Abstract

We report the implementation of an image sensor chip, termed wavefront image sensor chip (WIS), that can measure both intensity/amplitude and phase front variations of a light wave separately and quantitatively. By monitoring the tightly confined transmitted light spots through a circular aperture grid in a high Fresnel number regime, we can measure both intensity and phase front variations with a high sampling density (11 µm) and high sensitivity (the sensitivity of normalized phase gradient measurement is 0.1 mrad under the typical working condition). By using WIS in a standard microscope, we can collect both bright-field (transmitted light intensity) and normalized phase gradient images. Our experiments further demonstrate that the normalized phase gradient images of polystyrene microspheres, unstained and stained starfish embryos, and strongly birefringent potato starch granules are improved versions of their corresponding differential interference contrast (DIC) microscope images in that they are artifact-free and quantitative. Besides phase microscopy, WIS can benefit machine recognition, object ranging, and texture assessment for a variety of applications.

© 2010 OSA

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2009 (1)

2008 (1)

X. Q. Cui, M. Lew, and C. H. Yang, “Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. 93(9), 091113 (2008).
[CrossRef]

2007 (2)

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

J. G. Wu, Z. Yaqoob, X. Heng, L. M. Lee, X. Q. Cui, and C. H. Yang, “Full field phase imaging using a harmonically matched diffraction grating pair based homodyne quadrature interferometer,” Appl. Phys. Lett. 90(15), 151123 (2007).
[CrossRef]

2006 (5)

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

M. V. Sarunic, S. Weinberg, and J. A. Izatt, “Full-field swept-source phase microscopy,” Opt. Lett. 31(10), 1462–1464 (2006).
[CrossRef] [PubMed]

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[CrossRef] [PubMed]

2005 (1)

2004 (2)

B. C. Albensi, E. V. Ilkanich, G. Dini, and D. Janigro, “Elements of Scientific Visualization in Basic Neuroscience Research,” Bioscience 54(12), 1127–1137 (2004).
[CrossRef]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004).
[CrossRef] [PubMed]

2003 (2)

S. L. Stanley., “Amoebiasis,” Lancet 361(9362), 1025–1034 (2003).
[CrossRef] [PubMed]

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215(4-6), 285–288 (2003).
[CrossRef]

2002 (1)

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

2001 (1)

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

1998 (1)

1996 (1)

M. M. Haglund, M. S. Berger, and D. W. Hochman, “Enhanced optical imaging of human gliomas and tumor margins,” Neurosurgery 38(2), 308–317 (1996).
[CrossRef] [PubMed]

1994 (1)

R. J. Sommer and P. W. Sternberg, “Changes of induction and competence during the evolution of vulva development in nematodes,” Science 265(5168), 114–118 (1994).
[CrossRef] [PubMed]

1987 (1)

J. Van Blerkom, H. Bell, and G. Henry, “The occurrence, recognition and developmental fate of pseudo-multipronuclear eggs after in-vitro fertilization of human oocytes,” Hum. Reprod. 2(3), 217–225 (1987).
[PubMed]

1975 (1)

R. Hoffman and L. Gross, “The modulation contrast microscope,” Nature 254(5501), 586–588 (1975).
[CrossRef] [PubMed]

1971 (1)

R. V. Shack and B. C. Platt, “Production and use of a lenticular hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

1969 (1)

G. Nomarski, “New theory of image formation in differential interference microscopy,” J. Opt. Soc. Am. 59, 1524 (1969).

1942 (1)

F. Zernike, “Phase contrast, a new method for the microsopic observation of transparent objects,” Physica 9(7), 686–698 (1942).
[CrossRef]

Albensi, B. C.

B. C. Albensi, E. V. Ilkanich, G. Dini, and D. Janigro, “Elements of Scientific Visualization in Basic Neuroscience Research,” Bioscience 54(12), 1127–1137 (2004).
[CrossRef]

Arnison, M. R.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004).
[CrossRef] [PubMed]

Badizadegan, K.

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

Barty, A.

Bates, M.

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

Bell, H.

J. Van Blerkom, H. Bell, and G. Henry, “The occurrence, recognition and developmental fate of pseudo-multipronuclear eggs after in-vitro fertilization of human oocytes,” Hum. Reprod. 2(3), 217–225 (1987).
[PubMed]

Berger, M. S.

M. M. Haglund, M. S. Berger, and D. W. Hochman, “Enhanced optical imaging of human gliomas and tumor margins,” Neurosurgery 38(2), 308–317 (1996).
[CrossRef] [PubMed]

Betzig, E.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Bonifacino, J. S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Booth, M. J.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Carmon, Y.

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215(4-6), 285–288 (2003).
[CrossRef]

Choi, W.

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

Cogswell, C. J.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004).
[CrossRef] [PubMed]

Colomb, T.

Cuche, E.

Cui, X. Q.

X. Q. Cui, M. Lew, and C. H. Yang, “Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. 93(9), 091113 (2008).
[CrossRef]

J. G. Wu, Z. Yaqoob, X. Heng, L. M. Lee, X. Q. Cui, and C. H. Yang, “Full field phase imaging using a harmonically matched diffraction grating pair based homodyne quadrature interferometer,” Appl. Phys. Lett. 90(15), 151123 (2007).
[CrossRef]

Dasari, R. R.

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

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[CrossRef] [PubMed]

Davidson, M. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Denk, W.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Depeursinge, C.

Dini, G.

B. C. Albensi, E. V. Ilkanich, G. Dini, and D. Janigro, “Elements of Scientific Visualization in Basic Neuroscience Research,” Bioscience 54(12), 1127–1137 (2004).
[CrossRef]

Emery, Y.

Fang-Yen, C.

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

Feld, M. S.

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

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[CrossRef] [PubMed]

Gross, L.

R. Hoffman and L. Gross, “The modulation contrast microscope,” Nature 254(5501), 586–588 (1975).
[CrossRef] [PubMed]

Haglund, M. M.

M. M. Haglund, M. S. Berger, and D. W. Hochman, “Enhanced optical imaging of human gliomas and tumor margins,” Neurosurgery 38(2), 308–317 (1996).
[CrossRef] [PubMed]

Heng, X.

J. G. Wu, Z. Yaqoob, X. Heng, L. M. Lee, X. Q. Cui, and C. H. Yang, “Full field phase imaging using a harmonically matched diffraction grating pair based homodyne quadrature interferometer,” Appl. Phys. Lett. 90(15), 151123 (2007).
[CrossRef]

Henry, G.

J. Van Blerkom, H. Bell, and G. Henry, “The occurrence, recognition and developmental fate of pseudo-multipronuclear eggs after in-vitro fertilization of human oocytes,” Hum. Reprod. 2(3), 217–225 (1987).
[PubMed]

Hess, H. F.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Hochman, D. W.

M. M. Haglund, M. S. Berger, and D. W. Hochman, “Enhanced optical imaging of human gliomas and tumor margins,” Neurosurgery 38(2), 308–317 (1996).
[CrossRef] [PubMed]

Hoffman, R.

R. Hoffman and L. Gross, “The modulation contrast microscope,” Nature 254(5501), 586–588 (1975).
[CrossRef] [PubMed]

Ikeda, T.

Ilkanich, E. V.

B. C. Albensi, E. V. Ilkanich, G. Dini, and D. Janigro, “Elements of Scientific Visualization in Basic Neuroscience Research,” Bioscience 54(12), 1127–1137 (2004).
[CrossRef]

Izatt, J. A.

Janigro, D.

B. C. Albensi, E. V. Ilkanich, G. Dini, and D. Janigro, “Elements of Scientific Visualization in Basic Neuroscience Research,” Bioscience 54(12), 1127–1137 (2004).
[CrossRef]

Juskaitis, R.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Larkin, K. G.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004).
[CrossRef] [PubMed]

Lee, L. M.

J. G. Wu, Z. Yaqoob, X. Heng, L. M. Lee, X. Q. Cui, and C. H. Yang, “Full field phase imaging using a harmonically matched diffraction grating pair based homodyne quadrature interferometer,” Appl. Phys. Lett. 90(15), 151123 (2007).
[CrossRef]

Lew, M.

X. Q. Cui, M. Lew, and C. H. Yang, “Quantitative differential interference contrast microscopy based on structured-aperture interference,” Appl. Phys. Lett. 93(9), 091113 (2008).
[CrossRef]

Lindwasser, O. W.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Lippincott-Schwartz, J.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Lue, N.

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

Mack-Bucher, J. A.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Magistretti, P. J.

Marquet, P.

Mehta, S. B.

Neil, M. A. A.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Nomarski, G.

G. Nomarski, “New theory of image formation in differential interference microscopy,” J. Opt. Soc. Am. 59, 1524 (1969).

Nugent, K. A.

Oh, S.

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

Olenych, S.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Paganin, D.

Patterson, G. H.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Platt, B. C.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

R. V. Shack and B. C. Platt, “Production and use of a lenticular hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Popescu, G.

Rappaz, B.

Ribak, E. N.

Y. Carmon and E. N. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Opt. Commun. 215(4-6), 285–288 (2003).
[CrossRef]

Roberts, A.

Rueckel, M.

M. Rueckel, J. A. Mack-Bucher, and W. Denk, “Adaptive wavefront correction in two-photon microscopy using coherence-gated wavefront sensing,” Proc. Natl. Acad. Sci. U.S.A. 103(46), 17137–17142 (2006).
[CrossRef] [PubMed]

Rust, M. J.

M. J. Rust, M. Bates, and X. W. Zhuang, “Sub-diffraction-limit imaging by stochastic optical reconstruction microscopy (STORM),” Nat. Methods 3(10), 793–796 (2006).
[CrossRef] [PubMed]

Sarunic, M. V.

Shack, R.

B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” J. Refract. Surg. 17(5), S573–S577 (2001).
[PubMed]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular hartmann screen,” J. Opt. Soc. Am. 61, 656 (1971).

Sheppard, C. J. R.

S. B. Mehta and C. J. R. Sheppard, “Quantitative phase-gradient imaging at high resolution with asymmetric illumination-based differential phase contrast,” Opt. Lett. 34(13), 1924–1926 (2009).
[CrossRef] [PubMed]

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004).
[CrossRef] [PubMed]

Smith, N. I.

M. R. Arnison, K. G. Larkin, C. J. R. Sheppard, N. I. Smith, and C. J. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214(1), 7–12 (2004).
[CrossRef] [PubMed]

Sommer, R. J.

R. J. Sommer and P. W. Sternberg, “Changes of induction and competence during the evolution of vulva development in nematodes,” Science 265(5168), 114–118 (1994).
[CrossRef] [PubMed]

Sougrat, R.

E. Betzig, G. H. Patterson, R. Sougrat, O. W. Lindwasser, S. Olenych, J. S. Bonifacino, M. W. Davidson, J. Lippincott-Schwartz, and H. F. Hess, “Imaging intracellular fluorescent proteins at nanometer resolution,” Science 313(5793), 1642–1645 (2006).
[CrossRef] [PubMed]

Stanley, S. L.

S. L. Stanley., “Amoebiasis,” Lancet 361(9362), 1025–1034 (2003).
[CrossRef] [PubMed]

Sternberg, P. W.

R. J. Sommer and P. W. Sternberg, “Changes of induction and competence during the evolution of vulva development in nematodes,” Science 265(5168), 114–118 (1994).
[CrossRef] [PubMed]

Van Blerkom, J.

J. Van Blerkom, H. Bell, and G. Henry, “The occurrence, recognition and developmental fate of pseudo-multipronuclear eggs after in-vitro fertilization of human oocytes,” Hum. Reprod. 2(3), 217–225 (1987).
[PubMed]

Weinberg, S.

Wilson, T.

M. J. Booth, M. A. A. Neil, R. Juskaitis, and T. Wilson, “Adaptive aberration correction in a confocal microscope,” Proc. Natl. Acad. Sci. U.S.A. 99(9), 5788–5792 (2002).
[CrossRef] [PubMed]

Wu, J. G.

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Supplementary Material (1)

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Figures (10)

Fig. 1
Fig. 1

Wavefront image sensor chip. a, Schematic of the device under a vertical plane illumination. The WIS apertures (white circles) are defined on the metal (gray) coated 2D CMOS image sensor chip (light gray grid), the transparent spacer separates the apertures away from the image sensor chip, and the aperture projections (red circles) are evenly distributed on the image sensor chip. b, Change of the transmission and shift of the aperture projections under an unknown light wave. c, Simulation of the diffraction (in SU8 resin) of a 6 μm diameter WIS aperture defined on a perfect electric conductor (PEC) layer illuminated by a halogen lamp. d, The experimental data showing the self-focusing effect of a WIS aperture on an Al coated glass cover slip. The insets are the cross-sections of the aperture diffraction perpendicular to the z axis.

Fig. 2
Fig. 2

Measuring the diffraction of the WIS aperture under the illumination of a halogen lamp. A 6 µm aperture was first etched on an Al coated (150 nm thick) glass cover slip (refractive index of 1.5), and then illuminated by a halogen lamp (the central wavelength was 0.6 µm and the FWHM of the spectrum was 0.2 µm). The cross-sections of the aperture diffraction at different z plane was imaged by a microscope with an oil (refractive index of 1.5) immersed 100 × objective (N.A. = 1.3) by moving the focal plane of the microscope along z axis with a micrometer with the interval of 2 µm.

Fig. 3
Fig. 3

Prototypes of the WIS and WM. a, Apertures with 6 μm diameter and 11 μm spacing defined on the Al coated WIS. b, Fully integrated WIS is the size of a dime. c, Converting a standard optical microscope into a WM by simply adding the WIS onto the camera port.

Fig. 4
Fig. 4

Calibration experiment for the normalized phase gradient measurement of the WIS. a, b, The experimental setup under a vertical illumination and a tilted illumination which imposes a specific normalized phase gradient θx or θy with respect to the WIS. c, d, the normalized phase gradient responses of the WIS in both the x and y directions. Each data point is the average normalized phase gradient measurement of the 350 apertures from the central row of our WIS; each error bar corresponds to the standard deviation among them.

Fig. 5
Fig. 5

Normalized intensity gradient can also induce a shift to each aperture projection spot of the WIS.

Fig. 6
Fig. 6

Images of polystyrene microspheres. a, b, Bright-field and DIC images. c, d, e, Intensity, normalized phase gradient images of the WM in the y and x directions. The white arrows represent the directions of the contrast enhancement.

Fig. 8
Fig. 8

(Media 1) Images of an unstained starfish embryo in the late gastrula stage. a, b, Bright-field and DIC images. c, d, e, Intensity, normalized phase gradient images of the WM in the y and x directions. f, Phase-gradient-vector magnitude image. g, h, Normalized phase gradient images of the WM in the 135̊ and 45̊ directions. The white arrows represent the directions of the contrast enhancement. α: gastrocoel.

Fig. 10
Fig. 10

Images of potato starch granules. a, b, Bright-field and DIC images. c, d, e, Intensity, normalized phase gradient images of the WM in the y and x directions. The white arrows represent the directions of the contrast enhancement.

Fig. 7
Fig. 7

Removing the component of the normalized intensity gradient from the normalized phase gradient image of the WIS in the x direction. (a) Normalized phase gradient image measured by the WIS. (b) Normalized intensity gradient induced image. (c) Corrected normalized phase gradient image. (d) Comparison among the line profiles from the above three images.

Fig. 9
Fig. 9

Images of a stained starfish embryo in the early gastrula stage. a, b, Bright-field and DIC images. c, d, e, Intensity, normalized phase gradient images of the WM in the y and x directions. f, Comparison of the line profiles between the DIC image and normalized phase gradient image of the WM in the y direction. α: blastocoel, β: the background, and γ: the fertilization membrane.

Equations (8)

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Δ s P h a s G r a d ( x , y ) H θ x ( x , y ) n = H λ 2 π n φ ( x , y ) x ,
s ˜ 0 = T / 2 T / 2 I ( s ) exp ( i 2 π T s ) d s .
s ˜ 1 = T / 2 T / 2 I ( s Δ s ) exp ( i 2 π T s ) d s = T / 2 Δ s T / 2 Δ s I ( u ) exp ( i 2 π T ( u + Δ s ) ) d u = exp ( i 2 π T Δ s ) T / 2 Δ s T / 2 Δ s I ( u ) exp ( i 2 π T u ) d u exp ( i 2 π T Δ s ) s ˜ 0 .
Δ s = T 2 π [ a n g l e ( s ˜ 1 ) a n g l e ( s ˜ 0 ) ] .
s ˜ 0 = m = 2 2 , n = 2 2 I m n ( s ) exp ( i 2 π 5 n ) s ˜ 1 = m = 2 , 2 n = 2 2 I m n ( s Δ s ) exp ( i 2 π 5 n ) Δ s = 11 μ m 2 π [ a n g l e ( s ˜ 1 ) a n g l e ( s ˜ 0 ) ] .
Δ s I n t e n G r a d = a a a 2 t 2 a 2 t 2 s ( I 0 + s I x | 0 ) d s d t a a a 2 t 2 a 2 t 2 ( I 0 + s I x | 0 ) d s d t = a 2 I x | 0 4 I 0 ,
Δ θ I n t e n G r a d _ X = n a 2 I x | 0 4 H I 0 .
Δ θ P h a s G r a d _ X = Δ θ W I S _ X Δ θ I n t e n G r a d _ X .

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