Abstract

High-speed quantitative phase and amplitude imaging methods have led to numerous biological discoveries. For general samples, phase retrieval from a single-diffraction pattern has been an algorithmic and experimental challenge. Here we present a quantitative phase and amplitude imaging method applying an efficient support constraint to yield a rapid algorithmic convergence due to the removal of the twin image and spatial shift ambiguities. Compared to previous complex-valued imaging, our method is lenslet-free and relies neither on assumption based on sample sparsity nor interferometric measurements. Our method provides a robust method for imaging in materials and biological science, while its rapid imaging capability will benefit the investigation of dynamical processes.

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

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References

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2019 (1)

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

2018 (4)

2017 (3)

2016 (3)

2015 (2)

N. Burdet, X. Shi, D. Parks, J. N. Clark, X. Huang, S. D. Kevan, and I. K. Robinson, “Evaluation of partial coherence correction in X-ray ptychography,” Opt. Express 23(5), 5452–5467 (2015).
[Crossref] [PubMed]

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

2014 (1)

2013 (2)

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

2010 (1)

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[Crossref]

2009 (1)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

2008 (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

2007 (2)

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

S. Marchesini, “Invited article: a unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78(1), 011301 (2007).
[Crossref] [PubMed]

1998 (1)

1987 (2)

1986 (1)

1983 (2)

1982 (1)

Agbana, T. E.

Bosworth, B. T.

Bowman, R.

Brames, B. J.

Bunk, O.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Burdet, N.

Chapman, H. N.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[Crossref]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662 (1998).
[Crossref]

Chen, C. C.

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

Chen, C.-C.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Chung, J.

Clark, J. N.

Clemente, P.

Cohen, O.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Crimmins, T. R.

Cui, H.

Dai, Q.

David, C.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Dierolf, M.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Ding, W.

Durán, V.

Edgar, M. P.

Egami, R.

Eldar, Y. C.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Fienup, J. R.

Foster, M. A.

Gao, P.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

Garcia, J.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

Geng, Y.

Gibson, G. M.

Gong, H.

Guo, C.

He, X.

Horisaki, R.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Huang, X.

Ishikawa, T.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Kevan, S. D.

Kohmura, Y.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Kong, Y.

Kuang, C.

Lancis, J.

Lee, T.-K.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Liu, C.

Liu, S.

Liu, Z.

Lu, H.

Maiden, A. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Marchesini, S.

S. Marchesini, “Invited article: a unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78(1), 011301 (2007).
[Crossref] [PubMed]

Menzel, A.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Miao, J.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

J. Miao, D. Sayre, and H. N. Chapman, “Phase retrieval from the magnitude of the Fourier transforms of nonperiodic objects,” J. Opt. Soc. Am. A 15(6), 1662 (1998).
[Crossref]

Micó, V.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

Mitchell, K. J.

Nishino, Y.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Nugent, K. A.

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[Crossref]

Ou, X.

Padgett, M. J.

Pan, X.

Parks, D.

Pfeiffer, F.

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Pozzi, P.

Radwell, N.

Ramunno-Johnson, D.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Robinson, I. K.

Rodenburg, J. M.

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

Rodriguez, J. A.

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

Sayre, D.

Segev, M.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Shechtman, Y.

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

Shen, C.

Shi, X.

Shin, J.

So, P. T.

Soldevila, F.

Soloviev, O.

Song, C.

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Song, X.

Sun, A.

Suo, J.

Tajahuerce, E.

Tan, J.

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(5887), 379–382 (2008).
[Crossref] [PubMed]

Vdovin, G.

Verhaegen, M.

Wang, S.

Wang, Y.

Xu, R.

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

Xue, L.

Yang, C.

Yaqoob, Z.

Zalevsky, Z.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

Zhang, Y.

Zhao, G.

Zheng, C.

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

Zheng, J.

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

Zhou, R.

Zhu, J.

Zou, Y.

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

V. Micó, J. Zheng, J. Garcia, Z. Zalevsky, and P. Gao, “Resolution enhancement in quantitative phase microscopy,” Adv. Opt. Photonics 11(1), 135 (2019).
[Crossref]

Appl. Opt. (1)

Biomed. Opt. Express (1)

IEEE Signal Process. Mag. (1)

Y. Shechtman, Y. C. Eldar, O. Cohen, H. N. Chapman, J. Miao, and M. Segev, “Phase Retrieval with Application to Optical Imaging: A contemporary overview,” IEEE Signal Process. Mag. 32(3), 87–109 (2015).
[Crossref]

J. Appl. Cryst. (1)

J. A. Rodriguez, R. Xu, C. C. Chen, Y. Zou, and J. Miao, “Oversampling smoothness: an effective algorithm for phase retrieval of noisy diffraction intensities,” J. Appl. Cryst. 46(2), 312–318 (2013).
[Crossref] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (3)

Nat. Photonics (2)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier ptychographic microscopy,” Nat. Photonics 7(9), 739–745 (2013).
[Crossref] [PubMed]

H. N. Chapman and K. A. Nugent, “Coherent lensless X-ray imaging,” Nat. Photonics 4(12), 833–839 (2010).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

Optica (2)

Phys. Rev. B Condens. Matter Mater. Phys. (1)

C. Song, D. Ramunno-Johnson, Y. Nishino, Y. Kohmura, T. Ishikawa, C.-C. Chen, T.-K. Lee, and J. Miao, “Phase retrieval from exactly oversampled diffraction intensity through deconvolution,” Phys. Rev. B Condens. Matter Mater. Phys. 75(1), 012102 (2007).
[Crossref]

Rev. Sci. Instrum. (1)

S. Marchesini, “Invited article: a unified evaluation of iterative projection algorithms for phase retrieval,” Rev. Sci. Instrum. 78(1), 011301 (2007).
[Crossref] [PubMed]

Science (1)

P. Thibault, M. Dierolf, A. Menzel, O. Bunk, C. David, and F. Pfeiffer, “High-Resolution Scanning X-ray Diffraction Microscopy,” Science 321(5887), 379–382 (2008).
[Crossref] [PubMed]

Ultramicroscopy (1)

A. M. Maiden and J. M. Rodenburg, “An improved ptychographical phase retrieval algorithm for diffractive imaging,” Ultramicroscopy 109(10), 1256–1262 (2009).
[Crossref] [PubMed]

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Figures (8)

Fig. 1
Fig. 1 Three kinds of stagnation problems. (a) Object. (r) (b) Reconstructed object with twin image and spatial shift ambiguities. (c) Object (left) and its Fourier transform (right). (d) Fourier transform without the high frequency in the vertical direction (right) and object recovered from it with oscillating stripes (left).
Fig. 2
Fig. 2 (a) Iterative recovery process of phase retrieval with support constraint 1 of (b). Steps 1-5 illustrate the algorithm, following principles from phase retrieval. Step 1: initialize the object to be recovered. Step 2: the projection on the object space involves setting the components outside the support constraint to 0, while leaving the rest of the values unchanged. Step 3: the projection of the object onto the Fourier intensity set is accomplished by setting the modulus of the object in Fourier space to the measured Fourier intensity, and leaving the phase unchanged. Step 4: repeat the HIO algorithm based on steps 2-3 once more. (b) Two complementary support constraints. The length of the two patterns is n, the width of all the bars is 0.1n, and the side length of the equilateral triangles is 0.707n. The centroids of the equilateral triangles are at the center of the two patterns. The selection of specific parameters is shown in Fig. 3(c)-3(d).
Fig. 3
Fig. 3 Image reconstructions after 200 iterations from simulated diffraction patterns using our support constraints in Fig. 2(b) with different bar widths. (a1-a4) are the recovered amplitude with intermediate bar width value (0.1n). (b1-b4) are the recovered phase with intermediate bar width value (0.1n). (c-d) are the variations of the RMSE and SSIM of (a1-b4) with the ratio of the bar width to the length of the pattern. The curves with different colors represent different objects, while the curves with two line types represent amplitude and phase, respectively.
Fig. 4
Fig. 4 Image reconstructions after 200 iterations from simulated diffraction patterns with different constraints. (a-b) are the original amplitude and phase. (a1-b3) are the recovered amplitude and phase with a single circular support constraint (a1, b1), four overlapping circular support constraints (a2, b2) and our support constraint (a3, b3). (c-d) are the variation of the RMSE and SSIM of (a1-b3) with iteration number. The curves with different colors represent different support constraints, while the curves with two line types represent amplitude and phase, respectively.
Fig. 5
Fig. 5 Experimental verification of the proposed method. Captions: LS, laser source; BE, beam expander; L1, L2, lenses; OBJ, object; CL, condensing lens.
Fig. 6
Fig. 6 (a) Reconstruction results of the positive USAF test target. The region of Group 7, Element 1 is zoomed in and shown in the upper right corner. (b) The profiles along the red and black line segments in the upper right corner.
Fig. 7
Fig. 7 (a) Photograph of the negative amplitude mask with three characters of ‘OPT’. (b) The reconstructed intensity image obtained with the proposed method.
Fig. 8
Fig. 8 (a-b) Reconstructed intensity and phase images of the transmission grating with 10 pairs/mm period. (c) Measured quantitative phase line profiles for a few periods grating.

Equations (10)

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P S ρ(r)={ ρ(r)rS 0rS
E(k)={ I S (k) F[ρ(r)] | F[ρ(r)] | I S (k)=max( I S (k)) F[ρ(r)] I S (k)<max( I S (k))
P M ρ(r)= F 1 { E(k) }
I S (k)=F{ F 1 [I(k)] sinc(r/M) }
I(k)=w N 2 I M (k) max[ I M (k)]
ρ n+1 (r)={ P M ρ n (r)rS ρ n (r) P M ρ n (r)rS
W(k)=exp[ 1 2 (k/α) 2 ]
ρ(r)= ρ 1 (r)+ ρ 2 (r)δ(r r 0 )
F(k)= F 1 (k)+ F 2 (k)exp(i2πk r 0 )
| F(k) | 2 = | F 1 (k)+ F 2 (k)exp(i2πk r 0 ) | 2 = | F 1 (k) | 2 + | F 2 (k) | 2 +2| F 1 (k) || F 2 (k) |cos[2πk r 0 + φ 1 (k)+ φ 2 (k)]

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