Abstract

We present detailed theoretical evaluation and thorough experimental investigation of quantitative phase imaging using our previously demonstrated dual-plane in-line digital holographic microscopy technique [Opt. Lett. 35, 3426 (2010) [CrossRef]  ]. This evaluation is based on the recording of two interferograms at slightly different planes and numerically reconstructing the object information. The zero-order diffracted wave is eliminated by using the method of subtraction of average intensity of the entire hologram, and the twin-image diffracted wave is removed by Fourier domain processing of the two recorded holograms. Experiments are performed using controlled amplitude and phase objects and human muscle cells to demonstrate the potential of this technique.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).
    [CrossRef]
  2. J. Glückstad and P. C. Mogensen, “Optimal phase contrast in common-path interferometry,” Appl. Opt. 40, 268–282 (2001).
    [CrossRef]
  3. C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
    [CrossRef]
  4. Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
    [CrossRef]
  5. S. Bernet, A. Jesacher, S. Furhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14, 3792–3805 (2006).
    [CrossRef]
  6. N. Lue, W. Choi, G. Propescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Quantitative phase imaging of live cells using fast Fourier phase microscopy,” Appl. Opt. 46, 1836–1842 (2007).
    [CrossRef]
  7. S. V. King, A. Libertun, R. Piestun, and C. J. Cogswell, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
    [CrossRef]
  8. A. Anand and B. Javidi, “Three-dimensional microscopy with single-beam wavefront sensing and reconstruction from speckle fields,” Opt. Lett. 35, 766–768 (2010).
    [CrossRef]
  9. L. Camacho, V. Mico, Z. Zalevsky, and J. Garcia, “Quantitative phase microscopy using defocusing by means of a spatial light modulator,” Opt. Express 18, 6755–6764 (2010).
    [CrossRef]
  10. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005).
    [CrossRef]
  11. M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
    [CrossRef]
  12. F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
    [CrossRef]
  13. A. Khmaladze, M. Kim, and C.-M. Lo, “Phase imaging of cells by simultaneous dual-wavelength reflection digital holography,” Opt. Express 16, 10900–10911 (2008).
    [CrossRef]
  14. L. Yu, S. Mohanty, J. Zhang, S. Genc, M. K. Kim, M. W. Berns, and Z. Chen, “Digital holographic microscopy for quantitative cell dynamic evaluation during laser microsurgery,” Opt. Express 17, 12031–12038 (2009).
    [CrossRef]
  15. M. Antkowiak, M. L. Torres-Mapa, K. Dholakia, and F. J. Gunn-Moore, “Quantitative phase study of the dynamic cellular response in femtosecond laser photoporation,” Biomed. Opt. Express 1, 414–424 (2010).
    [CrossRef]
  16. U. Schnars and W. Juptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef]
  17. L. Xu, X. Peng, Z. Guo, J. Miao, and A. Asundi, “Imaging analysis of digital holography,” Opt. Express 13, 2444–2452 (2005).
    [CrossRef]
  18. I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40, 6177–6186 (2001).
    [CrossRef]
  19. C. P. Brophy, “Effect of intensity error correlation on the computed phase of the phase-shifting interferometry,” J. Opt. Soc. Am. A 7, 537–541 (1990).
    [CrossRef]
  20. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wavefront measuring interferometry: some systematic error sources,” Appl. Opt. 22, 3421–3432 (1983).
    [CrossRef]
  21. C. S. Gao, L. Zhang, H. T. Wang, J. Liao, and Y. Y. Zhu, “Phase-shifting error and its elimination in phase-shifting digital holography,” Opt. Lett. 27, 1687–1689 (2002).
    [CrossRef]
  22. X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006).
    [CrossRef]
  23. J.-P. Liu and T.-C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett. 34, 250–252 (2009).
    [CrossRef]
  24. N. T. Shaked, Y. Zhu, M. T. Rinehart, and A. Wax, “Two-step-only phase-shifting interferometry with optimized detector bandwidth for microscopy of live cells,” Opt. Express 17, 15585–15591 (2009).
    [CrossRef]
  25. N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative phase microscopy of live cell dynamics,” Opt. Lett. 34, 767–769 (2009).
    [CrossRef]
  26. N. T. Shaked, T. M. Newpher, M. D. Ehlers, and A. Wax, “Parallel on-axis holographic microscopy of biological cells and unicellular microorganism dynamics,” Appl. Opt. 49, 2872–2878 (2010).
    [CrossRef]
  27. Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
    [CrossRef]
  28. B. Das and C. Yelleswarapu, “Dual plane in-line digital holographic microscopy,” Opt. Lett. 35, 3426–3428 (2010).
    [CrossRef]
  29. G. Situ, J. P. Ryle, U. Gopinathan, and J. T. Sheridan, “Generalized in-line digital holographic technique based on intensity measurements at two different planes,” Appl. Opt. 47, 711–717 (2008).
    [CrossRef]
  30. T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005).
    [CrossRef]
  31. J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2004).
  32. C.-L. Hsieh, Y. Pu, R. Grange, and D. Psaltis, “Digital phase conjugation of second harmonic radiation emitted by nanoparticles in turbid media,” Opt. Express 18, 12283–12290 (2010).
    [CrossRef]
  33. F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
    [CrossRef]

2010

2009

2008

2007

2006

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
[CrossRef]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006).
[CrossRef]

S. Bernet, A. Jesacher, S. Furhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14, 3792–3805 (2006).
[CrossRef]

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

2005

2004

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[CrossRef]

2002

2001

1998

1994

1990

1983

Anand, A.

Antkowiak, M.

Aranda, F. J.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

Asundi, A.

Badizadegan, K.

Barty, A.

Belosi, F.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Bernet, S.

Berns, M. W.

Brophy, C. P.

Burow, R.

Cai, L. Z.

Camacho, L.

Charrière, F.

Chen, Z.

Choi, W.

Cogswell, C. J.

S. V. King, A. Libertun, R. Piestun, and C. J. Cogswell, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Colomb, T.

Cuche, E.

Das, B.

Dasari, R. R.

Depeursinge, C.

Dholakia, K.

Dong, G. Y.

Dubois, F.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Ehlers, M. D.

Elssner, K.-E.

Emery, Y.

Feld, M. S.

Furhapter, S.

Gao, C. S.

Garcia, J.

Genc, S.

Glückstad, J.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2004).

Gopinathan, U.

Grange, R.

Grzanna, J.

Gunn-Moore, F. J.

Guo, Z.

Hsieh, C.-L.

Ikeda, T.

Javidi, B.

Jesacher, A.

Juptner, W.

Kato, J.

Khmaladze, A.

Kim, M.

Kim, M. K.

Kimball, B. R.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

King, S. V.

S. V. King, A. Libertun, R. Piestun, and C. J. Cogswell, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Kothapalli, S.-R.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

Kühn, J.

Legros, J. C.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Liao, J.

Libertun, A.

S. V. King, A. Libertun, R. Piestun, and C. J. Cogswell, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Liu, J.-P.

Lo, C.-M.

Lue, N.

Magistretti, P. J.

Marian, A.

Marquet, P.

Maurer, C.

Meng, X. F.

Merkel, K.

Miao, J.

Mico, V.

Mizuno, J.

Mogensen, P. C.

Mohanty, S.

Montfort, F.

Newpher, T. M.

Nugent, K. A.

Ohta, S.

Osten, W.

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
[CrossRef]

Paganin, D.

Pedrini, G.

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
[CrossRef]

Peng, X.

Piestun, R.

S. V. King, A. Libertun, R. Piestun, and C. J. Cogswell, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Poon, T.-C.

Popescu, G.

Prodi, F.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Propescu, G.

Psaltis, D.

Pu, Y.

Queeckers, P.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Rao, D. V. G. L. N.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

Rappaz, B.

Rinehart, M. T.

Ritsch-Marte, M.

Roberts, A.

Ryle, J. P.

Santachiara, G.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Schnars, U.

Schwider, J.

Shaked, N. T.

Shen, X. X.

Sheridan, J. T.

Situ, G.

Spolaczyk, R.

Tiziani, H. J.

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
[CrossRef]

Torres-Mapa, M. L.

Travaini, S.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Vaillancourt, Y. R.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

Vedernikov, A.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Wang, H. T.

Wang, Y. R.

Wax, A.

Xu, L.

Xu, X. F.

Yamaguchi, I.

Yang, X. L.

Yelleswarapu, C.

Yelleswarapu, C. S.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

Yu, L.

Zalevsky, Z.

Zhang, J.

Zhang, L.

Zhang, Y.

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[CrossRef]

Zhu, Y.

Zhu, Y. Y.

Appl. Opt.

Appl. Phys. Lett.

C. S. Yelleswarapu, S.-R. Kothapalli, F. J. Aranda, D. V. G. L. N. Rao, Y. R. Vaillancourt, and B. R. Kimball, “Phase contrast imaging using photothermally induced phase transitions in liquid crystals,” Appl. Phys. Lett. 89, 211116 (2006).
[CrossRef]

Atmos. Res.

F. Prodi, G. Santachiara, S. Travaini, F. Belosi, A. Vedernikov, F. Dubois, P. Queeckers, and J. C. Legros, “Digital holography for observing aerosol particles undergoing Brownian motion in microgravity conditions,” Atmos. Res. 82, 379–384(2006).
[CrossRef]

Biomed. Opt. Express

J. Biomed. Opt.

S. V. King, A. Libertun, R. Piestun, and C. J. Cogswell, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Opt. Lett.

N. T. Shaked, M. T. Rinehart, and A. Wax, “Dual-interference-channel quantitative phase microscopy of live cell dynamics,” Opt. Lett. 34, 767–769 (2009).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Reconstruction of in-line digital holograms from two intensity measurements,” Opt. Lett. 29, 1787–1789 (2004).
[CrossRef]

B. Das and C. Yelleswarapu, “Dual plane in-line digital holographic microscopy,” Opt. Lett. 35, 3426–3428 (2010).
[CrossRef]

C. S. Gao, L. Zhang, H. T. Wang, J. Liao, and Y. Y. Zhu, “Phase-shifting error and its elimination in phase-shifting digital holography,” Opt. Lett. 27, 1687–1689 (2002).
[CrossRef]

X. F. Meng, L. Z. Cai, X. F. Xu, X. L. Yang, X. X. Shen, G. Y. Dong, and Y. R. Wang, “Two-step phase-shifting interferometry and its application in image encryption,” Opt. Lett. 31, 1414–1416 (2006).
[CrossRef]

J.-P. Liu and T.-C. Poon, “Two-step-only quadrature phase-shifting digital holography,” Opt. Lett. 34, 250–252 (2009).
[CrossRef]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30, 1165–1167 (2005).
[CrossRef]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23, 817–819 (1998).
[CrossRef]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30, 468–470 (2005).
[CrossRef]

A. Anand and B. Javidi, “Three-dimensional microscopy with single-beam wavefront sensing and reconstruction from speckle fields,” Opt. Lett. 35, 766–768 (2010).
[CrossRef]

F. Charrière, A. Marian, F. Montfort, J. Kühn, T. Colomb, E. Cuche, P. Marquet, and C. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31, 178–180 (2006).
[CrossRef]

Optik

Y. Zhang, G. Pedrini, W. Osten, and H. J. Tiziani, “Phase retrieval microscopy for quantitative phase-contrast imaging,” Optik 115, 94–96 (2004).
[CrossRef]

SPIE Rev.

M. K. Kim, “Principles and techniques of digital holographic microscopy,” SPIE Rev. 1, 018005 (2010).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 3rd ed.(Roberts & Company, 2004).

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 (8)

Fig. 1.
Fig. 1.

Schematic of the experimental setup of the dual-plane in-line DHM technique: M1 and M2, mirrors; BS1 and BS2, beam splitters; MO, microscope objective; FL, field lens; IM, image plane; P1 and P2, recording planes.

Fig. 2.
Fig. 2.

Schematic for computer simulations. The 3D transmission object is considered to be made up of the real images U, M, and B. BS, beam splitter.

Fig. 3.
Fig. 3.

Simulation results for the reconstruction of the three letters at the best focusing distances of (a) U, 140 mm; (b) M, 130 mm; and (c) B, 120 mm.

Fig. 4.
Fig. 4.

Reconstructed images of amplitude object, U.S. Air Force resolution chart, obtained using (a) this method and (b) the Fresnel transformation method with one of the recorded holograms.

Fig. 5.
Fig. 5.

Amplitude contrast images obtained for different values of the reconstruction distance z: (a) out-of-focus image (z too short, 110 mm), (b) in-focus image (z=120mm), and (c) out-of-focus image (z too long, 130 mm).

Fig. 6.
Fig. 6.

Experimental results of glass beads mounted in Citra mounting media: (a) regular intensity image, (b) and (c) reconstructed wrapped phase and surface plot of the final unwrapped phase using the method proposed in this paper, and (d), (e) reconstructed wrapped phase and surface plot of the final unwrapped phase using the method of HPM. The vertical bar represents the phase values in radians. (f) Comparison of the reconstructed phase profile of the polystyrene bead.

Fig. 7.
Fig. 7.

Reconstructed phase image of an optical fiber immersed in glycerol: (a) using the method proposed in this paper and (b) using HPM. (c) Transverse phase profile of the reconstructed images shown in (a) and (b).

Fig. 8.
Fig. 8.

Reconstructed experimental results for a human airway smooth muscle cell: (a) unwrapped phase image and (b) pseudo-3D plot of the unwrapped phase image. The vertical color bar represents the phase values in radians.

Equations (15)

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

I1(x1,y1;z)=|1+u1(x1,y1;z)|2=1+|u1(x1,y1;z)|2+u1(x1,y1;z)+u1*(x1,y1;z)
I2(x2,y2;z+Δz)=|1+u2(x2,y2;z+Δz)|2=1+|u2(x2,y2;z+Δz)|2+u2(x2,y2;z+Δz)+u2*(x2,y2;z+Δz),
ui(xi,yi;zi)=P{u0(x0,y0;0);zi}=12πu0(x0,y0;0)zi[exp[jkri]ri]dxd0y0,
l1(x1,y1;z)=I1(x1,y1;z)Iavgu1(x1,y1;z)+u1*(x1,y1;z),
l2(x2,y2;z+Δz)=I2(x2,y2;z+Δz)Iavgu2(x2,y2;z+Δz)+u2*(x2,y2;z+Δz),
Iavg=1N2k=0N1l=0N1I(kΔx,lΔy;zi),
u1*(x1,y1;z)=P{u2*(x2,y2;z+Δz);Δz}.
δl(x1,y1)=l1(x1,y1;z)P{l2(x2,y2;z+Δz);Δz}=u1(x1,y1;z)+u1*(x1,y1;z)P{u2(x2,y2;z+Δz);Δz}P{u2*(x2,y2;z+Δz);Δz}=u1(x1,y1;z)P{u2(x2,y2;z+Δz);Δz}=u1(x1,y1;z)P{u1(x1,y1;z);2Δz}.
u2(x2,y2;z+Δz)=P{u1(x1,y1;z);Δz}.
δI(fx,fy)=U(fx,fy;z)[1H(fx,fy;2Δz)],
u1(x1,y1;z)=I1{δI(fx,fy)1H(fx,fy;2Δz)},
H(fx,fy;zi)=exp[jkzi(1λ2fx2λ2fy2)1/2].
H(m,n;zi)=exp{jkzi[1(λmMδx)2(λnMδy)2]1/2},
[1H(fx,fy;2Δz)]0.
Δzλ2lMδN2δ2λ2(m2+n2),

Metrics