Abstract

Optical phase imaging enables visualization of transparent samples, numerical refocusing, and other computational processing. Typically phase is measured quantitatively using interferometric techniques such as digital holography. Researchers have demonstrated image enhancement by synthetic aperture imaging based on digital holography. In this work we introduce a novel imaging technique that implements synthetic aperture imaging using phase retrieval, a non-interferometric technique. Unlike digital holography, phase retrieval obviates the need for a reference arm and provides a more compact, less expensive, and more stable experimental setup. We call this technique synthetic aperture phase retrieval.

© 2014 Optical Society of America

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2013

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

P. Gao, G. Pedrini, W. Osten, “Structured illumination for resolution enhancement and autofocusing in digital holographic microscopy,” Opt. Lett. 38, 1328–1330 (2013).
[CrossRef] [PubMed]

Z. Jingshan, J. Dauwels, M. Vazquez, L. Waller, “Sparse ACEKF for phase reconstruction,” Opt. Express 21, 18125–18137 (2013).
[CrossRef] [PubMed]

2012

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

2010

2009

2008

2007

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

2006

2005

2003

2002

2001

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

D. Axelrod., “Selective imaging of surface fluorescence with very high aperture microscope objectives,” J. Biomed. Opt. 6, 6–13 (2001).
[CrossRef] [PubMed]

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[CrossRef]

1999

1998

1997

1994

1984

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

1983

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73(11), 1434–1441 (1983).
[CrossRef]

1982

1972

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

1952

H. G. Davies, M. H. F. Wilkins, “Interference microscopy and mass determination,” Nature 169, 541 (1952).
[CrossRef] [PubMed]

Allen, L.

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[CrossRef]

Almoro, P.

Anand, A.

Axelrod., D.

D. Axelrod., “Selective imaging of surface fluorescence with very high aperture microscope objectives,” J. Biomed. Opt. 6, 6–13 (2001).
[CrossRef] [PubMed]

Badizadegan, K.

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, M. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Barbastathis, G.

Barty, A.

Bright, V. M.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Burton, D.

Chhaniwal, V. K.

Choi, W.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, M. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Choi, Y.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

Cogswell, C. J.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Colomb, T.

Cormack, R. H.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Cuche, E.

Dasari, R.

Dasari, R. R.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

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

Dauwels, J.

Davies, H. G.

H. G. Davies, M. H. F. Wilkins, “Interference microscopy and mass determination,” Nature 169, 541 (1952).
[CrossRef] [PubMed]

Depeursinge, C.

Emery, Y.

Fang-Yen, C.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, M. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Feld, M.

Feld, M. S.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

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

Fienup, J. R.

Gao, P.

Gdeisat, M.

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

Goodman, J. W.

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

Gopinath, J. T.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Hanson, S.

Herraez, M.

Ikeda, T.

Jingshan, Z.

Juptner, W.

Kato, J.

Kim, K.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

Kim, M.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

Kou, S. S.

Lalor, M.

Lue, N.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Magistretti, P.

Magistretti, P. J.

Marquet, P.

Mizuno, J.

Niederriter, R. D.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Nugent, K. A.

Oh, S.

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Ohta, S.

Osten, W.

Oxley, M.

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[CrossRef]

Paganin, D.

Pedrini, G.

Popescu, G.

Rappaz, B.

Roberts, A.

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

Schnars, U.

Sheppard, C. J. R.

Streibl, N.

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

Sung, Y.

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

Y. Sung, W. Choi, C. Fang-Yen, K. Badizadegan, R. Dasari, M. Feld, “Optical diffraction tomography for high resolution live cell imaging,” Opt. Express 17, 266–277 (2009).
[CrossRef] [PubMed]

Teague, M. R.

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73(11), 1434–1441 (1983).
[CrossRef]

Tian, L.

Tiziani, H.

Vazquez, M.

Waller, L.

Watson, A. M.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Wilkins, M. H. F.

H. G. Davies, M. H. F. Wilkins, “Interference microscopy and mass determination,” Nature 169, 541 (1952).
[CrossRef] [PubMed]

Yamaguchi, I.

Zahreddine, R. N.

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

Zhang, T.

Zhang, Y.

Appl. Opt.

Applied Optics

R. D. Niederriter, A. M. Watson, R. N. Zahreddine, C. J. Cogswell, R. H. Cormack, V. M. Bright, J. T. Gopinath, “Electrowetting lenses for compensating phase and curvature distortion in arrayed laser systems,” Applied Optics 52, 3172 (2013).
[CrossRef] [PubMed]

J. Biomed. Opt.

D. Axelrod., “Selective imaging of surface fluorescence with very high aperture microscope objectives,” J. Biomed. Opt. 6, 6–13 (2001).
[CrossRef] [PubMed]

M. Kim, Y. Choi, C. Fang-Yen, Y. Sung, K. Kim, R. R. Dasari, M. S. Feld, W. Choi, “Three-dimensional differential interference contrast microscopy using synthetic aperture imaging,” J. Biomed. Opt. 17(2), 026003 (2012).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

M. R. Teague, “Deterministic phase retrieval: a Green’s function solution,” J. Opt. Soc. Am. A 73(11), 1434–1441 (1983).
[CrossRef]

Nat. Methods

W. Choi, C. Fang-Yen, K. Badizadegan, S. Oh, N. Lue, R. R. Dasari, M. S. Feld, “Tomographic phase microscopy,” Nat. Methods 4(9), 717–719 (2007).
[CrossRef] [PubMed]

Nature

H. G. Davies, M. H. F. Wilkins, “Interference microscopy and mass determination,” Nature 169, 541 (1952).
[CrossRef] [PubMed]

Opt. Commun.

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

L. Allen, M. Oxley, “Phase retrieval from series of images obtained by defocus variation,” Opt. Commun. 199, 65–75 (2001).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

R. W. Gerchberg, W. O. Saxton, “A practical algorithm for the determination of phase from image and diffraction plane pictures,” Optik 35, 227–246 (1972).

Other

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

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Figures (11)

Fig. 1
Fig. 1

Partition of the synthesized spectrum for aperture synthesis.

Fig. 2
Fig. 2

Experimental setup for synthetic aperture phase retrieval. M1: gimbal mount mirror; L1: lens (f = 300 mm); C: condenser lens (NA 1.25); OL: objective lens (NA 0.75); L2: tube lens (f = 200 mm).

Fig. 3
Fig. 3

Intensity images at zero degrees. Scale bar: 6 μm.

Fig. 4
Fig. 4

Angular scanning at back focal plane of the condenser lens.

Fig. 5
Fig. 5

Intensity images at 12.3 degrees. Scale bar: 6 μm.

Fig. 6
Fig. 6

Test case 1: Phase image at 0 degrees. Scale bar: 6 μm.

Fig. 7
Fig. 7

Phase image from off-axis interferometry. Scale bar: 6 μm.

Fig. 8
Fig. 8

Phase image at 11.0 degrees. Scale bar: 6 μm.

Fig. 9
Fig. 9

Test case 2: Synthesized phase image with 5 total angles. Scale bar: 6 μm.

Fig. 10
Fig. 10

Test case 3: Synthesized phase image with 9 total angles. Scale bar: 6 μm.

Fig. 11
Fig. 11

Resolution enhancement of particles on a glass slide.

Tables (2)

Tables Icon

Table 1 Phase retrieval test cases.

Tables Icon

Table 2 Phase speckle and background noise comparisons.

Equations (9)

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

P ( u , v ) = circ ( ( u / ( λ f ) ) 2 + ( v / ( λ f ) ) 2 N A / λ )
U in k ( x , y ) = exp [ j 2 π ( v x k x + v y k y ) ] ,
U f k ( u , v ) = P ( u , v ) 1 j λ f t ( x , y ) U in k ( x , y ) exp [ j 2 π λ f ( x u + y v ) ] d x d y = 1 j λ f P ( u , v ) T ( u λ f + v x k , v λ f + v y k ) U f k ( u λ f v x k , v λ f v y k ) = 1 j λ f P ( u λ f v x k , v λ f v y k ) T ( u λ f , v λ f )
U f s ( u , v ) = 1 j λ f k W k ( u , v ) P ( u λ f v x k , v λ f v y k ) T ( u λ f , v λ f ) = k W k ( u , v ) U f k ( u λ f v x k , v λ f v y k )
W 0 ( u , v ) = { 1 , if u 2 + v 2 < NA / λ , 0 , otherwise .
W k ( u , v ) = { 1 , if ( u , v ) quadrant k and u 2 + v 2 > NA / λ , 0 , otherwise .
W k ( u , v ) = { 1 2 , if ( u , v ) octant k and u 2 + v 2 > NA / λ , 1 4 , if ( u , v ) octant k 1 and u 2 + v 2 > NA / λ , 1 4 , if ( u , v ) octant k + 1 and u 2 + v 2 > NA / λ , 0 , otherwise ,
δ = κ λ N A
δ = κ λ N A + sin θ illum

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