Abstract

A new method for recovery the quantitative phase information of microscopic samples is presented. It is based on a spatial light modulator (SLM) and digital image processing as key elements to extract the sample’s phase distribution. By displaying a set of lenses with different focal power, the SLM produces a set of defocused images of the input sample at the CCD plane. Such recorded images are then numerically processed to retrieve phase information. This iterative process is based on the wave propagation equation and leads on a complex amplitude image containing information of both amplitude and phase distributions of the input sample diffracted wave front. The proposed configuration is a non-interferometric architecture (conventional transmission imaging mode) where no moving elements are included. Experimental results perfectly correlate with the results obtained by conventional digital holographic microscopy (DHM).

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    [CrossRef] [PubMed]
  8. F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and Ch. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  29. A. Anand, V. K. Chhaniwal, P. Almoro, G. Pedrini, and W. Osten, “Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval,” Opt. Lett. 34(10), 1522–1524 (2009).
    [CrossRef] [PubMed]
  30. P. F. Almoro, G. Pedrini, A. Anand, W. Osten, and S. G. Hanson, “Angular displacement and deformation analyses using a speckle-based wavefront sensor,” Appl. Opt. 48(5), 932–940 (2009).
    [CrossRef] [PubMed]
  31. P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33(4), 309–311 (2008).
    [CrossRef] [PubMed]
  32. G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004).
    [CrossRef] [PubMed]
  33. S. Fürhapter, A. Jesacher, S. Bernet, and M. Ritsch-Marte, “Spiral phase contrast imaging in microscopy,” Opt. Express 13(3), 689–694 (2005).
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    [CrossRef] [PubMed]

2009

2008

2007

2006

2005

2004

2003

2001

1998

1997

1994

1985

1984

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[CrossRef]

1983

1982

1978

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1978).

1948

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Almoro, P.

Almoro, P. F.

Anand, A.

Badizadegan, K.

Bao, P.

Barty, A.

Bernet, S.

Charrière, F.

Chhaniwal, V. K.

Colomb, T.

Cuche, E.

Dasari, R. R.

Deflores, L. P.

Depeursinge, Ch.

Dong, B. Z.

Emery, Y.

Ersoy, O. K.

Fang-Yen, C.

Feld, M. S.

Ferreira, C.

Fienup, J. R.

Fürhapter, S.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

García, J.

Garcia-Sucerquia, J.

Gerchberg, R. W.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1978).

Gu, B. Y.

Hanson, S. G.

Ikeda, T.

Iwai, H.

Javidi, B.

Jericho, M. H.

Jericho, S. K.

Jesacher, A.

Jüptner, W.

Kato, J.

Kemper, B.

Klages, P.

Kreuzer, H. J.

Kuehn, J.

Magistretti, P. J.

Marian, A.

Marquet, P.

Maurer, Ch.

McIntyre, T. J.

Micó, V.

Mizuno, J.

Montfort, F.

Nugent, K. A.

Ohta, S.

Osten, W.

Paganin, D.

Park, Y. K.

Pedrini, G.

Popescu, G.

Rappaz, B.

Reichelt, S.

Ritsch-Marte, M.

Roberts, A.

Saxton, W. O.

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1978).

Schnars, U.

Streibl, N.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[CrossRef]

Teague, M. R.

Tiziani, H.

Vaughan, J. C.

von Bally, G.

Wax, A.

Xu, W.

Yamaguchi, I.

Yang, G. Z.

Zalevsky, Z.

Zappe, H.

Zhang, F.

Zhang, T.

Zhang, Y.

Zhuang, J.

Appl. Opt.

J. R. Fienup, “Phase retrieval algorithms: a comparision,” Appl. Opt. 21(15), 2758–2769 (1982).
[CrossRef] [PubMed]

I. Yamaguchi, J. Kato, S. Ohta, and J. Mizuno, “Image formation in phase-shifting digital holography and applications to microscopy,” Appl. Opt. 40(34), 6177–6186 (2001).
[CrossRef]

U. Schnars and W. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33(2), 179–181 (1994).
[CrossRef] [PubMed]

G. Z. Yang, B. Z. Dong, B. Y. Gu, J. Zhuang, and O. K. Ersoy, “Gerchberg-Saxton and Yang-Gu algorithms for phase retrieval in a nonunitary transform system: a comparison,” Appl. Opt. 33(2), 209–218 (1994).
[CrossRef] [PubMed]

S. Reichelt and H. Zappe, “Combined Twyman-Green and Mach-Zehnder interferometer for microlens testing,” Appl. Opt. 44(27), 5786–5792 (2005).
[CrossRef] [PubMed]

J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, “Digital in-line holographic microscopy,” Appl. Opt. 45(5), 836–850 (2006).
[CrossRef] [PubMed]

P. Almoro, G. Pedrini, and W. Osten, “Complete wavefront reconstruction using sequential intensity measurements of a volume speckle field,” Appl. Opt. 45(34), 8596–8605 (2006).
[CrossRef] [PubMed]

B. Kemper and G. von Bally, “Digital holographic microscopy for live cell applications and technical inspection,” Appl. Opt. 47(4), A52–A61 (2008).
[CrossRef] [PubMed]

P. F. Almoro, G. Pedrini, A. Anand, W. Osten, and S. G. Hanson, “Angular displacement and deformation analyses using a speckle-based wavefront sensor,” Appl. Opt. 48(5), 932–940 (2009).
[CrossRef] [PubMed]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Nature

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[CrossRef] [PubMed]

Opt. Commun.

N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49(1), 6–10 (1984).
[CrossRef]

Opt. Express

Opt. Lett.

V. Micó, J. García, Z. Zalevsky, and B. Javidi, “Phase-shifting Gabor holography,” Opt. Lett. 34(10), 1492–1494 (2009).
[CrossRef] [PubMed]

A. Anand, V. K. Chhaniwal, P. Almoro, G. Pedrini, and W. Osten, “Shape and deformation measurements of 3D objects using volume speckle field and phase retrieval,” Opt. Lett. 34(10), 1522–1524 (2009).
[CrossRef] [PubMed]

T. J. McIntyre, Ch. Maurer, S. Bernet, and M. Ritsch-Marte, “Differential interference contrast imaging using a spatial light modulator,” Opt. Lett. 34(19), 2988–2990 (2009).
[CrossRef] [PubMed]

P. Bao, F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval using multiple illumination wavelengths,” Opt. Lett. 33(4), 309–311 (2008).
[CrossRef] [PubMed]

P. Almoro, G. Pedrini, and W. Osten, “Aperture synthesis in phase retrieval using a volume-speckle field,” Opt. Lett. 32(7), 733–735 (2007).
[CrossRef] [PubMed]

Y. K. Park, G. Popescu, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Fresnel particle tracing in three dimensions using diffraction phase microscopy,” Opt. Lett. 32(7), 811–813 (2007).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[CrossRef] [PubMed]

F. Charrière, A. Marian, F. Montfort, J. Kuehn, T. Colomb, E. Cuche, P. Marquet, and Ch. Depeursinge, “Cell refractive index tomography by digital holographic microscopy,” Opt. Lett. 31(2), 178–180 (2006).
[CrossRef] [PubMed]

H. Iwai, C. Fang-Yen, G. Popescu, A. Wax, K. Badizadegan, R. R. Dasari, and M. S. Feld, “Quantitative phase imaging using actively stabilized phase-shifting low-coherence interferometry,” Opt. Lett. 29(20), 2399–2401 (2004).
[CrossRef] [PubMed]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004).
[CrossRef] [PubMed]

P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and Ch. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett. 30(5), 468–470 (2005).
[CrossRef] [PubMed]

G. Pedrini, W. Osten, and Y. Zhang, “Wave-front reconstruction from a sequence of interferograms recorded at different planes,” Opt. Lett. 30(8), 833–835 (2005).
[CrossRef] [PubMed]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
[CrossRef] [PubMed]

A. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[CrossRef]

Optik (Stuttg.)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik (Stuttg.) 35, 237–246 (1978).

Other

L. P. Yaroslavsky, Digital Holography and Digital Image Processing: Principles, Methods, Algorithms (Kluwer, 2003).

T. Kreis, Handbook of holographic interferometry: optical and digital methods (Wiley-VCH, 2005).

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Figures (10)

Fig. 1
Fig. 1

Experimental setup drawing for phase retrieval in transmission mode.

Fig. 2
Fig. 2

Ray tracing for a 3D sample in the experimental setup: (a)-(b)-(c) correspond with the central-left-right part of the 3D sample (red-blue-green lines), respectively, when no lens, negative and positive lenses are displayed at the SLM, respectively. Notice that the polarizer has been removed for simplicity in the drawing.

Fig. 3
Fig. 3

From (a) to (i), raw direct images of the USAF test central part obtained when varying the power of the lens displayed at the SLM.

Fig. 4
Fig. 4

From (a) to (i), image compensation for the magnification being introduced by the lens displayed at the SLM for the USAF test central part.

Fig. 5
Fig. 5

(a) Direct imaging of the USAF test central part. (b) and (c) propagated images resulting without and with 6 cycles in the iteration process, respectively. (d) Representation of the normalized rmse (vertical coordinate) versus the number of cycles (horizontal coordinate).

Fig. 6
Fig. 6

(a) Representation of the normalized rmse (vertical coordinate) versus the number of cycles (horizontal coordinate). (b)-(c) Propagated image resulting after 1 and 13 iterations cycles, respectively, when images I’4-I’5-I’6 are eliminated in the iteration process.

Fig. 7
Fig. 7

Picture of the experimental setup in reflective configuration.

Fig. 8
Fig. 8

Two sections of the 3D biosample where different sperm cells are in focus. The images have been scaled to be equalized in magnification.

Fig. 9
Fig. 9

Real (a)-(b) and phase (c)-(d) distributions of the retrieved complex amplitude images obtained with the proposed approach and corresponding with the sections showed in Fig. 8.

Fig. 10
Fig. 10

3D representations of sperm cells from unwrapped phase distribution: (a) group of cells marked with a solid white line rectangle in Fig. 10(c), and 10(b) another group of sperm cells of the same biosample obtained with a conventional DHM configuration. Gray level scale represents optical phase in radians.

Equations (2)

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β ' = f S f T f O ( f S + f T e )
D = f T ( e f S ) e ( f S + f T )

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