Abstract

Modern optical imaging possesses a huge information capacity whose corresponding space-bandwidth product (SBP) reaches tens of megapixels. However, despite the advances in optical and electronic devices, the SBP of an optical microscope is greatly limited, resulting in a reduced field of view or resolution of an image. In this paper, we exploit the Kramers–Kronig relations in digital holography to achieve high SBP imaging, demonstrating a complex amplitude image that can surpass the SBP of a bright-field image. The capability of the proposed method is demonstrated by imaging static samples and biological tissues. We successfully measure a 4.2-megapixel complex amplitude image whose bright-field counterpart exhibits 16.7 megapixels.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2018 (1)

Y. Park, C. Depeursinge, and G. Popescu, “Quantitative phase imaging in biomedicine,” Nat. Photonics 12, 578–589 (2018).
[Crossref]

2016 (5)

H. Wang, Z. Göröcs, W. Luo, Y. Zhang, Y. Rivenson, L. A. Bentolila, and A. Ozcan, “Computational out-of-focus imaging increases the space-bandwidth product in lens-based coherent microscopy,” Optica 3, 1422–1429 (2016).
[Crossref]

A. Mecozzi, C. Antonelli, and M. Shtaif, “Kramers-Kronig coherent receiver,” Optica 3, 1220–1227 (2016).
[Crossref]

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

M. G. Shan, M. E. Kandel, H. Majeed, V. Nastasa, and G. Popescu, “White-light diffraction phase microscopy at doubled space-bandwidth product,” Opt. Express 24, 29033–29039 (2016).
[Crossref]

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photon. Eng. 2, 020201 (2016).
[Crossref]

2014 (4)

2013 (6)

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8, 331–359 (2013).
[Crossref]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

K. Khare, P. T. Ali, and J. Joseph, “Single shot high resolution digital holography,” Opt. Express 21, 2581–2591 (2013).
[Crossref]

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

D. Kim, R. Magnusson, M. Jin, J. Lee, and W. Chegal, “Complex object wave direct extraction method in off-axis digital holography,” Opt. Express 21, 3658–3668 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (3)

2009 (2)

2008 (2)

2007 (2)

2006 (2)

P. Lang, K. Yeow, A. Nichols, and A. Scheer, “Cellular imaging in drug discovery,” Nat. Rev. Drug. Discov. 5, 343–356 (2006).
[Crossref]

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

2005 (1)

2004 (4)

Y. M. Zhang, Q. N. Lu, and B. Z. Ge, “Elimination of zero-order diffraction in digital off-axis holography,” Opt. Commun. 240, 261–267 (2004).
[Crossref]

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[Crossref]

V. C. Abraham, D. L. Taylor, and J. R. Haskins, “High content screening applied to large-scale cell biology,” Trends Biotechnol. 22, 15–22 (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]

2003 (2)

N. Demoli, J. Mestrovic, and I. Sovic, “Subtraction digital holography,” Appl. Opt. 42, 798–804 (2003).
[Crossref]

M. Liebling, T. Blu, and M. A. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–560 (2003).
[Crossref]

2001 (1)

1999 (2)

1997 (1)

T. M. Kreis and W. P. O. Juptner, “Suppression of the DC term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[Crossref]

1996 (1)

1982 (1)

1969 (2)

G. T. Di Francia, “Degrees of freedom of an image,” J. Opt. Soc. Am. 59, 799–804 (1969).
[Crossref]

E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153–156 (1969).
[Crossref]

1966 (1)

H. Voelcker, “Demodulation of single-sideband signals via envelope detection,” IEEE Trans. Commun. Technol. 14, 22–30 (1966).
[Crossref]

1965 (1)

1926 (1)

Abraham, V. C.

V. C. Abraham, D. L. Taylor, and J. R. Haskins, “High content screening applied to large-scale cell biology,” Trends Biotechnol. 22, 15–22 (2004).
[Crossref]

Ali, P. T.

Antonelli, C.

Arai, Y.

T. Tahara, Y. Takahashi, and Y. Arai, “Image-quality improvement in space-bandwidth capacity-enhanced digital holography,” Opt. Eng. 53, 112313 (2014).
[Crossref]

Arfire, C.

Bentolila, L. A.

Bergoend, I.

Bhaduri, B.

Bian, Z.

Bishara, W.

Blu, T.

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[Crossref]

M. Liebling, T. Blu, and M. A. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–560 (2003).
[Crossref]

Boss, D.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Carson, J. R.

J. R. Carson, “Method and means for signaling with high-frequency waves,” U.S. patent applicationUS1449382A (March27, 1923).

Chang, C. C.

Chang, G.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Charriere, F.

Chegal, W.

Chen, G. L.

Cho, S.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Collot, L.

Colomb, T.

Coskun, A. F.

Cotte, Y.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Cuche, E.

Dasari, R. R.

Demoli, N.

Depeursinge, C.

Di Francia, G. T.

Doblas, A.

Dong, S.

Dorsch, R. G.

Emery, Y.

Evans, A.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8, 331–359 (2013).
[Crossref]

Feld, M. S.

Feldman, M.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8, 331–359 (2013).
[Crossref]

Ferreira, C.

Garcia-Sucerquia, J.

Ge, B. Z.

Y. M. Zhang, Q. N. Lu, and B. Z. Ge, “Elimination of zero-order diffraction in digital off-axis holography,” Opt. Commun. 240, 261–267 (2004).
[Crossref]

Ghaznavi, F.

F. Ghaznavi, A. Evans, A. Madabhushi, and M. Feldman, “Digital imaging in pathology: whole-slide imaging and beyond,” Annu. Rev. Pathol. 8, 331–359 (2013).
[Crossref]

Göröcs, Z.

Gross, M.

Guo, K.

Haskins, J. R.

V. C. Abraham, D. L. Taylor, and J. R. Haskins, “High content screening applied to large-scale cell biology,” Trends Biotechnol. 22, 15–22 (2004).
[Crossref]

Heo, J.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Horstmeyer, R.

Hu, C.

Ikeda, T.

Ina, H.

Jeong, Y.

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

Jin, M.

Jo, Y.

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Joseph, J.

Jourdain, P.

Y. Cotte, F. Toy, P. Jourdain, N. Pavillon, D. Boss, P. Magistretti, P. Marquet, and C. Depeursinge, “Marker-free phase nanoscopy,” Nat. Photonics 7, 113–117 (2013).
[Crossref]

Jung, J.

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Juptner, W. P. O.

T. M. Kreis and W. P. O. Juptner, “Suppression of the DC term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[Crossref]

Kandel, M. E.

Kawai, H.

Khare, K.

Kim, D.

Kim, K.

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photon. Eng. 2, 020201 (2016).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Kim, M. K.

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

Kobayashi, S.

Kramers, H. A.

H. A. Kramers, “La diffusion de la lumière par les atomes,” in Atti Cong. Intern. Fisici, (Transactions of Volta Centenary Congress) Como. (1927), Vol. 2, pp. 545–557.

Kreis, T. M.

T. M. Kreis and W. P. O. Juptner, “Suppression of the DC term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[Crossref]

Kronig, R. D. L.

Kuhn, J.

Kuo, M. K.

Lai, J.

Lang, P.

P. Lang, K. Yeow, A. Nichols, and A. Scheer, “Cellular imaging in drug discovery,” Nat. Rev. Drug. Discov. 5, 343–356 (2006).
[Crossref]

Le Clerc, F.

Lee, E.

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

Lee, J.

Lee, K.

K. Lee and Y. Park, “Quantitative phase imaging unit,” Opt. Lett. 39, 3630–3633 (2014).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Lee, M.

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

Lee, S.

M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
[Crossref]

K. Kim, J. Yoon, S. Shin, S. Lee, S.-A. Yang, and Y. Park, “Optical diffraction tomography techniques for the study of cell pathophysiology,” J. Biomed. Photon. Eng. 2, 020201 (2016).
[Crossref]

K. Lee, K. Kim, J. Jung, J. Heo, S. Cho, S. Lee, G. Chang, Y. Jo, H. Park, and Y. Park, “Quantitative phase imaging techniques for the study of cell pathophysiology: from principles to applications,” Sensors 13, 4170–4191 (2013).
[Crossref]

Li, Z.

Liebling, M.

M. Liebling, T. Blu, and M. Unser, “Complex-wave retrieval from a single off-axis hologram,” J. Opt. Soc. Am. A 21, 367–377 (2004).
[Crossref]

M. Liebling, T. Blu, and M. A. Unser, “Non-linear Fresnelet approximation for interference term suppression in digital holography,” Proc. SPIE 5207, 553–560 (2003).
[Crossref]

Lin, C. Y.

Liu, H.

Lohmann, A.

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M. Lee, E. Lee, J. Jung, H. Yu, K. Kim, J. Yoon, S. Lee, Y. Jeong, and Y. Park, “Label-free optical quantification of structural alterations in Alzheimer’s disease,” Sci. Rep. 6, 31034 (2016).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Experimental demonstration with a spectral overlap. (a)–(d). Experimental results using the proposed method showing a USAF 1951 resolution target (a) and (b), and a 10-μm-diameter polystyrene bead (c) and (d). (e)–(h) Experimental results using a conventional off-axis method showing the resolution target (e) and (f), and the polystyrene bead (g) and (h). (i) Interferogram in the experimental condition. (j) Fourier transform of (i). (Insets) Line profiles of (d) and (h). The red dashed lines correspond to a phase value of 2.73 rad. Scale bars indicate 10 μm.

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Fig. 2.
Fig. 2. Experimental demonstration without a spectral overlap. (a)–(d) Experimental results using the proposed method showing a 1951 USAF resolution target (a) and (b), and a 10-μm-diameter polystyrene bead (c) and (d). (e)–(h) Experimental results using a conventional off-axis method showing the resolution target (e) and (f), and the polystyrene bead (g and h). (i) Interferogram in the experimental condition. (j) Fourier transform of (i). (Insets) Line profiles of (d) and (h). The red dashed lines correspond to a phase value of 2.73 rad. Scale bars indicate 10 μm.

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Fig. 3.
Fig. 3. Experimental demonstration of wide field of view quantitative phase imaging. (a) Measured quantitative phase image of breast tissue with the proposed method. Insets show magnified images at different positions. (b) Fourier spectrum of an interferogram.

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Fig. 4.
Fig. 4. Experimental demonstration with anamorphic imaging. (a) Quantitative phase image of mouse brain tissue retrieved using the proposed method. (b) Corrected image of (a), where the multiple reflections induced by coverslips are removed (indicated with white arrows). (c) Fourier spectrum of an interferogram.

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Fig. 5.
Fig. 5. SBP per measurements and pixel count of detectors achieved in different works. Solid and dashed lines indicate the maximum achievable SBP per measurements of complex amplitude and intensity images, respectively, in different imaging techniques. The proposed method achieves a 4.2-megapixel complex amplitude image with a 12-megapixel detector (red circle, data shown in Fig. 4). The bright-field counterpart of the measured complex amplitude image has an SBP of 16.7 megapixels (dashed red circle). Achieved SBP per measurements and pixel count of detectors in the literatures (Refs. [5,7,8]) are denoted with colored circles.

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Equations (10)

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I ˜ ( ν ) = A ˜ ( ν ) + B ˜ ( ν − ν R ) + B ˜ * ( − ν − ν R ) ,
P ˜ ( ν ) = { 1 , | ν | ≤ NA obj / λ M 0 , | ν | > NA obj / λ M .
| ν R | > 3 NA obj λ M .
Re [ f ( ω ) ] = 1 π p.v. ∫ − ∞ ∞ Im [ f ( ω ′ ) ] ω ′ − ω d ω ′ ,
Im [ f ( ω ) ] = − 1 π p.v. ∫ − ∞ ∞ Re [ f ( ω ′ ) ] ω ′ − ω d ω ′ ,
Re [ χ ( r ) ] = log | 1 + β ( r ) | = 1 2 [ log I ( r ) − log | R ( r ) | 2 ] ,
Im [ χ ( r ) ] = arg [ 1 + β ( r ) ] .
χ ( r ) = ∑ n = 0 ∞ − 1 n n + 1 [ β ( r ) ] n + 1 ,
β ( r ) = 1 R 0 ∫ − ∞ ∞ S ˜ ( ν ‖ , r ⊥ ) exp [ i 2 π ( ν ‖ + | ν R | ) r ‖ ] d ν ‖ ,
| ν R | > NA obj λ M .

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