Abstract

Wavefront sensors are usually based on measuring the wavefront derivatives. The most commonly used approach to quantitatively reconstruct the wavefront uses discrete Fourier transform, which leads to artifacts when phase objects are located at the image borders. We propose here a simple approach to avoid these artifacts based on the duplication and antisymmetrization of the derivatives data, in the derivative direction, before integration. This approach completely erases the border effects by creating continuity and differentiability at the edge of the image. We finally compare this corrected approach to the literature on model images and quantitative phase images of biological microscopic samples, and discuss the effects of the artifacts on the particular application of dry mass measurements.

© 2012 Optical Society of America

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References

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    [CrossRef]

2012

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

2011

2009

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]

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

2008

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

W. Boucher, S. Velghe, B. Wattellier, and D. Gatinel, “Intraocular lens characterization using a quadric-wave lateral shearing interferometer wave front sensor,” Proc. SPIE 7102, 71020Q (2008).
[CrossRef]

2007

2006

2005

2004

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]

B. Wattellier, J. Fuchs, J. P. Zou, K. Abdeli, H. Pépin, and C. Haefner, “Repetition rate increase and diffraction-limited focal spots for a nonthermal-equilibrium100-tw nd:glass laser chain by use of adaptive optics,” Opt. Lett. 29, 2494–2496 (2004).
[CrossRef]

2000

1998

1997

1992

1991

1977

1971

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

1964

1952

R. Barer, “Interference microscopy and mass determination,” Nature 169, 366–367 (1952).
[CrossRef]

Abdeli, K.

Anderson, D. 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]

Baffou, G.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Barer, R.

R. Barer, “Interference microscopy and mass determination,” Nature 169, 366–367 (1952).
[CrossRef]

Bon, P.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[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]

Boucher, W.

W. Boucher, S. Velghe, B. Wattellier, and D. Gatinel, “Intraocular lens characterization using a quadric-wave lateral shearing interferometer wave front sensor,” Proc. SPIE 7102, 71020Q (2008).
[CrossRef]

Bradley, A.

Bunk, O.

Burge, J. H.

Cano, E.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

Chanteloup, J. C.

Chériaux, G.

Cogswell, C. J.

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[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, 7–12 (2004).
[CrossRef]

Cohen, M.

Colomb, T.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

David, C.

Dayton, D.

Depeursinge, C.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

Druon, F.

Durán-Ramírez, V. M.

Faure, J.

Fried, D. L.

Fuchs, J.

Gatinel, D.

W. Boucher, S. Velghe, B. Wattellier, and D. Gatinel, “Intraocular lens characterization using a quadric-wave lateral shearing interferometer wave front sensor,” Proc. SPIE 7102, 71020Q (2008).
[CrossRef]

Ghiglia, D.

D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Gonglewski, J.

Guérineau, N.

Gurineau, N.

Haefner, C.

Hudgin, R. H.

Ketelsen, D. A.

Khn, J.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

King, S. V.

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Kottler, C.

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, 7–12 (2004).
[CrossRef]

Liang, J.

Libertun, A.

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Magistretti, P. J.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

Maksimchuk, A.

Malacara-Doblado, D.

Malacara-Hernández, D.

Marquet, P.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

Martin, H. M.

Maucort, G.

Merlin, M.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Michau, V.

Monneret, S.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[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]

Morgan, K. S.

Mourou, G.

Muller, N.

Murgiuc, C.

Nantel, M.

Nees, J.

Paganin, D. M.

Pépin, H.

Pfeiffer, F.

Pierson, B.

Piestun, R.

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Platt, B. C.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Polleux, J.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Preza, C.

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

Primot, J.

Pritt, M.

D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Rappaz, B.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

Ribak, E. N.

Rigneault, H.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Robert, C.

Roddier, C.

Roddier, F.

Ronchi, V.

Rousset, G.

Salas-Peimbert, D. P.

Salmon, T. O.

Savatier, J.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Shack, R. V.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

Sheppard, C. J. 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]

Simanis, V.

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

Siu, K. K. W.

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, 7–12 (2004).
[CrossRef]

Spielbusch, B.

Talmi, A.

Thibos, L. N.

Trujillo-Schiaffino, G.

Vaughn, J. L.

Vdovin, G.

Velghe, S.

W. Boucher, S. Velghe, B. Wattellier, and D. Gatinel, “Intraocular lens characterization using a quadric-wave lateral shearing interferometer wave front sensor,” Proc. SPIE 7102, 71020Q (2008).
[CrossRef]

S. Velghe, J. Primot, N. Guérineau, M. Cohen, and B. Wattellier, “Wave-front reconstruction from multidirectional phasederivatives generated by multilateral shearing interferometers,” Opt. Lett. 30, 245–247 (2005).
[CrossRef]

Vernin, J.

Wattellier, B.

West, S. C.

Williams, D. R.

Young, R. S.

Zhu, M.

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Zou, J. P.

ACS Nano

G. Baffou, P. Bon, J. Savatier, J. Polleux, M. Zhu, M. Merlin, H. Rigneault, and S. Monneret, “Thermal imaging of nanostructures by quantitative optical phase analysis,” ACS Nano 6, 2452–2458 (2012).
[CrossRef]

Appl. Opt.

J. Biomed. Opt.

S. V. King, A. Libertun, R. Piestun, C. J. Cogswell, and C. Preza, “Quantitative phase microscopy through differential interference imaging,” J. Biomed. Opt. 13, 024020 (2008).
[CrossRef]

B. Rappaz, E. Cano, T. Colomb, J. Khn, C. Depeursinge, V. Simanis, P. J. Magistretti, and P. Marquet, “Noninvasive characterization of the fission yeast cell cycle by monitoring dry mass with digital holographic microscopy,” J. Biomed. Opt. 14, 034049 (2009).
[CrossRef]

J. Microsc.

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]

J. Opt. Soc. Am.

R. V. Shack and B. C. Platt, “Production and use of a lenticular Hartmann screen,” J. Opt. Soc. Am. 61, 656–660 (1971).

R. H. Hudgin, “Wave-front reconstruction for compensated imaging,” J. Opt. Soc. Am. 67, 375–378 (1977).
[CrossRef]

J. Opt. Soc. Am. A

Nature

R. Barer, “Interference microscopy and mass determination,” Nature 169, 366–367 (1952).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

W. Boucher, S. Velghe, B. Wattellier, and D. Gatinel, “Intraocular lens characterization using a quadric-wave lateral shearing interferometer wave front sensor,” Proc. SPIE 7102, 71020Q (2008).
[CrossRef]

Other

D. Ghiglia and M. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Simulated object: a sharp and uniform object is placed at one image boundary. (b) Reconstructed image [CPM, derivative data calculated from (a)]. (c) Error map (b)–(a) where artifacts are clearly visible. (d) Same as (c) but flipped with respect to vertical dashed line visible on (c); a dipole radiationlike shape is visible. (e) Monopole spiral phase distribution centered on the bottom intersection between the object disc and the left border of image (a). (f) Opposite spiral phase compared to (e), centered on the top intersection between the object disc and the left border of image (a). In this particular object, the sum of (e) and (f) gives (d).

Fig. 2.
Fig. 2.

Reconstruction of the OPD distribution of a living COS-7 cell from its gradients using CPM. (a) Measured OPD derivative along the vertical direction. (b) Measured OPD derivative along the horizontal direction. (c) Reconstructed OPD when the cell is fully included in the microscope field of view. (d), (e), (f) Same as (a), (b), and (c) with the cell clearly going over the image limits. (g) Error map of (f) due to boundary effects.

Fig. 3.
Fig. 3.

Comparison between reconstructed phase distributions using a basic integration (left), an MDI [22] (middle), and ASDI (right). (a), (b), (c) Derivative data along x (left) and y (right) axes. (d) Phase reconstruction using Eq. (2), where boundary artifacts are clearly visible due to the hidden phase. (e) Extended derivative data along x (left) and y (right) axes using a symmetrical approach. (f) Phase reconstruction from (e) using CPM. (g) Final phase reconstructed using MDI; boundary artifacts are limited but still here. (h) Same as (e) using a antisymmetrical approach, in the derivative direction, to fulfil Eq. (7) requirements. (i) Same as (f) with (h) data. (j) Final phase reconstruction using ASDI; no boundary-induced artifact is visible.

Fig. 4.
Fig. 4.

(a) Drosophila embryo (scheme): the darkness is proportional to the sample thickness, and the imaged zone is represented by a black dash rectangle. (b) Drosophila OPD gradient along x. (c) Drosophila OPD gradient along y. (d) OPD obtained by basic FFT integration algorithm of gradients (a) and (b); boundary artifacts are present. (e) Same as (d) using MDI; boundary artifacts are reduced but still visible. (f) Same as (d) using ASDI; no artifact is visible. (g) OPD error of (d) [obtained by subtraction with (f)].

Fig. 5.
Fig. 5.

(a) OPD image obtained with the basic CPM integration; the image presents artifacts. (c) OPD image obtained with the antisymmetrized derivative algorithm; the image is boundary artifact-free. (c) Error map (a)–(c). (d) Segmentation image; the background is in black, and each other color represents a distinct cell. (e) Histogram of the segmented cell dry mass of the image (d). Brown, using (a); red, using MDI (image not presented here); orange, using (c).

Tables (2)

Tables Icon

Table 1. Comparison of Relative Standard Deviation error of OPD Reconstruction of the Fig. 3 Simulated Object for Three Integration Methods

Tables Icon

Table 2. Comparison of Dry Mass Study on the OPD Image Obtained with Three Different Algorithms (Data of Fig. 5)

Equations (8)

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

W(x,y)=FT1[νx·FT(W/x)[νx,νy]+νy·FT(W/y)[νx,νy]νx2+νy2],
W(x,y)=FT1[FT(W/x)[νx,νy]+i·FT(W/y)[νx,νy]νx+i·νy],
rot([xWyW])0(xW)y(yW)x,
Wh(z)=φ0·Arg(j[zzj]rj)π,
{xWMDI=[xW(x,y)xW(x,y)xW(x,y)xW(x,y)]yWMDI=[yW(x,y)yW(x,y)yW(x,y)yW(x,y)].
We=[W(x,y)W(x,y)W(x,y)W(x,y)].
{xWe=[xW(x,y)xW(x,y)xW(x,y)xW(x,y)]yWe=[yW(x,y)yW(x,y)yW(x,y)yW(x,y)].
m=1αcellOPD·dS,

Metrics