Abstract

Differential phase contrast (DPC) is a non-interferometric quantitative phase imaging method achieved by using an asymmetric imaging procedure. We report a pupil modulation differential phase contrast (PMDPC) imaging method by filtering a sample’s Fourier domain with half-circle pupils. A phase gradient image is captured with each half-circle pupil, and a quantitative high resolution phase image is obtained after a deconvolution process with a minimum of two phase gradient images. Here, we introduce PMDPC quantitative phase image reconstruction algorithm and realize it experimentally in a 4f system with an SLM placed at the pupil plane. In our current experimental setup with the numerical aperture of 0.36, we obtain a quantitative phase image with a resolution of 1.73μm after computationally removing system aberrations and refocusing. We also extend the depth of field digitally by 20 times to ±50μm with a resolution of 1.76μm.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref]
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2016 (2)

X. Ou, J. Chung, R. Horstmeyer, and C. Yang, “Aperture scanning Fourier ptychographic microscopy,” Biomed. Opt. Express 7(8), 3140–3150 (2016).
[Crossref] [PubMed]

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nature Photonics 10(2), 68–71 (2016).
[Crossref]

2015 (6)

2014 (5)

2013 (6)

2012 (1)

2011 (2)

2010 (1)

2009 (1)

2006 (2)

2004 (1)

1998 (1)

1997 (1)

1985 (1)

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[Crossref] [PubMed]

1984 (2)

D. K. Hamilton and C. J. Sheppard, “Differential phase contrast in scanning optical microscopy,” Journal of microscopy 133(1), 27–39 (1984).
[Crossref]

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

1982 (1)

1975 (1)

1967 (1)

S. Lowenthal and Y. Belvaux, “Observation of phase objects by optically processed Hilbert transform,” Appl. Phys. Lett. 11(2), 49–51 (1967).
[Crossref]

1955 (1)

G. Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Radium 16(9), 9S–11S (1955).

1948 (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

1942 (1)

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

Barankov, R.

Baritaux, J. C.

Barty, A. N. T. O. N.

Belvaux, Y.

S. Lowenthal and Y. Belvaux, “Observation of phase objects by optically processed Hilbert transform,” Appl. Phys. Lett. 11(2), 49–51 (1967).
[Crossref]

Bernet, S.

Bertero, M.

M. Bertero and P. Boccacc, Introduction to inverse problems in imaging (CRC, 1998).
[Crossref]

Bhaduri, B.

Bian, Z.

Boccacc, P.

M. Bertero and P. Boccacc, Introduction to inverse problems in imaging (CRC, 1998).
[Crossref]

Chu, K. K.

Chung, J.

Claus, R. A.

Collier, R.

R. Collier, Optical holography (Elsevier, 2013).

Coté, D.

Daradich, A.

Dasari, R. R.

Dauwels, J.

Davison, I.

Ding, H.

Dong, S.

Feld, M. S.

Fienup, J. R.

Ford, T. N.

Fürhapter, S.

Gabor, D.

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Gasecka, A.

Gillette, M. U.

Goodman, J. W.

Gross, L.

Guo, K.

Hamilton, D. K.

D. K. Hamilton and C. J. Sheppard, “Differential phase contrast in scanning optical microscopy,” Journal of microscopy 133(1), 27–39 (1984).
[Crossref]

Heintzmann, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nature Photonics 10(2), 68–71 (2016).
[Crossref]

Hoffman, R.

Horstmeyer, R.

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nature Photonics 10(2), 68–71 (2016).
[Crossref]

X. Ou, J. Chung, R. Horstmeyer, and C. Yang, “Aperture scanning Fourier ptychographic microscopy,” Biomed. Opt. Express 7(8), 3140–3150 (2016).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
[Crossref] [PubMed]

R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped Fourier coding for optical aberration removal,” Opt. Express 22(20), 24062–24080 (2014).
[Crossref] [PubMed]

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22(11), 13586–13599 (2014).
[Crossref] [PubMed]

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

G. Zheng, X. Ou, R. Horstmeyer, and C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21, 15131–15143 (2013).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

Iglesias, I.

I. Iglesias and F. Vargas-Martin, “Quantitative phase microscopy of transparent samples using a liquid crystal display,” Journal of biomedical optics 18(2), 026015(2013).
[Crossref]

I. Iglesias, “Pyramid phase microscopy,” Opt. Lett. 36, 3636–3638 (2011).
[Crossref] [PubMed]

Ikeda, T.

Jesacher, A.

Jingshan, Z.

Joo, C.

Jung, D.

Kachar, B.

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[Crossref] [PubMed]

Kim, U.

Kubota, S.

Lee, D.

Lowenthal, S.

S. Lowenthal and Y. Belvaux, “Observation of phase objects by optically processed Hilbert transform,” Appl. Phys. Lett. 11(2), 49–51 (1967).
[Crossref]

Maurer, C.

Mehta, S. B.

Mertz, J.

Millet, L.

Mir, M.

Naulleau, P. P.

Neureuther, A. R.

Nomarski, G.

G. Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Radium 16(9), 9S–11S (1955).

Nugent, K. A.

Ou, X.

Paganin, D.

Parthasarathy, Ashwin. B.

Popescu, G.

Ritsch-Marte, M.

Roberts, A.

Rogers, J.

Ryu, S.

Sheppard, C. J.

Sheppard, C. J. R.

Shiradkar, R.

Streibl, N.

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

Tangella, K.

Tian, L.

Unarunotai, S.

Vargas-Martin, F.

I. Iglesias and F. Vargas-Martin, “Quantitative phase microscopy of transparent samples using a liquid crystal display,” Journal of biomedical optics 18(2), 026015(2013).
[Crossref]

Vest, C. M.

C. M. Vest, Holographic Interferometry (John Wiley and Sons, Inc., 1979).

Waller, L.

Wang, J.

Wang, Z.

Xin, H.

Yamaguchi, I.

Yang, C.

Zernike, F.

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

Zhang, T.

Zheng, G.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

S. Lowenthal and Y. Belvaux, “Observation of phase objects by optically processed Hilbert transform,” Appl. Phys. Lett. 11(2), 49–51 (1967).
[Crossref]

Biomed. Opt. Express (4)

J. Opt. Soc. Am. A (2)

J. Phys. Radium (1)

G. Nomarski, “Differential microinterferometer with polarized waves,” J. Phys. Radium 16(9), 9S–11S (1955).

Journal of biomedical optics (1)

I. Iglesias and F. Vargas-Martin, “Quantitative phase microscopy of transparent samples using a liquid crystal display,” Journal of biomedical optics 18(2), 026015(2013).
[Crossref]

Journal of microscopy (1)

D. K. Hamilton and C. J. Sheppard, “Differential phase contrast in scanning optical microscopy,” Journal of microscopy 133(1), 27–39 (1984).
[Crossref]

Nature (1)

D. Gabor, “A new microscopic principle,” Nature 161(4098), 777–778 (1948).
[Crossref] [PubMed]

Nature photonics (1)

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

R. Horstmeyer, R. Heintzmann, G. Popescu, L. Waller, and C. Yang, “Standardizing the resolution claims for coherent microscopy,” Nature Photonics 10(2), 68–71 (2016).
[Crossref]

Opt. Commun. (1)

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

Opt. Express (9)

Z. Jingshan, R. A. Claus, J. Dauwels, L. Tian, and L. Waller, “Transport of intensity phase imaging by intensity spectrum fitting of exponentially spaced defocus planes,” Opt. Express 22(9), 10661–10674 (2014).
[Crossref] [PubMed]

S. Bernet, A. Jesacher, S. Fürhapter, C. Maurer, and M. Ritsch-Marte, “Quantitative imaging of complex samples by spiral phase contrast microscopy,” Opt. Express 14(9), 3792–3805 (2006).
[Crossref] [PubMed]

X. Ou, R. Horstmeyer, G. Zheng, and C. Yang, “High numerical aperture Fourier ptychography: principle, implementation and characterization,” Opt. Express 23(3), 3472–3491 (2015).
[Crossref] [PubMed]

R. Horstmeyer, X. Ou, J. Chung, G. Zheng, and C. Yang, “Overlapped Fourier coding for optical aberration removal,” Opt. Express 22(20), 24062–24080 (2014).
[Crossref] [PubMed]

S. Dong, R. Horstmeyer, R. Shiradkar, K. Guo, X. Ou, Z. Bian, H. Xin, and G. Zheng, “Aperture-scanning Fourier ptychography for 3D refocusing and super-resolution macroscopic imaging,” Opt. Express 22(11), 13586–13599 (2014).
[Crossref] [PubMed]

L. Tian and L. Waller, “Quantitative differential phase contrast imaging in an LED array microscope,” Opt. Express 23(9), 11394–11403 (2015).
[Crossref] [PubMed]

R. A. Claus, P. P. Naulleau, A. R. Neureuther, and L. Waller, “Quantitative phase retrieval with arbitrary pupil and illumination,” Opt. Express 23, 26672–26682 (2015).
[Crossref] [PubMed]

G. Zheng, X. Ou, R. Horstmeyer, and C. Yang, “Characterization of spatially varying aberrations for wide field-of-view microscopy,” Opt. Express 21, 15131–15143 (2013).
[Crossref] [PubMed]

Z. Wang, L. Millet, M. Mir, H. Ding, S. Unarunotai, J. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express 19, 1016–1026 (2011).
[Crossref] [PubMed]

Opt. Lett. (9)

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] [PubMed]

I. Iglesias, “Pyramid phase microscopy,” Opt. Lett. 36, 3636–3638 (2011).
[Crossref] [PubMed]

Ashwin. B. Parthasarathy, K. K. Chu, T. N. Ford, and J. Mertz, “Quantitative phase imaging using a partitioned detection aperture,” Opt. Lett. 37 (19), 4062–4064 (2012).
[Crossref] [PubMed]

R. Barankov and J. Mertz, “Single-exposure surface profilometry using partitioned aperture wavefront imaging,” Opt. Lett. 38, 3961–3964 (2013).
[Crossref] [PubMed]

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

L. Tian, J. Wang, and L. Waller, “3D differential phase-contrast microscopy with computational illumination using an LED array,” Opt. Lett. 39(5), 1326–1329 (2014).
[Crossref] [PubMed]

A. N. T. O. N. Barty, K. A. Nugent, D. Paganin, and A. Roberts, “Quantitative optical phase microscopy,” Opt. Lett. 23(11), 817–819 (1998).
[Crossref]

X. Ou, R. Horstmeyer, C. Yang, and G. Zheng, “Quantitative phase imaging via Fourier ptychographic microscopy,” Opt. Lett. 38(22), 4845–4848 (2013).
[Crossref] [PubMed]

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
[Crossref] [PubMed]

Optica (1)

Physica (1)

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

Science (1)

B. Kachar, “Asymmetric illumination contrast: a method of image formation for video light microscopy,” Science 227, 766–768 (1985).
[Crossref] [PubMed]

Other (5)

M. Bertero and P. Boccacc, Introduction to inverse problems in imaging (CRC, 1998).
[Crossref]

R. Collier, Optical holography (Elsevier, 2013).

J. W. Goodman, Introduction to Fourier optics (Roberts and Company Publishers, 2005).

C. M. Vest, Holographic Interferometry (John Wiley and Sons, Inc., 1979).

J. Chung, H. Lu, X. Ou, H. Zhou, and C. Yang, “Wide-field Fourier ptychographic microscopy using laser illumination source,” http://arxiv.org/abs/1602.02901 .

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Figures (11)

Fig. 1
Fig. 1

Principle of PMDPC algorithm. (a) A 4f optical system setup with an adjustable pupil. A simulated complex sample (b) is placed at the front focal plane of l1 and modulated at pupil plane by half-circle pupil functions (c), forming phase gradient images on camera (d). In PMDPC reconstruction process, IDPC (e) is constructed by phase gradient images. The Fourier spectrum of IDPC (f) is deconvoled with DPC transfer function (g). Reconstructed phase (h) is obtained after deconvolution process following Eq. (10). The PMDPC reconstructed phase is comparable with diffraction limited phase information of the sample (i).

Fig. 2
Fig. 2

Red solid line plots the relationship between the reconstruction error, E and the peak-to-trough phase magnitude of the sample, ϕpeak–to–trough. Blue dashed line indicates where E/ϕpeak–to–trough equals to 5%. When ϕpeak–to–trough ≤ 0.74π, E/ϕpeak–to–trough is below 5%. Inserted figures (a) and (b) show the PMDPC reconstructed phase images when ϕpeak–to–trough equals to 0.4π and 1.6π, respectively. The ground truth and reconstructed phase profile along the red dashed line are also plotted in both cases on the right side.

Fig. 3
Fig. 3

PMDPC Experimental setup. Light from a He-Ne laser passes through a rotating diffuser and l1, coupled into a multimode fiber. l2 collimates the beam coming out of the fiber which then incidents the sample. Light from the sample is collected by the objective (Olympus 20× 0.4NA, f = 9mm). The objective’s focal plane is relayed by lenses l3 and l4 to the surface SLM (liquid crystal on silicon display, model: Holoeye LC-R 1080, refresh rate: 60Hz). The modulated light passes through the tube lens (Thorlabs ITL200, f = 200mm) to form a phase gradient image on the CCD. LP1 and LP2 are polarizers with perpendicular polarization directions to achieve the SLM’s amplitude modulation.

Fig. 4
Fig. 4

PMDPC phase reconstruction result of 10μm microbeads. (a) shows vertical and horizontal phase gradient image pairs and corresponding pupil functions. (b) and (c) are PMDPC and FPM reconstructed phase images and right side of them are zoom-in images of the boxed square. (d) plot the phase distribution along the black dashed line across the bead diameter of both reconstructed results and microbead sample’s estimated phase profile. (scale bar: 50μm)

Fig. 5
Fig. 5

Siemens star phase target resolution calibration process.(a) shows captured phase gradient images and corresponding pupil functions. DPC images (b) of each pupil pair are constructed following equation 7. (c) shows PMDPC reconstructed phase (i) and captured intensity (ii). (e) shows the phase image after deconvolution with calibrated pupil aberrations mapped in (d). (f) is the phase image after refocusing to the sample plane. (g) plots the phase distribution along the dashed circle in (f). (scale bar: 10μm)

Fig. 6
Fig. 6

Depth of field extension demonstration. Intensity images captured under 20×, 0.4NA objective when Siemens star phase target is defocused to different z planes are shown in (a) correspondingly. (b) shows the sample reconstruction results when z = −48μm, where resolution is greatly blurred due to defocusing. (c)–(f) are the phase images after digitally propagating back to the sample plane. Phase distributions along the dashed red circles are plotted on the right side of each image separately.

Fig. 7
Fig. 7

PMDPC image of frog blood sample. (a) and (b) are reconstructed intensity and phase distributions obtained following the procedure in Fig. 5. Phase contrast image (c) is generated with the reconstructed field. The same area of the sample is also imaged under a conventional phase contrast microscope for comparison, shown in (d). (scale bar: 50μm)

Fig. 8
Fig. 8

Phase imaging with different numbers of measurements. The first two rows in (a) show PMDPC reconstruction results using one pair and two pairs of phase gradient image measurements, respectively. The difference between the reconstruction results are shown in the third row. Comparison with FPM reconstruction is shown in (b) with microbead sample. Reconstruction error, E is shown for both 1-pair and 2-pairs reconstruction results.

Fig. 9
Fig. 9

Illumination NA analysis. (a) shows the relation of NAi with Fourier plane. The fiber end is imaged to SLM plane with a magnification ratio of fobj/f2. (b) shows the SLM display pattern considering the finite NAi in experiment (not scaled to real size, only for demonstration to show the center clearly, unit: pixel).

Fig. 10
Fig. 10

Finite NAi simulation. (a) is sample’s original phase, (b)–(d) are reconstruction results with different illumination NA. Reconstruction errors, E are calculated with Eq. (11).

Fig. 11
Fig. 11

PMDPC phase sensitivity. A 40 × 40 region is selected in the reconstructed phase image, where no features are present. The sensitivity is calculated as 0.034 rad.

Equations (17)

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I ( x , y ) = | 1 { { o ( x , y ) } P ( u , v ) } | 2 .
I ˜ ( u , v ) = [ O ( u , v ) P ( u , v ) ] * [ O * ( u , v ) P * ( u , v ) ]
I ˜ ( u , v ) = O ( u ξ , v η ) O * ( ξ , η ) P ( u ξ , v η ) P * ( ξ , η ) d ξ d η .
I ˜ ( u , v ) = P ( 0 ) P * ( 0 ) δ ( u , v ) + H amp A ( u , v ) + H ph Φ ( u , v ) ,
H amp = [ P ( u , v ) P * ( 0 ) + P ( 0 ) P * ( u , v ) ] ,
H ph = i [ P ( u , v ) P * ( 0 ) P ( 0 ) P * ( u , v ) ] .
I DPC = I 1 I 2 I 1 + I 2 .
I ˜ DPC ( u , v ) = H DPC ( u , v ) Φ ( u , v ) ,
H DPC ( u , v ) = H 1 , ph ( u , v ) H 2 , ph ( u , v ) 2 P ( 0 ) P * ( 0 ) .
ϕ r ( u , v ) = 1 { j H j , DPC * ( u , v ) I ˜ j , DPC ( u , v ) j | H j , DPC | 2 + } ,
E = 1 N x , y | ϕ ϕ r + α | 2
I ( x , y ) = | o ( x , y ) | 2 .
o ( x , y ) = | o ( x , y ) | e i ϕ ( x , y ) = I ( x , y ) e i ϕ ( x , y ) .
λ NA = 633 nm 0.36 = 1.75 μ m .
d zero frequency = f obj f 2 × d fiber = 9 mm 45 mm × 300 μ m = 60 μ m
I ˜ ( u , v ) = | P ( 0 ) | 2 δ ( u , v ) + H ph Φ ( u , v ) + n ˜ ( u , v ) .
I ( x , y ) = 1 + H { ϕ } ( x , y ) + n ( x , y ) ,

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