PubMed]

S. S. Kou, L. Waller, G. Barbastathis, and C. J. R. Sheppard, Opt. Lett. 35, 447 (2010).
[CrossRef] [PubMed]

L. Waller, Y. Luo, and G. Barbastathis, in AIP Conf. Proc. 1236, 76 (2010).
[CrossRef]

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography, OSA Technical Digest Series (Optical Society of America2010), paper JMA7.

Watson, J.

Wilkins, S.

T. Gureyev and S. Wilkins, Opt. Commun. 147, 229 (1998).
[CrossRef]

Woods, S.

Xiaojun, X.

Yifeng, G.

Zhu, Y.

M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
[CrossRef]

Zongfu, J.

AIP Conf. Proc.

L. Waller, Y. Luo, and G. Barbastathis, in AIP Conf. Proc. 1236, 76 (2010).
[CrossRef]

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1969).

J. Microsc.

C. J. Bellair, C. L. Curl, B. E. Allman, P. J. Harris, A. Roberts, L. M. D. Delbridge, and K. A. Nugent, J. Microsc. 214, 62 (2004).
[CrossRef] [PubMed]

E. Barone-Nugent, A. Barty, and K. Nugent, J. Microsc. 206, 194 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Commun.

T. Gureyev and S. Wilkins, Opt. Commun. 147, 229 (1998).
[CrossRef]

P. Blanchard and A. Greenaway, Opt. Commun. 183, 29 (2000).
[CrossRef]

N. Streibl, Opt. Commun. 49, 6 (1984).
[CrossRef]

Opt. Eng.

A. Sinha, G. Barbastathis, W. Liu, and D. Psaltis, Opt. Eng. 43, 1959 (2004).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

D. Paganin and K. Nugent, Phys. Rev. Lett. 80, 2586 (1995).
[CrossRef]

Phys. Today

K. Nugent, D. Paganin, and T. Gureyev, Phys. Today 54, 27 (2001).
[CrossRef]

Ultramicrosc.

M. Beleggia, M. Schofield, V. Volkov, and Y. Zhu, Ultramicrosc. 102, 37 (2002).
[CrossRef]

S. Bajt, A. Barty, K. A. Nugent, M. McCartney, M. Wall, and D. Paganin, Ultramicrosc. 83, 67 (2000).
[CrossRef]

Other

Y. Luo, P. J. Gelsinger, E. De Leon, J. Harwell, J. K. Barton, R. K. Kostuk, and G. Barbastathis, in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2009), paper FME7.

G. Barbastathis, in Photorefractive Materials and Their Applications 3 (Springer, 2007), pp. 51–76.
[CrossRef]

P. van Heerden, in Vol. MS 171 of SPIE Milestone Series (2001), p. 427.

N. Loomis, L. Waller, and G. Barbastathis, in Digital Holography, OSA Technical Digest Series (Optical Society of America2010), paper JMA7.

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Figures (5)

Fig. 1
Fig. 1

Schematic of a VHM system. The VH is located on the Fourier plane of the 4 f system, and each multiplexed grating acts as a spatial-spectral filter to simultaneously project images from different depths on a CCD camera, laterally separated. MO is microscope objective.

Fig. 2
Fig. 2

(a) Geometric grating analysis and (b) Bragg circle diagram for wavelength degeneracy.

Fig. 3
Fig. 3

Phase recovery from a VHM image. (a) Intensity image captured by the camera; (b), (c) extracted background normalized images, overfocused and underfocused by the same amount; and (d) recovered phase solution displayed as height.

Fig. 4
Fig. 4

Comparison of phase recovery methods with an onion skin object. (a) Phase from traditional TIE method ( Δ z = 50 μm ), (b) phase from a single-shot VHM system (grating Δ z = 50 μm ), and (c) difference between two results (radians).

Fig. 5
Fig. 5

Higher-order TIE imaging using a VH recorded with five multiplexed gratings: (a) intensity image captured by the camera, (b) extracted background normalized images comprising a focal stack, and (c) phase result using fourth-order TIE as compared to first-order TIE.

Equations (5)

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

k i 1 k d 1 = k i 2 k d 2 = K ,
| k i 1 | = | k d 1 | = 2 π n 1 λ 1 ,
| k i 2 | = | k d 2 | = 2 π n 2 λ 2 ,
θ λ = K 4 π n sin ( α θ ) ,
I ( x , y ) z = λ 2 π · ( I ( x , y ) ϕ ( x , y ) ) ,

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