Abstract

In this paper, we extend our recent work on partially coherent quantitative phase imaging (pcQPI) from two-dimensional (2D) to three-dimensional (3D) imaging of weakly scattering samples. Due to the mathematical complexity, most theoretical modeling of quantitative phase image formation under partial coherence has focused on thin, well-focused samples. It is unclear how these abberations are affected by defocusing. Also, as 3D QPI techniques continue to develop, a better model needs to be developed to understand and quantify these aberrations when imaging thicker samples. Here, using the first order Born’s approximation, we derived a mathematical framework that provides an intuitive model of image formation under varying degrees of coherence. Our description provides a clear connection between the halo effect and phase underestimation, defocusing and the 3D structure of the sample under investigation. Our results agree very well with the experiments and show that the microscope objective defines the sectioning ability of the imaging system while the condenser lens is responsible for the halo effect.

© 2016 Optical Society of America

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References

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2016 (7)

J. C. Wyant, “The evolution of interferometry from metrology to biomedical applications,” Proc. SPIE 9718, 97180 (2016).

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination,” Proc. SPIE 9718, 97180 (2016).

C. J. Sheppard and S. B. Mehta, “Phase microscope imaging in phase space,” Proc. SPIE 9178A, 97180 (2016).

J. Dohet-Eraly, C. Yourassowsky, A. El Mallahi, and F. Dubois, “Partial spatial coherence illumination in digital holographic microscopy: quantitative analysis of the resulting noise reduction,” Proc. SPIE 9890, 989004 (2016).

J. Dohet-Eraly, C. Yourassowsky, A. E. Mallahi, and F. Dubois, “Quantitative assessment of noise reduction with partial spatial coherence illumination in digital holographic microscopy,” Opt. Lett. 41(1), 111–114 (2016).
[Crossref] [PubMed]

Y. I. Nesterets and T. E. Gureyev, “Partially coherent contrast-transfer-function approximation,” J. Opt. Soc. Am. A 33(4), 464–474 (2016).
[Crossref] [PubMed]

A. Ahmad, V. Dubey, G. Singh, V. Singh, and D. S. Mehta, “Quantitative phase imaging of biological cells using spatially low and temporally high coherent light source,” Opt. Lett. 41(7), 1554–1557 (2016).
[Crossref]

2015 (6)

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2(2), 104–111 (2015).
[Crossref]

S. Aknoun, P. Bon, J. Savatier, B. Wattellier, and S. Monneret, “Quantitative retardance imaging of biological samples using quadriwave lateral shearing interferometry,” Opt. Express 23(12), 16383–16406 (2015).
[Crossref] [PubMed]

M. H. Jenkins and T. K. Gaylord, “Quantitative phase microscopy via optimized inversion of the phase optical transfer function,” Appl. Opt. 54(28), 8566–8579 (2015).
[Crossref] [PubMed]

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective,” Opt. Lasers Eng. 71, 20–32 (2015).
[Crossref]

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

2014 (6)

2013 (5)

2012 (3)

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Z. Yin, T. Kanade, and M. Chen, “Understanding the phase contrast optics to restore artifact-free microscopy images for segmentation,” Med. Image Anal. 16(5), 1047–1062 (2012).
[Crossref] [PubMed]

B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett. 37(6), 1094–1096 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (2)

S. B. Mehta and C. J. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” ‎,” J. Mod. Opt. 57(9), 718–739 (2010).
[Crossref]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

2005 (1)

2004 (1)

2000 (1)

M. Somekh, C. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

1998 (1)

1995 (1)

D. Zicha and G. Dunn, “An image processing system for cell behaviour studies in subconfluent cultures,” J. Microsc. 179(1), 11–21 (1995).
[Crossref]

1985 (1)

1981 (1)

T. Wilson and C. J. Sheppard, “The halo effect of image processing by spatial frequency filtering,” Optik (Stuttg.) 59, 19–23 (1981).

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[Crossref] [PubMed]

Ahmad, A.

Aknoun, S.

Asundi, A.

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective,” Opt. Lasers Eng. 71, 20–32 (2015).
[Crossref]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38(18), 3538–3541 (2013).
[Crossref] [PubMed]

Badizadegan, K.

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004).
[Crossref] [PubMed]

Barbastathis, G.

Best, C. A.

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

Bhaduri, B.

Bian, Z.

Bon, P.

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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Chen, M.

Z. Yin, T. Kanade, and M. Chen, “Understanding the phase contrast optics to restore artifact-free microscopy images for segmentation,” Med. Image Anal. 16(5), 1047–1062 (2012).
[Crossref] [PubMed]

Chen, Q.

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective,” Opt. Lasers Eng. 71, 20–32 (2015).
[Crossref]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38(18), 3538–3541 (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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Clark, J. N.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Dasari, R. R.

Deflores, L. P.

Devaney, A. J.

Dimarzio, C. A.

Ding, H.

Do, M. N.

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

Dohet-Eraly, J.

J. Dohet-Eraly, C. Yourassowsky, A. El Mallahi, and F. Dubois, “Partial spatial coherence illumination in digital holographic microscopy: quantitative analysis of the resulting noise reduction,” Proc. SPIE 9890, 989004 (2016).

J. Dohet-Eraly, C. Yourassowsky, A. E. Mallahi, and F. Dubois, “Quantitative assessment of noise reduction with partial spatial coherence illumination in digital holographic microscopy,” Opt. Lett. 41(1), 111–114 (2016).
[Crossref] [PubMed]

Dong, S.

Dubey, V.

Dubois, F.

Dunn, G.

D. Zicha and G. Dunn, “An image processing system for cell behaviour studies in subconfluent cultures,” J. Microsc. 179(1), 11–21 (1995).
[Crossref]

Edwards, C.

Edwards, C. A.

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

El Mallahi, A.

J. Dohet-Eraly, C. Yourassowsky, A. El Mallahi, and F. Dubois, “Partial spatial coherence illumination in digital holographic microscopy: quantitative analysis of the resulting noise reduction,” Proc. SPIE 9890, 989004 (2016).

A. El Mallahi, C. Minetti, and F. Dubois, “Automated three-dimensional detection and classification of living organisms using digital holographic microscopy with partial spatial coherent source: application to the monitoring of drinking water resources,” Appl. Opt. 52(1), A68–A80 (2013).
[Crossref] [PubMed]

Falaggis, K.

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination,” Proc. SPIE 9718, 97180 (2016).

Feld, M. S.

Gaudette, T. J.

Gaylord, T. K.

Gillette, M. U.

Goddard, L. L.

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

C. Edwards, B. Bhaduri, T. Nguyen, B. G. Griffin, H. Pham, T. Kim, G. Popescu, and L. L. Goddard, “Effects of spatial coherence in diffraction phase microscopy,” Opt. Express 22(5), 5133–5146 (2014).
[Crossref] [PubMed]

B. Bhaduri, C. Edwards, H. Pham, R. J. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photonics 6(1), 57–119 (2014).
[Crossref]

C. Edwards, B. Bhaduri, B. G. Griffin, L. L. Goddard, and G. Popescu, “Epi-illumination diffraction phase microscopy with white light,” Opt. Lett. 39(21), 6162–6165 (2014).
[Crossref] [PubMed]

T. H. Nguyen, C. Edwards, L. L. Goddard, and G. Popescu, “Quantitative phase imaging with partially coherent illumination,” Opt. Lett. 39(19), 5511–5514 (2014).
[Crossref] [PubMed]

Goh, J.

M. Somekh, C. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

Griffin, B. G.

Guo, K.

Gureyev, T. E.

Harder, R.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Henle, M. L.

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Hogenboom, D. O.

Horstmeyer, R.

Huang, X.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Ikeda, T.

Iwai, H.

Jenkins, M. H.

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 (Basel) 13(4), 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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Kalyanov, A.

A. Kalyanov, N. Talaykova, and V. Ryabukho, “Formal theory of diffraction phase microscopy,” Proc. SPIE 9448, 944817 (2014).

Kanade, T.

Z. Yin, T. Kanade, and M. Chen, “Understanding the phase contrast optics to restore artifact-free microscopy images for segmentation,” Med. Image Anal. 16(5), 1047–1062 (2012).
[Crossref] [PubMed]

Kim, K.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Kim, T.

Kim, Y.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

Kim, Y.-J.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

Kozacki, T.

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination,” Proc. SPIE 9718, 97180 (2016).

Kuriabova, T.

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

Lee, K.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

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 (Basel) 13(4), 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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Levine, A. J.

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

Lindberg, S. C.

Majeed, H.

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

Mallahi, A. E.

Martinez-Carranza, J.

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination,” Proc. SPIE 9718, 97180 (2016).

Mehta, D. S.

Mehta, S. B.

C. J. Sheppard and S. B. Mehta, “Phase microscope imaging in phase space,” Proc. SPIE 9178A, 97180 (2016).

S. B. Mehta and C. J. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” ‎,” J. Mod. Opt. 57(9), 718–739 (2010).
[Crossref]

Millet, L.

Minetti, C.

Mir, M.

Monneret, S.

Nesterets, Y. I.

Nguyen, T.

Nguyen, T. H.

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

B. Bhaduri, C. Edwards, H. Pham, R. J. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photonics 6(1), 57–119 (2014).
[Crossref]

T. H. Nguyen, C. Edwards, L. L. Goddard, and G. Popescu, “Quantitative phase imaging with partially coherent illumination,” Opt. Lett. 39(19), 5511–5514 (2014).
[Crossref] [PubMed]

Ou, X.

Park, H.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Park, Y.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

Petruccelli, J. C.

Pham, H.

Popescu, G.

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

C. Edwards, B. Bhaduri, T. Nguyen, B. G. Griffin, H. Pham, T. Kim, G. Popescu, and L. L. Goddard, “Effects of spatial coherence in diffraction phase microscopy,” Opt. Express 22(5), 5133–5146 (2014).
[Crossref] [PubMed]

B. Bhaduri, C. Edwards, H. Pham, R. J. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photonics 6(1), 57–119 (2014).
[Crossref]

C. Edwards, B. Bhaduri, B. G. Griffin, L. L. Goddard, and G. Popescu, “Epi-illumination diffraction phase microscopy with white light,” Opt. Lett. 39(21), 6162–6165 (2014).
[Crossref] [PubMed]

T. H. Nguyen, C. Edwards, L. L. Goddard, and G. Popescu, “Quantitative phase imaging with partially coherent illumination,” Opt. Lett. 39(19), 5511–5514 (2014).
[Crossref] [PubMed]

B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett. 37(6), 1094–1096 (2012).
[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(2), 1016–1026 (2011).
[Crossref] [PubMed]

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005).
[Crossref] [PubMed]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004).
[Crossref] [PubMed]

Qu, W.

Robinson, I. K.

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Rogers, J.

Ryabukho, V.

A. Kalyanov, N. Talaykova, and V. Ryabukho, “Formal theory of diffraction phase microscopy,” Proc. SPIE 9448, 944817 (2014).

Savatier, J.

See, C.

M. Somekh, C. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

Sheppard, C. J.

C. J. Sheppard and S. B. Mehta, “Phase microscope imaging in phase space,” Proc. SPIE 9178A, 97180 (2016).

S. B. Mehta and C. J. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” ‎,” J. Mod. Opt. 57(9), 718–739 (2010).
[Crossref]

T. Wilson and C. J. Sheppard, “The halo effect of image processing by spatial frequency filtering,” Optik (Stuttg.) 59, 19–23 (1981).

Shin, S.

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

Shiradkar, R.

Singh, G.

Singh, V.

Somekh, M.

M. Somekh, C. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

Streibl, N.

Talaykova, N.

A. Kalyanov, N. Talaykova, and V. Ryabukho, “Formal theory of diffraction phase microscopy,” Proc. SPIE 9448, 944817 (2014).

Tian, L.

Unarunotai, S.

Vaughan, J. C.

Waller, L.

L. Tian and L. Waller, “3D intensity and phase imaging from light field measurements in an LED array microscope,” Optica 2(2), 104–111 (2015).
[Crossref]

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective,” Opt. Lasers Eng. 71, 20–32 (2015).
[Crossref]

Wang, Z.

Wattellier, B.

Wilson, T.

T. Wilson and C. J. Sheppard, “The halo effect of image processing by spatial frequency filtering,” Optik (Stuttg.) 59, 19–23 (1981).

Wyant, J. C.

J. C. Wyant, “The evolution of interferometry from metrology to biomedical applications,” Proc. SPIE 9718, 97180 (2016).

Xin, H.

Yang, C.

Yin, Z.

Z. Yin, T. Kanade, and M. Chen, “Understanding the phase contrast optics to restore artifact-free microscopy images for segmentation,” Med. Image Anal. 16(5), 1047–1062 (2012).
[Crossref] [PubMed]

Yourassowsky, C.

J. Dohet-Eraly, C. Yourassowsky, A. E. Mallahi, and F. Dubois, “Quantitative assessment of noise reduction with partial spatial coherence illumination in digital holographic microscopy,” Opt. Lett. 41(1), 111–114 (2016).
[Crossref] [PubMed]

J. Dohet-Eraly, C. Yourassowsky, A. El Mallahi, and F. Dubois, “Partial spatial coherence illumination in digital holographic microscopy: quantitative analysis of the resulting noise reduction,” Proc. SPIE 9890, 989004 (2016).

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[Crossref] [PubMed]

Zheng, G.

Zhou, R. J.

B. Bhaduri, C. Edwards, H. Pham, R. J. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photonics 6(1), 57–119 (2014).
[Crossref]

Zicha, D.

D. Zicha and G. Dunn, “An image processing system for cell behaviour studies in subconfluent cultures,” J. Microsc. 179(1), 11–21 (1995).
[Crossref]

Zuo, C.

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective,” Opt. Lasers Eng. 71, 20–32 (2015).
[Crossref]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38(18), 3538–3541 (2013).
[Crossref] [PubMed]

Adv. Opt. Photonics (1)

B. Bhaduri, C. Edwards, H. Pham, R. J. Zhou, T. H. Nguyen, L. L. Goddard, and G. Popescu, “Diffraction phase microscopy: principles and applications in materials and life sciences,” Adv. Opt. Photonics 6(1), 57–119 (2014).
[Crossref]

Appl. Opt. (2)

J. Microsc. (1)

D. Zicha and G. Dunn, “An image processing system for cell behaviour studies in subconfluent cultures,” J. Microsc. 179(1), 11–21 (1995).
[Crossref]

J. Mod. Opt. (1)

S. B. Mehta and C. J. Sheppard, “Using the phase-space imager to analyze partially coherent imaging systems: bright-field, phase contrast, differential interference contrast, differential phase contrast, and spiral phase contrast,” ‎,” J. Mod. Opt. 57(9), 718–739 (2010).
[Crossref]

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

Med. Image Anal. (1)

Z. Yin, T. Kanade, and M. Chen, “Understanding the phase contrast optics to restore artifact-free microscopy images for segmentation,” Med. Image Anal. 16(5), 1047–1062 (2012).
[Crossref] [PubMed]

Nat. Commun. (1)

J. N. Clark, X. Huang, R. Harder, and I. K. Robinson, “High-resolution three-dimensional partially coherent diffraction imaging,” Nat. Commun. 3, 993 (2012).
[Crossref] [PubMed]

Opt. Commun. (1)

M. Somekh, C. See, and J. Goh, “Wide field amplitude and phase confocal microscope with speckle illumination,” Opt. Commun. 174(1-4), 75–80 (2000).
[Crossref]

Opt. Express (5)

Opt. Lasers Eng. (1)

C. Zuo, Q. Chen, L. Tian, L. Waller, and A. Asundi, “Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective,” Opt. Lasers Eng. 71, 20–32 (2015).
[Crossref]

Opt. Lett. (10)

T. H. Nguyen, C. Edwards, L. L. Goddard, and G. Popescu, “Quantitative phase imaging with partially coherent illumination,” Opt. Lett. 39(19), 5511–5514 (2014).
[Crossref] [PubMed]

C. Edwards, B. Bhaduri, B. G. Griffin, L. L. Goddard, and G. Popescu, “Epi-illumination diffraction phase microscopy with white light,” Opt. Lett. 39(21), 6162–6165 (2014).
[Crossref] [PubMed]

C. Zuo, Q. Chen, W. Qu, and A. Asundi, “Noninterferometric single-shot quantitative phase microscopy,” Opt. Lett. 38(18), 3538–3541 (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]

D. O. Hogenboom, C. A. Dimarzio, T. J. Gaudette, A. J. Devaney, and S. C. Lindberg, “Three-dimensional images generated by quadrature interferometry,” Opt. Lett. 23(10), 783–785 (1998).
[Crossref] [PubMed]

G. Popescu, L. P. Deflores, J. C. Vaughan, K. Badizadegan, H. Iwai, R. R. Dasari, and M. S. Feld, “Fourier phase microscopy for investigation of biological structures and dynamics,” Opt. Lett. 29(21), 2503–2505 (2004).
[Crossref] [PubMed]

T. Ikeda, G. Popescu, R. R. Dasari, and M. S. Feld, “Hilbert phase microscopy for investigating fast dynamics in transparent systems,” Opt. Lett. 30(10), 1165–1167 (2005).
[Crossref] [PubMed]

B. Bhaduri, H. Pham, M. Mir, and G. Popescu, “Diffraction phase microscopy with white light,” Opt. Lett. 37(6), 1094–1096 (2012).
[Crossref] [PubMed]

A. Ahmad, V. Dubey, G. Singh, V. Singh, and D. S. Mehta, “Quantitative phase imaging of biological cells using spatially low and temporally high coherent light source,” Opt. Lett. 41(7), 1554–1557 (2016).
[Crossref]

J. Dohet-Eraly, C. Yourassowsky, A. E. Mallahi, and F. Dubois, “Quantitative assessment of noise reduction with partial spatial coherence illumination in digital holographic microscopy,” Opt. Lett. 41(1), 111–114 (2016).
[Crossref] [PubMed]

Optica (1)

Optik (Stuttg.) (1)

T. Wilson and C. J. Sheppard, “The halo effect of image processing by spatial frequency filtering,” Optik (Stuttg.) 59, 19–23 (1981).

Proc. Natl. Acad. Sci. U.S.A. (1)

Y. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A. 107(15), 6731–6736 (2010).
[Crossref] [PubMed]

Proc. SPIE (7)

J. C. Wyant, “The evolution of interferometry from metrology to biomedical applications,” Proc. SPIE 9718, 97180 (2016).

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Enhanced lateral resolution for phase retrieval based on the transport of intensity equation with tilted illumination,” Proc. SPIE 9718, 97180 (2016).

S. Shin, Y. Kim, K. Lee, K. Kim, Y.-J. Kim, H. Park, and Y. Park, “Common-path diffraction optical tomography with a low-coherence illumination for reducing speckle noise,” Proc. SPIE 9336, 933629 (2015).

T. H. Nguyen, H. Majeed, C. A. Edwards, M. N. Do, L. L. Goddard, and G. Popescu, “Halo-free quantitative phase imaging with partially coherent light,” Proc. SPIE 9336, 93360 (2015).

C. J. Sheppard and S. B. Mehta, “Phase microscope imaging in phase space,” Proc. SPIE 9178A, 97180 (2016).

J. Dohet-Eraly, C. Yourassowsky, A. El Mallahi, and F. Dubois, “Partial spatial coherence illumination in digital holographic microscopy: quantitative analysis of the resulting noise reduction,” Proc. SPIE 9890, 989004 (2016).

A. Kalyanov, N. Talaykova, and V. Ryabukho, “Formal theory of diffraction phase microscopy,” Proc. SPIE 9448, 944817 (2014).

Science (1)

F. Zernike, “How I discovered phase contrast,” Science 121(3141), 345–349 (1955).
[Crossref] [PubMed]

Sensors (Basel) (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 (Basel) 13(4), 4170–4191 (2013).
[Crossref] [PubMed]

Other (6)

Z. Monemhaghdoust, P. De Gol, F. Montfort, Y. Emery, C. Depeursinge, and C. Moser, “Towards an incoherent off-axis digital holographic microscope,” in SPIE BiOS(International Society for Optics and Photonics2015), pp. 93360E–93360E–93365.

G. Popescu, Quantitative Phase Imaging of Cells and Tissues (Mcgraw-Hill, 2011).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University, 1995).

J. W. Goodman, Statistical Optics (John Wiley & Sons, 2015).

J. W. Goodman, Statistical Optics (Wiley-Interscience, 1985).

D. Gabor, “Microscopy by reconstructed wave-fronts,” in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences (The Royal Society, 1949), pp. 454–487.
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

A diffraction phase microscopy setup where two replicas of the total field at the output port of the microscope are generated by a diffraction grating. One of them is conjugated to the camera plane. The other is low-pass filtered by a physical pinhole to create a reference field. Interference fringes of these two fields are recorded by the camera and the measured phase of interest, ϕ( r ), is obtained using the Hilbert transform. For more details, see [29].

Fig. 2
Fig. 2

Experimental (left) and simulated (right) thickness measurements in nanometers for 3D PC-QPI imaging of 20 μm width, 123 nm thick micropillars at N A c =0.0072. (a) and (b) show the thickness recovered from ϕ( r ) at the sample plane. (c) and (d) are thickness measurements at + 10 μm from the sample plane (forward scattering). (e), (f) show the xz cross-section for the thickness measurements at y = 0.0 μm. The halo and phase reduction can be seen for all these z-steps.

Fig. 3
Fig. 3

Comparison between the experimental and simulated profiles for 123 nm quartz pillars for different values of N A con at the plane of sample (a), (b) and at 10.0 μm from the plane of sample (c) and (d).

Fig. 4
Fig. 4

(a) Three different x-z cross-sections of for 3 different values of the numerical apertures of the condenser. (b) Amplitude spectrum at z = 0.0 um and z = 15.0 um for tree values of NAcon. (c)-(e) Amplitude spectra for 3 different values of z at NAcon = 0.0036, 0.0072 and 0.014, respectively.

Fig. 5
Fig. 5

(a) x-y and x-z cross-sections of a simulated micropillar of dimensions 30 x 30 x 25 µm3. (b) x-z and 3 x-y cross sections of the “ideal” phase, φ. The dashed rectangle denotes the locations of the micropillar. The next three cross-sections are evaluated at three different planes z = 0 µm, z = −10 µm, and z = 20 µm, denoted by while lines in the first x-z cross-section, respectively. (c) x-z cross-sections of the measured phase, ϕ, evaluated at three different values of N A con , namely 0.0036, 0.0072 and 0.014.

Equations (12)

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

ϕ( r )φ( r )φ( r ) r h i ( r )=φ( r ) r [ δ ( 3 ) ( r ) h i ( r ) ].
J t,r ( r,r )= U i + U s , U io * + U so * t ( r,r )= J i,io ( r,r )+ J s,io ( r,r )+ J i,so ( r,r )+ J s,so ( r,r ),
J i,io ( r,r )= S ˜ ( 0 ),
J s,io ( r,r )=i S ˜ ( 0 )φ( r ),
J i,so ( r,r;0 )=i S ˜ ( 0 )[ φ( r ) r h i ( r ) ].
arg[ J t,r ( r,r,0 ) ]=arctan[ Im( J t,r ) / Re( J t,r ) ] =arctan{ [ J s,io ( r,r )+ J i,so ( r,r;0 ) ] / J i,io ( r,r ) } =φ( r ) r [ δ ( 3 ) ( r ) h i ( r ) ].
J s,io ( r,r )= U s ( r ,z,t ) U i * ( r' ' ,z,t ) d 2 r' ' t = β ¯ 2 X( r' ) U i ( r ' ,z',t )g( rr' ) d 3 r' U i * ( r' ' ,z,t ) d 2 r' ' t = β ¯ 2 X( r' ) J ii ( r ' ,z',r' ' ,z )g( rr' ) d 3 r' d 2 r' ' .
J s,io ( r,r )= β ¯ 2 X( r' ) S ˜ ( k )exp[ i k .( r ' r' ' )+iq( k )(z'z) ] d 2 k g( rr' ) d 3 r' d 2 r' ' = S ˜ ( 0 ) β ¯ 2 X( r' )g( rr' )exp[ i n ¯ β ¯ (zz') ] d 3 r' = S ˜ ( 0 ) β ¯ 2 { X r [ gexp( i n ¯ β ¯ z ) ] }( r ).
φ( r )=[ β ¯ / ( 2 n ¯ ) ][ X r k 1 ( e i( q n ¯ β ¯ )z ) ]( r ).
J i,so ( r,r )= U i ( r ,z,t ) U s * ( r ' ,z,t ) d 2 r ' t = β ¯ 2 X * ( r'' ) U i ( r ,z,t ) U i * ( r' ' ,z'',t ) g * ( r'r'' ) d 3 r'' d 2 r ' = β ¯ 2 X * ( r'' ) J ii ( r ,z,r' ' ,z'' ) g * ( r ' r' ' ,zz'' ) d 3 r'' d 2 r ' .
J i,so ( r,r )= β ¯ 2 X( r'' ){ S ˜ ( k ) exp[ i k .( r r' ' )+iq( k )(zz'') ] d 2 k } g * ( r ' r' ' ,zz'' ) d 3 r'' d 2 r ' = β ¯ 2 X( r'' ){ S ˜ ( k ) exp[ i k .( r r' ' )+iq( k )(zz'') ] d 2 k } { g * ( r ' r' ' ,zz'' ) d 2 r ' } d 3 r''.
J i,so ( r,r )=i β ¯ / ( 2 n ¯ ) X( r'' ){ S ˜ ( k ) exp[ i k .( r r' ' )+i[ q( k ) n ¯ β ¯ ](zz'') ] d 2 k } d 3 r'' =i β ¯ / ( 2 n ¯ ) X( r'' )[ k 1 ( e i( q n ¯ β ¯ )( zz'' ) ) r S ]( rr'' ) d 3 r'' =i[ β ¯ / ( 2 n ¯ ) ]{ X r k 1 ( e i( q n ¯ β ¯ )z ) r [ S( r )δ( z ) ] } =i S ˜ ( 0 ){ X r { [ β ¯ / ( 2 n ¯ ) ] k 1 ( e i( q n ¯ β ¯ )z ) } r { [ S( r ) / S ˜ ( 0 ) ]δ( z ) } }( r ) =i S ˜ ( 0 ){ X r { [ β ¯ / ( 2 n ¯ ) ] k 1 ( e i( q n ¯ β ¯ )z ) } r h i }( r )=i S ˜ ( 0 ){ φ r h i }( r ),

Metrics