Abstract

We present a fast and robust non-interferomentric wavefield retrieval approach suitable for imaging of both amplitude and phase distributions of scalar coherent beams. It is based on the diversity of the intensity measurements obtained under controlled astigmatism and it can be easily implemented in standard imaging systems. Its application for imaging in microscopy is experimentally studied. Relevant examples illustrate the approach capabilities for image super-resolution, numerical refocusing, quantitative imaging and phase mapping.

© 2011 OSA

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2011 (1)

2010 (4)

2009 (2)

2008 (2)

V. Mico, Z. Zalevsky, C. Ferreira, and J. García, “Superresolution digital holographic microscopy for three-dimensional samples,” Opt. Express 16, 19260–19270 (2008).
[CrossRef]

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

2007 (2)

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[CrossRef]

T. C. Petersen and V. J. Keast, “Astigmatic intensity equation for electron microscopy based phase retrieval,” Ultramicroscopy 107, 635–643 (2007).
[CrossRef] [PubMed]

2006 (2)

2005 (2)

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] [PubMed]

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 321–324 (2005).
[CrossRef]

2004 (2)

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[CrossRef]

2003 (3)

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11, 3234–3241 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (3)

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

L. J. Allen, M. P. Oxley, and D. Paganin, “Computational aberration correction for an arbitrary linear imaging system,” Phys. Rev. Lett. 87, 123902 (2001).
[CrossRef] [PubMed]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[CrossRef]

2000 (1)

1999 (1)

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

1998 (1)

1997 (2)

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

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

1994 (1)

1988 (1)

1985 (1)

1983 (1)

1982 (1)

1972 (1)

R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Abe, Y.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

Alieva, T.

Allen, L. J.

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 321–324 (2005).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[CrossRef]

L. J. Allen, M. P. Oxley, and D. Paganin, “Computational aberration correction for an arbitrary linear imaging system,” Phys. Rev. Lett. 87, 123902 (2001).
[CrossRef] [PubMed]

Badizadegan, K.

Barty, A.

Bernet, S.

Brock, R. S.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Burton, D. R.

Calvo, M. L.

Cámara, A.

Cederquist, J. N.

Chapman, H. N.

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Charalambous, P.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Charrière, F.

Cheben, P.

Cheong, F. C.

Choi, W.

Colomb, T.

Cuche, E.

Dasari, R. R.

Depeursinge, C.

Duadi, H.

Emery, Y.

Fang-Yen, C.

Fassl, S.

Faulkner, H. M. L.

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[CrossRef]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[CrossRef]

Feld, M. S.

Ferreira, C.

Fienup, J. R.

García, J.

Garcia-Sucerquia, J.

Gdeisat, M. A.

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 35, 237–246 (1972).

Granero, L.

Grier, D. G.

Henderson, C. A.

Herráez, M. A.

Hu, X.-H.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

ichi Kato, J.

Ichihashi, Y.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

Ito, T.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

Ivanov, C. D.

Jacobs, K. M.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Jericho, M. H.

Jericho, S. K.

Keast, V. J.

T. C. Petersen and V. J. Keast, “Astigmatic intensity equation for electron microscopy based phase retrieval,” Ultramicroscopy 107, 635–643 (2007).
[CrossRef] [PubMed]

Khan, S.

Kirz, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Klages, P.

Konforti, N.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

Kreuzer, H. J.

Krishnatreya, B. J.

Kuehn, J.

Lalor, M. J.

Lu, J. Q.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Ma, X.

X. Ma, J. Q. Lu, R. S. Brock, K. M. Jacobs, P. Yang, and X.-H. Hu, “Determination of complex refractive index of polystyrene microspheres from 370 to 1610 nm,” Phys. Med. Biol. 48, 4165 (2003).
[CrossRef]

Magistretti, P. J.

Mancuso, A. P.

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Marian, A.

Marquet, P.

Marron, J. C.

Martínez-Matos, O.

Masuda, N.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

Maurer, C.

McBride, W.

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 321–324 (2005).
[CrossRef]

McIntyre, T. J.

Mendlovic, D.

D. Mendlovic, Z. Zalevsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407–414 (1997).
[CrossRef]

Miao, J.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Mico, V.

Micó, V.

Mizuno, J.

Montfort, F.

Nakayama, H.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

Nikolov, I. D.

Nugent, K. A.

C. A. Henderson, G. J. Williams, A. G. Peele, H. M. Quiney, and K. A. Nugent, “Astigmatic phase retrieval: an experimental demonstration,” Opt. Express 17, 11905–11915 (2009).
[CrossRef] [PubMed]

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 321–324 (2005).
[CrossRef]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[CrossRef]

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

O’Leary, N. L.

W. McBride, N. L. O’Leary, K. A. Nugent, and L. J. Allen, “Astigmatic electron diffraction imaging: a novel mode for structure determination,” Acta Crystallogr., Sect. A: Found. Crystallogr. 61, 321–324 (2005).
[CrossRef]

Ohta, S.

Osten, W.

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11, 3234–3241 (2003).
[CrossRef] [PubMed]

Oxley, M. P.

L. J. Allen, M. P. Oxley, and D. Paganin, “Computational aberration correction for an arbitrary linear imaging system,” Phys. Rev. Lett. 87, 123902 (2001).
[CrossRef] [PubMed]

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[CrossRef]

Paganin, D.

L. J. Allen, H. M. L. Faulkner, K. A. Nugent, M. P. Oxley, and D. Paganin, “Phase retrieval from images in the presence of first-order vortices,” Phys. Rev. E 63, 037602 (2001).
[CrossRef]

L. J. Allen, M. P. Oxley, and D. Paganin, “Computational aberration correction for an arbitrary linear imaging system,” Phys. Rev. Lett. 87, 123902 (2001).
[CrossRef] [PubMed]

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

Paxman, R. G.

Pedrini, G.

F. Zhang, G. Pedrini, and W. Osten, “Phase retrieval of arbitrary complex-valued fields through aperture-plane modulation,” Phys. Rev. A 75, 043805 (2007).
[CrossRef]

Y. Zhang, G. Pedrini, W. Osten, and H. Tiziani, “Whole optical wave field reconstruction from double or multi in-line holograms by phase retrieval algorithm,” Opt. Express 11, 3234–3241 (2003).
[CrossRef] [PubMed]

Peele, A. G.

C. A. Henderson, G. J. Williams, A. G. Peele, H. M. Quiney, and K. A. Nugent, “Astigmatic phase retrieval: an experimental demonstration,” Opt. Express 17, 11905–11915 (2009).
[CrossRef] [PubMed]

K. A. Nugent, A. G. Peele, H. N. Chapman, and A. P. Mancuso, “Unique phase recovery for nonperiodic objects,” Phys. Rev. Lett. 91, 203902 (2003).
[CrossRef] [PubMed]

Petersen, T. C.

T. C. Petersen and V. J. Keast, “Astigmatic intensity equation for electron microscopy based phase retrieval,” Ultramicroscopy 107, 635–643 (2007).
[CrossRef] [PubMed]

Quiney, H. M.

Rappaz, B.

Ritsch-Marte, M.

Roberts, A.

Rodenburg, J. M.

J. M. Rodenburg and H. M. L. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85, 4795–4797 (2004).
[CrossRef]

H. M. L. Faulkner and J. M. Rodenburg, “Movable aperture lensless transmission microscopy: a novel phase retrieval algorithm,” Phys. Rev. Lett. 93, 023903 (2004).
[CrossRef] [PubMed]

Rodrigo, J. 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 35, 237–246 (1972).

Sayre, D.

J. Miao, P. Charalambous, J. Kirz, and D. Sayre, “Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens,” Nature 400, 342–344 (1999).
[CrossRef]

Schnars, U.

Shimobaba, T.

T. Shimobaba, T. Ito, N. Masuda, Y. Abe, Y. Ichihashi, H. Nakayama, N. Takada, A. Shiraki, and T. Sugie, “Numerical calculation library for diffraction integrals using the graphic processing unit: the GPU-based wave optics library,” J. Opt. A, Pure Appl. Opt. 10, 075308 (2008).
[CrossRef]

Shiraki, A.

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Figures (11)

Fig. 1
Fig. 1

Flow chart of the proposed wavefield retrieval algorithm, where * stands for the complex conjugate.

Fig. 2
Fig. 2

(a) Intensity and phase distributions of the LG 2 , 4 + input signal. (b) The wavefield ωN , M (x, y) retrieved after N × M = 96 iterations using several constraint images M. (c) Evolution of the RMSE as a function of the number of iterations and constraint images by using the proposed algorithm. (d) The RMSE evolution for the case of the algorithm type 2, in which arithmetic averaging for wavefield estimation is performed in each iteration step.

Fig. 3
Fig. 3

Experimental setup used for the digital lens Lj (x, y) generation. BS is a cube beam splitter, RL1 and RL2 are spherical relay lenses (with a diameter of 5.1 cm) working as telescope 0.4×, focal lengths: f1 = 25 cm and f2 = 10 cm, in our case. SF is a spatial filter located at Fourier plane of RL1 for filtering of unwanted diffraction terms caused by the discrete structure of the SLM display.

Fig. 4
Fig. 4

(a) Setup scheme for transmission microscopy. (b) Extension of the recording area by moving the CCD chip in order to achieve super-resolution in the retrieved image.

Fig. 5
Fig. 5

(a) Retrieved image of a high-resolution test target (USAF). (b) Image enhancement obtained using the proposed SA super-resolution technique. (c) Intensity distribution of the retrieved wavefield corresponding to onion skin specimen and its superresolved image (d). Nucleus as well as the cell membranes are clearly distinguished, as observed in the corresponding zoomed insets.

Fig. 6
Fig. 6

Experimental setup for wavefield retrieval of the light scattered by the sample, which is imaged by means of the microscope objective (MO). The specimen is illuminated by focusing a collimated laser beam using a condenser.

Fig. 7
Fig. 7

(a) Intensity distribution of the specimen imaged at plane z 0 = 0 using the setup depicted in Fig. 6. Intensity and phase distributions of the retrieved wavefield are shown in (b) and (c), respectively. (d) Unwrapped phase distribution corresponding to the central region of the imaged specimen (b). (e) 3D representation of the unwrapped phase that reveals the cell structure of the onion skin object.

Fig. 8
Fig. 8

(a) Aggregate of polystyrene spheres imaged at plane z 0 = 0 using the setup depicted in Fig. 6. Intensity and phase distributions of the retrieved wavefield are shown in (b) and (c), respectively. (d) Unwrapped phase distribution and its 3D representation (e).

Fig. 9
Fig. 9

Numerical refocusing of the retrieved field [z = 0 μm, corresponding with Fig. 8(b) and 8(c)] reveals the particle position at several propagation distances z. The particles are labeled as their appear focused, by locating the maximum of the diffracted light.

Fig. 10
Fig. 10

Numerical reconstruction at several propagation distances z of the in-line hologram shown in Fig. 8(a).

Fig. 11
Fig. 11

(a) Averaged phase profile ϕ of the polystyrene bead #7. (b) Square of the phase profile (ϕ 2) and the fit corresponding to Eq. (5).

Equations (5)

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f o u t ( r o ; j ) = exp ( i 2 π z / λ ) i λ z f ( r i n ) L j ( r i n ) exp ( i π ( x o x i n ) 2 + ( y o y i n ) 2 λ z ) d r i n ,
L j ( x , y ) = exp ( i π ( x + ( 1 ) j y ) 2 2 λ f j ) ,
LG p , l ± ( r ; w ) = ( 2 π x ± i y w ) i p l ( 2 π w 2 r 2 ) exp ( π w 2 r 2 ) ,
RMSE ( k , j ) = ( [ E j ( r ) k , j ( r ) ] 2 d r ) 1 / 2 × ( [ E j ( r ) ] 2 d r ) 1 / 2 .
ϕ 2 ( x , y ) = 16 π 2 ( n b n s ) 2 λ 2 ( R 2 r 2 ) ,

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