Abstract

We present a method for single-shot phase imaging with randomized light (SPIRaL). In SPIRaL, the complex (amplitude and phase) field of an object illuminated with a randomized coherent beam is captured with an image sensor, without the need for any reference light. The object field is retrieved from the single captured intensity image by a compressive sensing-based algorithm with a sparsity constraint. SPIRaL has higher observation speed, light efficiency, and flexibility of the implementation compared with previous methods. We demonstrate SPIRaL numerically and experimentally.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Experimental demonstration of single-shot phase imaging with a coded aperture

Ryoichi Horisaki, Riki Egami, and Jun Tanida
Opt. Express 23(22) 28691-28697 (2015)

Subpixel reconstruction for single-shot phase imaging with coded diffraction

Ryoichi Horisaki, Taichi Kojima, Kyoji Matsushima, and Jun Tanida
Appl. Opt. 56(27) 7642-7647 (2017)

Single-shot phase imaging with a coded aperture

Ryoichi Horisaki, Yusuke Ogura, Masahiko Aino, and Jun Tanida
Opt. Lett. 39(22) 6466-6469 (2014)

References

  • View by:
  • |
  • |
  • |

  1. B. Bhaduri, C. Edwards, H. Pham, R. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photon. 6, 57–119 (2014).
    [Crossref]
  2. 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] [PubMed]
  3. P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 20901 (2014).
    [Crossref]
  4. G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photon. 4, 472–553 (2012).
    [Crossref]
  5. J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
    [Crossref] [PubMed]
  6. E. N. Leith and J. Upatnieks, “Reconstructed wavefronts and communication theory,” J. Opt. Soc. Am. 52, 1123–1128 (1962).
    [Crossref]
  7. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
    [Crossref] [PubMed]
  8. J. R. Fienup, “Phase retrieval algorithms: a comparison,” Appl. Opt. 21, 2758–2769 (1982).
    [Crossref] [PubMed]
  9. P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
    [Crossref] [PubMed]
  10. G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
    [Crossref]
  11. N. Streibl, “Phase imaging by the transport equation of intensity,” Opt. Commun. 49, 6–10 (1984).
    [Crossref]
  12. R. Horisaki, Y. Ogura, M. Aino, and J. Tanida, “Single-shot phase imaging with a coded aperture,” Opt. Lett. 39, 6466–6469 (2014).
    [Crossref] [PubMed]
  13. R. Horisaki and J. Tanida, “Multidimensional object acquisition by single-shot phase imaging with a coded aperture,” Opt. Express 23, 9696–9704 (2015).
    [Crossref] [PubMed]
  14. R. Horisaki, R. Egami, and J. Tanida, “Experimental demonstration of single-shot phase imaging with a coded aperture,” Opt. Express 23, 28691–28697 (2015).
    [Crossref] [PubMed]
  15. D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory 52, 1289–1306 (2006).
    [Crossref]
  16. A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” J. Opt. Soc. Am. A 29, 1847–1859 (2012).
    [Crossref]
  17. A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
    [Crossref] [PubMed]
  18. E. J. Candès, X. Li, and M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” Appl. Comput. Harmon. Anal. 39, 277–299 (2014).
  19. P. Gao, G. Pedrini, C. Zuo, and W. Osten, “Phase retrieval using spatially modulated illumination,” Opt. Lett. 39, 3615–3618 (2014).
    [Crossref] [PubMed]
  20. A. Suzuki and Y. Takahashi, “Dark-field X-ray ptychography,” Opt. Express 23, 16429–16438 (2015).
    [Crossref] [PubMed]
  21. J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
    [Crossref]
  22. M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Adv. Opt. Photonics 7, 241–275 (2015).
    [Crossref]
  23. E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
    [Crossref]
  24. R. Horisaki, N. Fukata, and J. Tanida, “A compressive active stereo imaging system with random pattern projection,” Appl. Phys. Express 5, 72501 (2012).
    [Crossref]
  25. H. Matsui, R. Horisaki, and J. Tanida, “Computational structured illumination,” Appl. Opt. 54, 8742–8746 (2015).
    [Crossref] [PubMed]
  26. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  27. A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
    [Crossref] [PubMed]
  28. L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376–2389 (2014).
    [Crossref] [PubMed]
  29. R. W. Gerchberg and W. O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).
  30. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
    [Crossref]
  31. M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
    [Crossref]
  32. S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Image Proc. 57, 2479–2493 (2009).
    [Crossref]
  33. L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
    [Crossref]
  34. R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
    [Crossref]

2015 (6)

2014 (6)

2013 (3)

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] [PubMed]

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

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

2012 (4)

A. Fannjiang and W. Liao, “Phase retrieval with random phase illumination,” J. Opt. Soc. Am. A 29, 1847–1859 (2012).
[Crossref]

G. Nehmetallah and P. P. Banerjee, “Applications of digital and analog holography in three-dimensional imaging,” Adv. Opt. Photon. 4, 472–553 (2012).
[Crossref]

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

R. Horisaki, N. Fukata, and J. Tanida, “A compressive active stereo imaging system with random pattern projection,” Appl. Phys. Express 5, 72501 (2012).
[Crossref]

2011 (1)

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
[Crossref]

2009 (2)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Image Proc. 57, 2479–2493 (2009).
[Crossref]

2008 (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

2007 (2)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

2006 (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory 52, 1289–1306 (2006).
[Crossref]

1997 (1)

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

1988 (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

1984 (1)

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

1982 (1)

1972 (1)

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

1962 (1)

Aino, M.

Allain, M.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Banerjee, P. P.

Belkebir, K.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Bhaduri, B.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Candès, E. J.

E. J. Candès, X. Li, and M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” Appl. Comput. Harmon. Anal. 39, 277–299 (2014).

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] [PubMed]

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] [PubMed]

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Depeursinge, C.

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 20901 (2014).
[Crossref]

Dierolf, M.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Donoho, D. L.

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory 52, 1289–1306 (2006).
[Crossref]

Edwards, C.

Egami, R.

Eluru, G.

M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Adv. Opt. Photonics 7, 241–275 (2015).
[Crossref]

Fannjiang, A.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Fienup, J. R.

Figueiredo, M. A. T.

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Image Proc. 57, 2479–2493 (2009).
[Crossref]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Fukata, N.

R. Horisaki, N. Fukata, and J. Tanida, “A compressive active stereo imaging system with random pattern projection,” Appl. Phys. Express 5, 72501 (2012).
[Crossref]

Gao, P.

Geng, J.

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
[Crossref]

Gerchberg, R. W.

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

Gianoncelli, A.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Girard, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Goddard, L. L.

Goldstein, R. M.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gorthi, S. S.

M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Adv. Opt. Photonics 7, 241–275 (2015).
[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] [PubMed]

Horisaki, R.

Horstmeyer, R.

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

Ishikawa, T.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

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] [PubMed]

Jung, 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] [PubMed]

Kaulich, B.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Kim, K.

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] [PubMed]

Le Moal, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Lee, K.

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] [PubMed]

Lee, 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] [PubMed]

Leith, E. N.

Li, X.

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376–2389 (2014).
[Crossref] [PubMed]

E. J. Candès, X. Li, and M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” Appl. Comput. Harmon. Anal. 39, 277–299 (2014).

Liao, W.

Magistretti, P. J.

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 20901 (2014).
[Crossref]

Maiden, A.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Maiden, A. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

Marquet, P.

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 20901 (2014).
[Crossref]

Matsui, H.

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Miao, J.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Morrison, G.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Mudry, E.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Murnane, M. M.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Nehmetallah, G.

Nguyen, T. H.

Nicoletti, C.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Nowak, R. D.

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Image Proc. 57, 2479–2493 (2009).
[Crossref]

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Ogura, Y.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Osten, W.

Park, H.

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] [PubMed]

Park, 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] [PubMed]

Pedrini, G.

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Pham, H.

Popescu, G.

Ramchandran, K.

Robinson, I. K.

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Rodenburg, J.

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Rodenburg, J. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Savatier, J.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Saxena, M.

M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Adv. Opt. Photonics 7, 241–275 (2015).
[Crossref]

Saxton, W. O.

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

Sentenac, A.

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Soltanolkotabi, M.

E. J. Candès, X. Li, and M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” Appl. Comput. Harmon. Anal. 39, 277–299 (2014).

Streibl, N.

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

Suzuki, A.

Takahashi, Y.

Tanida, J.

Thibault, P.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

Tian, L.

Upatnieks, J.

Waller, L.

Werner, C. L.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Wright, S. J.

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Image Proc. 57, 2479–2493 (2009).
[Crossref]

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

Yamaguchi, I.

Yang, C.

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

Zebker, H. A.

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Zhang, T.

Zheng, G.

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

Zhou, R.

Zuo, C.

Adv. Opt. Photon. (2)

Adv. Opt. Photonics (2)

J. Geng, “Structured-light 3D surface imaging: a tutorial,” Adv. Opt. Photonics 3, 128–160 (2011).
[Crossref]

M. Saxena, G. Eluru, and S. S. Gorthi, “Structured illumination microscopy,” Adv. Opt. Photonics 7, 241–275 (2015).
[Crossref]

Appl. Comput. Harmon. Anal. (1)

E. J. Candès, X. Li, and M. Soltanolkotabi, “Phase retrieval from coded diffraction patterns,” Appl. Comput. Harmon. Anal. 39, 277–299 (2014).

Appl. Opt. (2)

Appl. Phys. Express (1)

R. Horisaki, N. Fukata, and J. Tanida, “A compressive active stereo imaging system with random pattern projection,” Appl. Phys. Express 5, 72501 (2012).
[Crossref]

Biomed. Opt. Express (1)

IEEE J. Sel. Top. Signal Process. (1)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1, 586–597 (2007).
[Crossref]

IEEE Trans. Image Proc. (2)

S. J. Wright, R. D. Nowak, and M. A. T. Figueiredo, “Sparse reconstruction by separable approximation,” IEEE Trans. Image Proc. 57, 2479–2493 (2009).
[Crossref]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: Two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Proc. 16, 2992–3004 (2007).
[Crossref]

IEEE Trans. Info. Theory (1)

D. L. Donoho, “Compressed sensing,” IEEE Trans. Info. Theory 52, 1289–1306 (2006).
[Crossref]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Nat. Commun. (1)

A. Maiden, G. Morrison, B. Kaulich, A. Gianoncelli, and J. Rodenburg, “Soft X-ray spectromicroscopy using ptychography with randomly phased illumination,” Nat. Commun. 4, 1669 (2013).
[Crossref] [PubMed]

Nat. Photonics (2)

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

E. Mudry, K. Belkebir, J. Girard, J. Savatier, E. Le Moal, C. Nicoletti, M. Allain, and A. Sentenac, “Structured illumination microscopy using unknown speckle patterns,” Nat. Photonics 6, 312–315 (2012).
[Crossref]

Neurophotonics (1)

P. Marquet, C. Depeursinge, and P. J. Magistretti, “Review of quantitative phase-digital holographic microscopy: promising novel imaging technique to resolve neuronal network activity and identify cellular biomarkers of psychiatric disorders,” Neurophotonics 1, 20901 (2014).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (3)

Opt. Lett. (3)

Optik (1)

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

Phys. D (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. D 60, 259–268 (1992).
[Crossref]

Radio Science (1)

R. M. Goldstein, H. A. Zebker, and C. L. Werner, “Satellite radar interferometry: Two-dimensional phase unwrapping,” Radio Science 23, 713–720 (1988).
[Crossref]

Science (2)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-resolution scanning X-ray diffraction microscopy,” Science 321, 379–382 (2008).
[Crossref] [PubMed]

J. Miao, T. Ishikawa, I. K. Robinson, and M. M. Murnane, “Beyond crystallography: diffractive imaging using coherent x-ray light sources,” Science 348, 530–535 (2015).
[Crossref] [PubMed]

Sensors (1)

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] [PubMed]

Ultramicroscopy (1)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109, 1256–1262 (2009).
[Crossref] [PubMed]

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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 (6)

Fig. 1
Fig. 1

Setup of SPIRaL.

Fig. 2
Fig. 2

Simulation of SPIRaL. The (a) amplitude and (b) phase of the object. The (c) amplitude and (d) phase of the illumination, where the upper-right parts show magnified patterns. (e) The captured image. The (f) amplitude and (g) phase of the reconstructed result. Phases are normalized in the interval [−π, π].

Fig. 3
Fig. 3

Relationship between the measurement noise and the reconstruction fidelity in the simulation in Fig. 2.

Fig. 4
Fig. 4

SPIRaL experiment with a mixture of oil and water. The (a) amplitude and (b) phase, which is normalized in the interval [−π, π], of the illumination, where the upper-right parts show magnified patterns. (e) The captured image. The (d) amplitude and (e) phase, which is normalized in the interval [0, 6π], of the reconstructed result. (f) Image of the region surounded by the square in Fig. (d) observed with a microscope, where the scale bar is 300 μm.

Fig. 5
Fig. 5

Experimental evaluation of the spatial resolution with a wire. The (a) amplitude and (b) phase of the illumination, where the upper-right parts show magnified patterns. (c) The captured image, where the both sides are replaced with zeros. (d) The reconstructed amplitude, where the upper-right part shows the magnified image of the square area, and (e) the reconstructed phase. (f) The line profile indicated by the black broken line in the magnified image on Fig. (d). Phases are normalized in the interval [−π, π].

Fig. 6
Fig. 6

Experimental evaluation of the phase measurement with a convex lens. The (a) amplitude and (b) phase, which is normalized in the interval [−π, π], of the illumination, where the upper-right parts show magnified patterns. (c) The captured image. The (d) amplitude and (e) phase, which is normalized in the interval [0, 9π], of the reconstructed result. The line profiles of the (f) amplitude and (g) phase indicated by the white broken line in Fig. (d).

Equations (6)

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

| g | 2 = | P z Mf | 2 ,
| g | 2 = | P z 2 P z 1 Mf | 2 ,
g ^ = arg min g | g | 2 | P z 2 a | 2 2 ,
f ^ = arg min f a P z 1 Mf 2 + τ ( f ) ,
g ^ = ( | g | 2 | P z 2 a | 2 ) 1 2 P z 2 a ,
δ z λ w ,

Metrics