Abstract

Multifilter phase imaging with partially coherent light (MFPI-PC) and phase optical transfer function recovery (POTFR) are two viable defocus-based, two-dimensional quantitative phase imaging (QPI) methods. While both methods use transfer function inversion, MFPI-PC is based on the in-focus intensity derivative, while POTFR is based on the intensity difference between symmetrically defocused images. This paper compares and contrasts MFPI-PC and POTFR. Six disadvantages (five in MFPI-PC and one in POTFR) are identified. Improvement strategies to overcome each of the six shortcomings are identified and implemented, and both methods are shown to be clearly improved. The revised MFPI-PC is shown to be more accurate than the original MFPI-PC and generally more accurate than the revised POTFR. The revised POTFR is shown to be inherently faster than the original POTFR and also slightly faster than the revised MFPI-PC.

© 2019 Optical Society of America

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References

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2019 (1)

2018 (2)

2017 (1)

2016 (1)

2015 (2)

2014 (8)

P. Bon, S. Lécart, E. Fort, and S. Lévêque-Fort, “Fast label-free cytoskeletal network imaging in living mammalian cells,” Biophys. J. 106, 1588–1595 (2014).
[Crossref]

M. Mihailescu, R. C. Popescu, A. Matei, A. Acasandrei, I. A. Paun, and M. Dinescu, “Investigation of osteoblast cells behavior in polymeric 3D micropatterned scaffolds using digital holographic microscopy,” Appl. Opt. 53, 4850–4858 (2014).
[Crossref]

M. Endrizzi, F. A. Vittoria, P. C. Diemoz, R. Lorenzo, R. D. Speller, U. H. Wagner, C. Rau, I. K. Robinson, and A. Olivo, “Phase-contrast microscopy at high x-ray energy with a laboratory setup,” Opt. Lett. 39, 3332–3335 (2014).
[Crossref]

J. Martinez-Carranza, K. Falaggis, and T. Kozacki, “Optimum plane selection for transport-of-intensity-equation-based solvers,” Appl. Opt. 53, 7050–7058 (2014).
[Crossref]

K. Falaggis, T. Kozacki, and M. Kujawinska, “Optimum plane selection criteria for single-beam phase retrieval techniques based on the contrast transfer function,” Opt. Lett. 39, 30–33 (2014).
[Crossref]

M. H. Jenkins, J. M. Long, and T. K. Gaylord, “Multifilter phase imaging with partially coherent light,” Appl. Opt. 53, D29–D39 (2014).
[Crossref]

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, 10661–10674 (2014).
[Crossref]

A. Shanker, L. Tian, M. Sczyrba, B. Connolly, A. Neureuther, and L. Waller, “Transport of intensity phase imaging in the presence of curl effects induced by strongly absorbing photomasks,” Appl. Opt. 53, J1–J6 (2014).
[Crossref]

2013 (9)

C. Zuo, Q. Chen, Y. J. Yu, and A. Asundi, “Transport-of-intensity phase imaging using Savitzky–Golay differentiation filter–theory and applications,” Opt. Express 21, 5346–5362 (2013).
[Crossref]

S. Gasilov, A. Mittone, E. Brun, A. Bravin, S. Grandl, and P. Coan, “On the possibility of quantitative refractive-index tomography of large biomedical samples with hard x-rays,” Biomed. Opt. Express 4, 1512–1518 (2013).
[Crossref]

T. Feng, M. H. Jenkins, F. Yan, and T. K. Gaylord, “Joint residual stress/refractive index characterization of large-mode-area erbium-doped fibers,” J. Lightwave Technol. 31, 2426–2433 (2013).
[Crossref]

C. L. Zheng, K. Scheerschmidt, H. Kirmse, I. Hausler, and W. Neumann, “Imaging of three-dimensional (Si, Ge) nanostructures by off-axis electron holography,” Ultramicroscopy 124, 108–116 (2013).
[Crossref]

J. Marrison, L. Raty, P. Marriott, and P. O’Toole, “Ptychography–a label free, high-contrast imaging technique for live cells using quantitative phase information,” Sci. Rep. 3, 2369 (2013).
[Crossref]

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

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 13, 4170–4191 (2013).
[Crossref]

B. Joshi, I. Barman, N. C. Dingari, N. Cardenas, J. S. Soares, R. R. Dasari, and S. Mohanty, “Label-free route to rapid, nanoscale characterization of cellular structure and dynamics through opaque media,” Sci. Rep. 3, 1–8 (2013).
[Crossref]

J. Klossa, B. Wattelier, T. Happillon, D. Toubas, L. de Laulanie, V. Untereiner, P. Bon, and M. Manfait, “Quantitative phase imaging and Raman micro-spectroscopy applied to malaria,” Diagn. Pathol. 8, S42-1–S42-4 (2013).
[Crossref]

2012 (3)

2011 (7)

2009 (1)

2008 (2)

W. S. Rockward, A. L. Thomas, B. Zhao, and C. A. DiMarzio, “Quantitative phase measurements using optical quadrature microscopy,” Appl. Opt. 47, 1684–1696 (2008).
[Crossref]

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref]

2007 (2)

2006 (2)

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]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the Born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006).
[Crossref]

2005 (3)

2004 (1)

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, 7–12 (2004).
[Crossref]

2002 (1)

E. D. Barone-Nugent, A. Barty, and K. A. Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206, 194–203 (2002).
[Crossref]

1997 (1)

1994 (1)

1991 (1)

P. A. Gorry, “General least-squares smoothing and differentiation of nonuniformly spaced data by the convolution method,” Anal. Chem. 63, 534–536 (1991).
[Crossref]

1977 (1)

J. P. Guigay, “Fourier-transform analysis of Fresnel diffraction patterns and in-line holograms,” Optik 49, 121–125 (1977).

1975 (1)

1955 (1)

G. Nomarski and A. R. Weill, “Application à la métallographie des méthodes interférentielles à deux ondes polarisées,” Rev. Metall. 52, 121–134 (1955).
[Crossref]

1942 (1)

F. Zernike, “Phase contrast, a new method for the microscopic observation of transparent objects Part II,” Physica 9, 974–986 (1942).
[Crossref]

Acasandrei, A.

Aknoun, S.

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, 7–12 (2004).
[Crossref]

Asundi, A.

Bachim, B. L.

Backman, V.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the Born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006).
[Crossref]

Badizadegan, K.

N. Lue, W. Choi, G. Popescu, T. Ikeda, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Quantitative phase imaging of live cells using fast Fourier phase microscopy,” Appl. Opt. 46, 1836–1842 (2007).
[Crossref]

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the Born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006).
[Crossref]

Balla, A.

Z. Wang, K. Tangella, A. Balla, and G. Popescu, “Tissue refractive index as marker of disease,” J. Biomed. Opt. 16, 116017 (2011).
[Crossref]

Bao, Y.

Barbastathis, G.

Barman, I.

B. Joshi, I. Barman, N. C. Dingari, N. Cardenas, J. S. Soares, R. R. Dasari, and S. Mohanty, “Label-free route to rapid, nanoscale characterization of cellular structure and dynamics through opaque media,” Sci. Rep. 3, 1–8 (2013).
[Crossref]

J. W. Kang, N. Lue, C.-R. Kong, I. Barman, N. C. Dingari, S. J. Goldfless, J. C. Niles, R. R. Dasari, and M. S. Feld, “Combined confocal Raman and quantitative phase microscopy system for biomedical diagnosis,” Biomed. Opt. Express 2, 2484–2492 (2011).
[Crossref]

Barone-Nugent, E. D.

E. D. Barone-Nugent, A. Barty, and K. A. Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206, 194–203 (2002).
[Crossref]

Barty, A.

E. D. Barone-Nugent, A. Barty, and K. A. Nugent, “Quantitative phase-amplitude microscopy I: optical microscopy,” J. Microsc. 206, 194–203 (2002).
[Crossref]

Bashir, R.

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref]

Bednarz, M.

M. Mir, Z. Wang, Z. Shen, M. Bednarz, R. Bashir, I. Golding, S. G. Prasanth, and G. Popescu, “Optical measurement of cycle-dependent cell growth,” Proc. Natl. Acad. Sci. USA 108, 13124–13129 (2011).
[Crossref]

Beran, M. J.

M. J. Beran and G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, 1964).

Bhaduri, B.

Boistel, R.

Bon, P.

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, 16383–16406 (2015).
[Crossref]

P. Bon, S. Lécart, E. Fort, and S. Lévêque-Fort, “Fast label-free cytoskeletal network imaging in living mammalian cells,” Biophys. J. 106, 1588–1595 (2014).
[Crossref]

J. Klossa, B. Wattelier, T. Happillon, D. Toubas, L. de Laulanie, V. Untereiner, P. Bon, and M. Manfait, “Quantitative phase imaging and Raman micro-spectroscopy applied to malaria,” Diagn. Pathol. 8, S42-1–S42-4 (2013).
[Crossref]

P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express 17, 13080–13094 (2009).
[Crossref]

Boone, C. W.

M. Hunter, V. Backman, G. Popescu, M. Kalashnikov, C. W. Boone, A. Wax, V. Gopal, K. Badizadegan, G. D. Stoner, and M. S. Feld, “Tissue self-affinity and polarized light scattering in the Born approximation: a new model for precancer detection,” Phys. Rev. Lett. 97, 138102 (2006).
[Crossref]

Bravin, A.

Brun, E.

Burvall, A.

Cardenas, N.

B. Joshi, I. Barman, N. C. Dingari, N. Cardenas, J. S. Soares, R. R. Dasari, and S. Mohanty, “Label-free route to rapid, nanoscale characterization of cellular structure and dynamics through opaque media,” Sci. Rep. 3, 1–8 (2013).
[Crossref]

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 13, 4170–4191 (2013).
[Crossref]

Chen, Q.

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 13, 4170–4191 (2013).
[Crossref]

Choi, W.

Claus, R. A.

Cloetens, P.

M. Langer, P. Cloetens, J. P. Guigay, and F. Peyrin, “Quantitative comparison of direct phase retrieval algorithms in in-line phase tomography,” Med. Phys. 35, 4556–4566 (2008).
[Crossref]

J. P. Guigay, M. Langer, R. Boistel, and P. Cloetens, “Mixed transfer function and transport of intensity approach for phase retrieval in the Fresnel region,” Opt. Lett. 32, 1617–1619 (2007).
[Crossref]

Coan, P.

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, 7–12 (2004).
[Crossref]

Connolly, B.

Dasari, R. R.

Dauwels, J.

de Laulanie, L.

J. Klossa, B. Wattelier, T. Happillon, D. Toubas, L. de Laulanie, V. Untereiner, P. Bon, and M. Manfait, “Quantitative phase imaging and Raman micro-spectroscopy applied to malaria,” Diagn. Pathol. 8, S42-1–S42-4 (2013).
[Crossref]

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Diemoz, P. C.

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Biomed. Opt. Express (2)

Biophys. J. (1)

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Figures (9)

Fig. 1.
Fig. 1. Simulation of the phases recovered from WLS-MFPI-PC and fast POTFR using disk illumination. The units on the gray bars are radians. The ranges of the phases are all from $ - {0.58}$ to $ + {0.62}$ radians. (a) The phase recovered from WLS-MFPI-PC using 31 uniform planes. ${\rm NRMSE} = {0.077}$. (b) The phase recovered from fast POTFR using 31 uniform planes. ${\rm NRMSE} = {0.080}$. (c) The phase recovered from WLS-MFPI-PC using seven uniform planes. ${\rm NRMSE} = {0.122}$. (d) The phase recovered from fast POTFR using seven uniform planes. ${\rm NRMSE} = {0.146}$. (e) The phase recovered from WLS-MFPI-PC using seven nonuniform planes. ${\rm NRMSE} = {0.121}$. (f) The phase recovered from fast POTFR using seven nonuniform planes. ${\rm NRMSE} = {0.155}$.
Fig. 2.
Fig. 2. Logarithm plots of the NRMSEs of the recovered phases with disk illumination at various ${{\rm NA}_{\rm o}}$ and ${{\rm NA}_{\rm c}}$ using WLS-MFPI-PC and fast POTFR. Both the ${{\rm NA}_{\rm o}}$ and ${{\rm NA}_{\rm c}}$ range from 0.01 to 0.55. The scales of all color bars are from $ - {0.91}$ to 0. (a) NRMSEs from WLS-MFPI-PC using 31 uniform planes. (b) NRMSEs from fast POTFR using 31 uniform planes. (c) NRMSEs from WLS-MFPI-PC using seven uniform planes. (d) NRMSEs from fast POTFR using seven uniform planes. (e) NRMSEs from WLS-MFPI-PC using seven nonuniform planes. (f) NRMSEs from fast POTFR using seven nonuniform planes.
Fig. 3.
Fig. 3. 2D plots of the relative differences in NRMSE between WLS-MFPI-PC and fast POTFR for disk illumination. Both the ${{\rm NA}_{\rm o}}$ and ${{\rm NA}_{\rm c}}$ range from 0.01 to 0.55. The gray bar scales are cropped from $ - {0.1}$ to 0.1. Intensities at (a) 31 uniform planes, (b) seven uniform planes, and (c) seven nonuniform planes are used.
Fig. 4.
Fig. 4. Simulation of the phases recovered from WLS-MFPI-PC and fast POTFR using annular illumination and seven nonuniform planes. The units on the gray bars are radians. The ranges of the recovered phases are all from $ - {0.58}$ to $ + {0.62}$ radians. (a) Phase recovered from WLS-MFPI-PC. ${\rm NRMSE} = {0.136}$. (b) Phase recovered from fast POTFR. ${\rm NRMSE} = {0.193}$.
Fig. 5.
Fig. 5. Logarithm plots of the NRMSEs from (a) WLS-MFPI-PC and (b) fast POTFR of the recovered phases with annular illumination at various ${{\rm NA}_{\rm c}}$ and ${{\rm NA}_{{\rm ci}}}$ using WLS-MFPI-PC and fast POTFR with seven nonuniform planes. The ${{\rm NA}_{\rm c}}$ ranges from 0.01 to 0.55, and the ${{\rm NA}_{{\rm ci}}}$ ranges from 0 to 0.54. The scales of all color bars are from $ - {1.11}$ to 0.
Fig. 6.
Fig. 6. Simulation of the phases recovered from WLS-MFPI-PC and fast POTFR using absorptive objects. The absorption coefficient is $\beta = 0.1$. The units on the gray bars are radians, except in (b) they are dimensionless. The ranges of the phases are all from $ - {0.58}$ to $ + {0.62}$ radians. (a) Ideal phase. (b) Absorption pattern $a({\boldsymbol x})$. (c) Phase recovered from WLS-MFPI-PC. ${\rm NRMSE} = {0.141}$. (d) Phase recovered from fast POTFR. ${\rm NRMSE} = {0.191}$.
Fig. 7.
Fig. 7. Logarithm plots of the NRMSEs of the recovered phases with absorption coefficient $\beta $ using (a) WLS-MFPI-PC and (b) fast POTFR. The absorption coefficient $\beta $ ranges from 0 to 0.5, and the logarithm of NRMSE ranges from $ - {1.1}$ to $ - {0.2}$. Different curves are recovered from different noise levels. The higher curves are from larger noise.
Fig. 8.
Fig. 8. Logarithm plots of the NRMSEs of the recovered phases with phase amplitude $\alpha $ using (a) WLS-MFPI-PC and (b) fast POTFR. The phase amplitude $\alpha $ ranges from 0 to 3, and the logarithm of NRMSE ranges from $ - {1.1}$ to $ - {0.1}$. Different curves are recovered from different noise levels.
Fig. 9.
Fig. 9. Logarithm plots of the NRMSEs of the recovered phases with various phase and absorption patterns using WLS-MFPI-PC and fast POTFR. The patterns are named using letters a through l. (a) and (c) are errors of WLS-MFPI-PC, while (b) and (d) are errors of fast POTFR. (a) and (b) are recovered under the noise of ${\rm SNR} = 40\,\, {\rm dB}$ (color bars are from $ - {0.87}$ to $ - {0.43}$), while (c) and (d) are recovered without noise (color bars are from $ - {1.22}$ to $ - {0.69}$).

Tables (3)

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Table 1. Comparisons of Some Properties of Original MFPI-PC and POTFRa

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Table 2. Comparison of Computation Time of a 2D POTF Using Original Formula (2D Integral) and the New Formula (Semi-Analytical)a

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Table 3. Comparison of Some Properties of WLS-MFPI-PC and Fast POTFRa

Equations (18)

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H ϕ P C ( ρ ) = 2 k 0 H ( ρ , η ) exp ( 2 π i η z ) d η ,
N R M S E = ( [ ϕ r ( x , y ) ϕ 0 ( x , y ) ] 2 ϕ 0 ( x , y ) 2 ) 1 / 2 ,
D = N R M S E 1 N R M S E 2 1 ,
t ( x ) = exp [ i ϕ ( x ) β a ( x ) ] ,
I z ( x ) = B + h z ( x ) ϕ ( x ) ,
I ~ z ( ρ ) = B δ ( ρ ) + H z ( ρ ) Φ ( ρ ) .
v ( r ) = Δ k 0 2 [ n ( r ) 2 n 0 2 ] ,
I ( r ) = B + h ( r ) v ( r ) ,
I ~ ( f ) = B δ ( f ) + H ( f ) V ( f ) .
I z ( x ) = I ( x , z ) .
h z ( x ) ϕ ( x ) = [ h ( x , z ) v ( x , z ) ] z = z ,
Δ n ( x , z ) = ϕ ( x ) δ ( z ) / k 0 ,
Δ n = n n 0
v ( r ) = 2 k 0 2 Δ n ( r ) .
v ( x , z ) = 2 k 0 ϕ ( x ) δ ( z ) .
h z ( x ) ϕ ( x ) = 2 k 0 [ h ( x , z ) δ ( z ) ] z = z ϕ ( x ) .
h z ( x ) = 2 k 0 h ( x , z ) .
H z ( ρ ) = 2 k 0 H ( ρ , η ) exp ( 2 π i η z ) d η ,

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