Abstract

The differential-interference-contrast (DIC) microscope is of widespread use in life sciences as it enables noninvasive visualization of transparent objects. The goal of this work is to model the image formation process of thick three-dimensional objects in DIC microscopy. The model is based on the principles of electromagnetic wave propagation and scattering. It simulates light propagation through the components of the DIC microscope to the image plane using a combined geometrical and physical optics approach and replicates the DIC image of the illuminated object. The model is evaluated by comparing simulated images of three-dimensional spherical objects with the recorded images of polystyrene microspheres. Our computer simulations confirm that the model captures the major DIC image characteristics of the simulated object, and it is sensitive to the defocusing effects.

© 2014 Optical Society of America

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  1. D. Agard and J. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302, 676–681 (1983).
    [CrossRef]
  2. S. Bradbury and P. Evennett, Contrast Techniques in Light Microscopy. Microscopy Handbooks 34 (Bios Scientific, 1996).
  3. J. Padawer, “The Nomarski interference-contrast microscope. An experimental basis for the image interpretation,” J. R. Microsc. Soc. 88, 305–349 (1967).
  4. M. Pluta, Advanced Light Microscopy, Vol. 2 (Elsevier Science, 1988).
  5. W. Lang, “Nomarski differential interference contrast microscopy. I. Fundamentals and experimental designs,” Zeiss Information 70, 114–120 (1968).
  6. W. Lang, “Nomarski differential interference contrast microscopy. II. Formation of the interference image,” Zeiss Information 71, 12–16 (1969).
  7. M. Arnison, K. Larkin, C. Sheppard, N. Smith, and C. Cogswell, “Linear phase imaging using differential interference contrast microscopy,” J. Microsc. 214, 7–12 (2004).
    [CrossRef]
  8. N. Axelrod, A. Radko, A. Lewis, and N. Ben-Yosef, “Topographic profiling and refractive-index analysis by use of differential interference contrast with bright-field intensity and atomic force imaging,” Appl. Opt. 43, 2272–2284 (2004).
    [CrossRef]
  9. F. Kagalwala, F. Lanni, and T. Kanade, “Computational model of DIC microscopy: from observations to measurements,” Technical report CMU-R1 TR (Carnegie Mellon University, 2000).
  10. C. Preza, D. Snyder, and J. Conchello, “Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,” J. Opt. Soc. Am. A 16, 2185–2199 (1999).
    [CrossRef]
  11. E. Van-Munster, L. Van-Vliet, and J. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
    [CrossRef]
  12. M. Born and E. Wolf, Principles of Optics, 4th ed. (Cambridge University, 1999).
  13. S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156 (2009).
    [CrossRef]
  14. S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, in conjunction with ICCV’07, Rio de Janeiro, Brazil (2007).
  15. S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).
  16. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).
  17. M. Slaney, “Imaging with diffraction tomography,” Ph.D. thesis (Purdue University, 1985).
  18. H. Sierra, C. A. DiMarzio, and D. H. Brooks, “3D effects in DIC images of extended objects,” Proc. SPIE 7184, 71840D (2009).
  19. H. Sierra, C. A. DiMarzio, and D. H. Brooks, “Modeling phase microscopy of transparent three-dimensional objects: a product-of-convolutions approach,” J. Opt. Soc. Am. A 26, 1268–1276 (2009).
    [CrossRef]
  20. J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).
  21. P. Török, S. J. Hewlett, and P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
    [CrossRef]
  22. E. Kashdan and E. Turkel, “A high order accurate method for the frequency domain Maxwell’s equations across interfaces,” J. Sci. Comput. 27, 75–95 (2006).
    [CrossRef]
  23. E. Kashdan and E. Turkel, “High order accurate modelling of electromagnetic wave propagation across media: grid conforming bodies,” J. Comput. Phys. 218, 816–835 (2006).
    [CrossRef]
  24. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  25. R. Munro and P. Török, “Vectorial, high numerical aperture study of Nomarski’s differential interference contrast microscope,” Opt. Express 13, 6833–6847 (2005).
    [CrossRef]
  26. M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469 (2006).
    [CrossRef]
  27. P. Barber and S. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).
  28. A. Taflove and C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).
  29. W. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980).
    [CrossRef]
  30. C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  31. M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (NASA Goddard Institute for Space Studies, 2006).
  32. MicroscopyU, http://www.microscopyu.com/ .
  33. S. Schaub, D. Alexander, and J. Barton, “Theoretical model of the laser imaging of small aerosols: applications to aerosol sizing,” Appl. Opt. 30, 4777–4784 (1991).
    [CrossRef]
  34. C. D. Meinhart and S. T. Wereley, “The theory of diffraction-limited resolution in microparticle image velocimetry,” Meas. Sci. Technol. 14, 1047–1053 (2003).
    [CrossRef]
  35. B. Ovryn and S. Izen, “Imaging of transparent spheres through a planar interface using a high-numerical-aperture optical microscope,” J. Opt. Soc. Am. A 17, 1202–1213 (2000).
    [CrossRef]
  36. P. David and P. Rabinowitz, Methods of Numerical Integration (Academic, 1975).
  37. W. Gautschi, Orthogonal Polynomials: Computation and Approximation (Oxford University, 2004).
  38. O. M. Primer, http://micro.magnet.fsu.edu/primer/ .
  39. S. Inoué and K. Spring, Video Microscopy: The Fundamentals, 2nd ed. (Plenum, 1997).
  40. H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. B 63, 737–744 (1950).
  41. J. Sijbers and A. Postnov, “Reduction of ring artifacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
    [CrossRef]
  42. S. Trattner, E. Kashdan, H. Greenspan, and N. Sochen, “Human embryo under the DIC microscope—vectorial approach to the electromagnetic scattering simulation,” in Proceedings of 8th International Conference on Spectral and High-Order Accurate Methods (ICOSAHOM), Trondheim, Norway (2009).
  43. S. Trattner, M. Feigin, E. Kashdan, and N. Sochen, “GPU accelerated electromagnetic scattering and diffraction in 3D microscopic image formation,” in Proceedings of the 3rd Workshop on GPUs for Computer Vision, Barcelona, Spain (2011).
  44. M. Feigin, “Computational methods in image analysis,” Ph.D. thesis (Tel Aviv University, 2012).

2009 (3)

2006 (3)

E. Kashdan and E. Turkel, “A high order accurate method for the frequency domain Maxwell’s equations across interfaces,” J. Sci. Comput. 27, 75–95 (2006).
[CrossRef]

E. Kashdan and E. Turkel, “High order accurate modelling of electromagnetic wave propagation across media: grid conforming bodies,” J. Comput. Phys. 218, 816–835 (2006).
[CrossRef]

M. Shribak and S. Inoué, “Orientation-independent differential interference contrast microscopy,” Appl. Opt. 45, 460–469 (2006).
[CrossRef]

2005 (1)

2004 (3)

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

N. Axelrod, A. Radko, A. Lewis, and N. Ben-Yosef, “Topographic profiling and refractive-index analysis by use of differential interference contrast with bright-field intensity and atomic force imaging,” Appl. Opt. 43, 2272–2284 (2004).
[CrossRef]

J. Sijbers and A. Postnov, “Reduction of ring artifacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[CrossRef]

2003 (1)

C. D. Meinhart and S. T. Wereley, “The theory of diffraction-limited resolution in microparticle image velocimetry,” Meas. Sci. Technol. 14, 1047–1053 (2003).
[CrossRef]

2000 (1)

1999 (1)

1997 (2)

E. Van-Munster, L. Van-Vliet, and J. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

P. Török, S. J. Hewlett, and P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

1991 (1)

1983 (1)

D. Agard and J. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302, 676–681 (1983).
[CrossRef]

1980 (1)

1969 (1)

W. Lang, “Nomarski differential interference contrast microscopy. II. Formation of the interference image,” Zeiss Information 71, 12–16 (1969).

1968 (1)

W. Lang, “Nomarski differential interference contrast microscopy. I. Fundamentals and experimental designs,” Zeiss Information 70, 114–120 (1968).

1967 (1)

J. Padawer, “The Nomarski interference-contrast microscope. An experimental basis for the image interpretation,” J. R. Microsc. Soc. 88, 305–349 (1967).

1950 (1)

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. B 63, 737–744 (1950).

Agard, D.

D. Agard and J. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302, 676–681 (1983).
[CrossRef]

Alexander, D.

Arnison, M.

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

Aten, J.

E. Van-Munster, L. Van-Vliet, and J. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Axelrod, N.

Barber, P.

P. Barber and S. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

Barham, P. M.

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. B 63, 737–744 (1950).

Barton, J.

Ben-Yosef, N.

Bohren, C.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Born, M.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Cambridge University, 1999).

Bradbury, S.

S. Bradbury and P. Evennett, Contrast Techniques in Light Microscopy. Microscopy Handbooks 34 (Bios Scientific, 1996).

Brooks, D. H.

Cogswell, C.

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

Conchello, J.

David, P.

P. David and P. Rabinowitz, Methods of Numerical Integration (Academic, 1975).

DiMarzio, C. A.

Evennett, P.

S. Bradbury and P. Evennett, Contrast Techniques in Light Microscopy. Microscopy Handbooks 34 (Bios Scientific, 1996).

Feigin, M.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156 (2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, in conjunction with ICCV’07, Rio de Janeiro, Brazil (2007).

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

S. Trattner, M. Feigin, E. Kashdan, and N. Sochen, “GPU accelerated electromagnetic scattering and diffraction in 3D microscopic image formation,” in Proceedings of the 3rd Workshop on GPUs for Computer Vision, Barcelona, Spain (2011).

M. Feigin, “Computational methods in image analysis,” Ph.D. thesis (Tel Aviv University, 2012).

Gautschi, W.

W. Gautschi, Orthogonal Polynomials: Computation and Approximation (Oxford University, 2004).

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Greenspan, H.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156 (2009).
[CrossRef]

S. Trattner, E. Kashdan, H. Greenspan, and N. Sochen, “Human embryo under the DIC microscope—vectorial approach to the electromagnetic scattering simulation,” in Proceedings of 8th International Conference on Spectral and High-Order Accurate Methods (ICOSAHOM), Trondheim, Norway (2009).

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, in conjunction with ICCV’07, Rio de Janeiro, Brazil (2007).

Greenspan, M.

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

Hagness, C.

A. Taflove and C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Hewlett, S. J.

P. Török, S. J. Hewlett, and P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Hill, S.

P. Barber and S. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

Hopkins, H. H.

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. B 63, 737–744 (1950).

Huffman, D.

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Inoué, S.

Izen, S.

Kagalwala, F.

F. Kagalwala, F. Lanni, and T. Kanade, “Computational model of DIC microscopy: from observations to measurements,” Technical report CMU-R1 TR (Carnegie Mellon University, 2000).

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

Kanade, T.

F. Kagalwala, F. Lanni, and T. Kanade, “Computational model of DIC microscopy: from observations to measurements,” Technical report CMU-R1 TR (Carnegie Mellon University, 2000).

Kashdan, E.

E. Kashdan and E. Turkel, “High order accurate modelling of electromagnetic wave propagation across media: grid conforming bodies,” J. Comput. Phys. 218, 816–835 (2006).
[CrossRef]

E. Kashdan and E. Turkel, “A high order accurate method for the frequency domain Maxwell’s equations across interfaces,” J. Sci. Comput. 27, 75–95 (2006).
[CrossRef]

S. Trattner, M. Feigin, E. Kashdan, and N. Sochen, “GPU accelerated electromagnetic scattering and diffraction in 3D microscopic image formation,” in Proceedings of the 3rd Workshop on GPUs for Computer Vision, Barcelona, Spain (2011).

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

S. Trattner, E. Kashdan, H. Greenspan, and N. Sochen, “Human embryo under the DIC microscope—vectorial approach to the electromagnetic scattering simulation,” in Proceedings of 8th International Conference on Spectral and High-Order Accurate Methods (ICOSAHOM), Trondheim, Norway (2009).

Lacis, A.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (NASA Goddard Institute for Space Studies, 2006).

Lang, W.

W. Lang, “Nomarski differential interference contrast microscopy. II. Formation of the interference image,” Zeiss Information 71, 12–16 (1969).

W. Lang, “Nomarski differential interference contrast microscopy. I. Fundamentals and experimental designs,” Zeiss Information 70, 114–120 (1968).

Lanni, F.

F. Kagalwala, F. Lanni, and T. Kanade, “Computational model of DIC microscopy: from observations to measurements,” Technical report CMU-R1 TR (Carnegie Mellon University, 2000).

Larkin, K.

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

Lewis, A.

Meinhart, C. D.

C. D. Meinhart and S. T. Wereley, “The theory of diffraction-limited resolution in microparticle image velocimetry,” Meas. Sci. Technol. 14, 1047–1053 (2003).
[CrossRef]

Mishchenko, M.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (NASA Goddard Institute for Space Studies, 2006).

Munro, R.

Ovryn, B.

Padawer, J.

J. Padawer, “The Nomarski interference-contrast microscope. An experimental basis for the image interpretation,” J. R. Microsc. Soc. 88, 305–349 (1967).

Pluta, M.

M. Pluta, Advanced Light Microscopy, Vol. 2 (Elsevier Science, 1988).

Postnov, A.

J. Sijbers and A. Postnov, “Reduction of ring artifacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[CrossRef]

Preza, C.

Rabinowitz, P.

P. David and P. Rabinowitz, Methods of Numerical Integration (Academic, 1975).

Radko, A.

Schaub, S.

Sedat, J.

D. Agard and J. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302, 676–681 (1983).
[CrossRef]

Sheppard, C.

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

Shribak, M.

Sierra, H.

Sijbers, J.

J. Sijbers and A. Postnov, “Reduction of ring artifacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[CrossRef]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

M. Slaney, “Imaging with diffraction tomography,” Ph.D. thesis (Purdue University, 1985).

Smith, N.

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

Snyder, D.

Sochen, N.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156 (2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, in conjunction with ICCV’07, Rio de Janeiro, Brazil (2007).

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

S. Trattner, E. Kashdan, H. Greenspan, and N. Sochen, “Human embryo under the DIC microscope—vectorial approach to the electromagnetic scattering simulation,” in Proceedings of 8th International Conference on Spectral and High-Order Accurate Methods (ICOSAHOM), Trondheim, Norway (2009).

S. Trattner, M. Feigin, E. Kashdan, and N. Sochen, “GPU accelerated electromagnetic scattering and diffraction in 3D microscopic image formation,” in Proceedings of the 3rd Workshop on GPUs for Computer Vision, Barcelona, Spain (2011).

Spring, K.

S. Inoué and K. Spring, Video Microscopy: The Fundamentals, 2nd ed. (Plenum, 1997).

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).

Taflove, A.

A. Taflove and C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

Török, P.

R. Munro and P. Török, “Vectorial, high numerical aperture study of Nomarski’s differential interference contrast microscope,” Opt. Express 13, 6833–6847 (2005).
[CrossRef]

P. Török, S. J. Hewlett, and P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Trattner, S.

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Validity criterion for the Born approximation convergence in microscopy imaging,” J. Opt. Soc. Am. A 26, 1147–1156 (2009).
[CrossRef]

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, in conjunction with ICCV’07, Rio de Janeiro, Brazil (2007).

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

S. Trattner, M. Feigin, E. Kashdan, and N. Sochen, “GPU accelerated electromagnetic scattering and diffraction in 3D microscopic image formation,” in Proceedings of the 3rd Workshop on GPUs for Computer Vision, Barcelona, Spain (2011).

S. Trattner, E. Kashdan, H. Greenspan, and N. Sochen, “Human embryo under the DIC microscope—vectorial approach to the electromagnetic scattering simulation,” in Proceedings of 8th International Conference on Spectral and High-Order Accurate Methods (ICOSAHOM), Trondheim, Norway (2009).

Travis, L.

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (NASA Goddard Institute for Space Studies, 2006).

Turkel, E.

E. Kashdan and E. Turkel, “High order accurate modelling of electromagnetic wave propagation across media: grid conforming bodies,” J. Comput. Phys. 218, 816–835 (2006).
[CrossRef]

E. Kashdan and E. Turkel, “A high order accurate method for the frequency domain Maxwell’s equations across interfaces,” J. Sci. Comput. 27, 75–95 (2006).
[CrossRef]

Van-Munster, E.

E. Van-Munster, L. Van-Vliet, and J. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Van-Vliet, L.

E. Van-Munster, L. Van-Vliet, and J. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

Varga, P.

P. Török, S. J. Hewlett, and P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

Wereley, S. T.

C. D. Meinhart and S. T. Wereley, “The theory of diffraction-limited resolution in microparticle image velocimetry,” Meas. Sci. Technol. 14, 1047–1053 (2003).
[CrossRef]

Westin, C.-F.

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

Wiscombe, W.

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 4th ed. (Cambridge University, 1999).

Appl. Opt. (4)

J. Comput. Phys. (1)

E. Kashdan and E. Turkel, “High order accurate modelling of electromagnetic wave propagation across media: grid conforming bodies,” J. Comput. Phys. 218, 816–835 (2006).
[CrossRef]

J. Microsc. (3)

P. Török, S. J. Hewlett, and P. Varga, “The role of specimen-induced spherical aberration in confocal microscopy,” J. Microsc. 188, 158–172 (1997).
[CrossRef]

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

E. Van-Munster, L. Van-Vliet, and J. Aten, “Reconstruction of optical pathlength distributions from images obtained by a wide-field differential interference contrast microscope,” J. Microsc. 188, 149–157 (1997).
[CrossRef]

J. Opt. Soc. Am. A (4)

J. R. Microsc. Soc. (1)

J. Padawer, “The Nomarski interference-contrast microscope. An experimental basis for the image interpretation,” J. R. Microsc. Soc. 88, 305–349 (1967).

J. Sci. Comput. (1)

E. Kashdan and E. Turkel, “A high order accurate method for the frequency domain Maxwell’s equations across interfaces,” J. Sci. Comput. 27, 75–95 (2006).
[CrossRef]

Meas. Sci. Technol. (1)

C. D. Meinhart and S. T. Wereley, “The theory of diffraction-limited resolution in microparticle image velocimetry,” Meas. Sci. Technol. 14, 1047–1053 (2003).
[CrossRef]

Nature (1)

D. Agard and J. Sedat, “Three-dimensional architecture of a polytene nucleus,” Nature 302, 676–681 (1983).
[CrossRef]

Opt. Express (1)

Phys. Med. Biol. (1)

J. Sijbers and A. Postnov, “Reduction of ring artifacts in high resolution micro-CT reconstructions,” Phys. Med. Biol. 49, N247–N253 (2004).
[CrossRef]

Proc. Phys. Soc. B (1)

H. H. Hopkins and P. M. Barham, “The influence of the condenser on microscopic resolution,” Proc. Phys. Soc. B 63, 737–744 (1950).

Proc. SPIE (1)

H. Sierra, C. A. DiMarzio, and D. H. Brooks, “3D effects in DIC images of extended objects,” Proc. SPIE 7184, 71840D (2009).

Zeiss Information (2)

W. Lang, “Nomarski differential interference contrast microscopy. I. Fundamentals and experimental designs,” Zeiss Information 70, 114–120 (1968).

W. Lang, “Nomarski differential interference contrast microscopy. II. Formation of the interference image,” Zeiss Information 71, 12–16 (1969).

Other (22)

F. Kagalwala, F. Lanni, and T. Kanade, “Computational model of DIC microscopy: from observations to measurements,” Technical report CMU-R1 TR (Carnegie Mellon University, 2000).

S. Bradbury and P. Evennett, Contrast Techniques in Light Microscopy. Microscopy Handbooks 34 (Bios Scientific, 1996).

M. Pluta, Advanced Light Microscopy, Vol. 2 (Elsevier Science, 1988).

S. Trattner, M. Feigin, H. Greenspan, and N. Sochen, “Can Born approximate the unborn? A new validity criterion for the Born approximation in microscopic imaging,” in Mathematical Methods in Biomedical Image Analysis (MMBIA) Workshop, in conjunction with ICCV’07, Rio de Janeiro, Brazil (2007).

S. Trattner, E. Kashdan, M. Feigin, M. Greenspan, C.-F. Westin, and N. Sochen, “DIC microscopic imaging of living cell and error analysis of Born approximation,” in Proceedings of 3rd Workshop on Microscopic Image Analysis with Applications in Biology, in conjunction with MICCAI’08 (2008).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE, 1988).

M. Slaney, “Imaging with diffraction tomography,” Ph.D. thesis (Purdue University, 1985).

M. Born and E. Wolf, Principles of Optics, 4th ed. (Cambridge University, 1999).

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

J. J. Stamnes, Waves in Focal Regions (Adam Hilger, 1986).

P. Barber and S. Hill, Light Scattering by Particles: Computational Methods (World Scientific, 1990).

A. Taflove and C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 3rd ed. (Artech House, 2005).

C. Bohren and D. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

M. Mishchenko, L. Travis, and A. Lacis, Scattering, Absorption and Emission of Light by Small Particles (NASA Goddard Institute for Space Studies, 2006).

MicroscopyU, http://www.microscopyu.com/ .

S. Trattner, E. Kashdan, H. Greenspan, and N. Sochen, “Human embryo under the DIC microscope—vectorial approach to the electromagnetic scattering simulation,” in Proceedings of 8th International Conference on Spectral and High-Order Accurate Methods (ICOSAHOM), Trondheim, Norway (2009).

S. Trattner, M. Feigin, E. Kashdan, and N. Sochen, “GPU accelerated electromagnetic scattering and diffraction in 3D microscopic image formation,” in Proceedings of the 3rd Workshop on GPUs for Computer Vision, Barcelona, Spain (2011).

M. Feigin, “Computational methods in image analysis,” Ph.D. thesis (Tel Aviv University, 2012).

P. David and P. Rabinowitz, Methods of Numerical Integration (Academic, 1975).

W. Gautschi, Orthogonal Polynomials: Computation and Approximation (Oxford University, 2004).

O. M. Primer, http://micro.magnet.fsu.edu/primer/ .

S. Inoué and K. Spring, Video Microscopy: The Fundamentals, 2nd ed. (Plenum, 1997).

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Figures (12)

Fig. 1.
Fig. 1.

Diagram of principal components of DIC microscope.

Fig. 2.
Fig. 2.

Diagram of the DIC image formation process with the field notations at key planes.

Fig. 3.
Fig. 3.

Transition of light through the first DIC module.

Fig. 4.
Fig. 4.

Polarization planes of the split waves with respect to the incident field direction.

Fig. 5.
Fig. 5.

Diagram of the thin lens approximation: f is the focal length, zo is the object-to-lens distance, and zi is the lens-to-image plane distance.

Fig. 6.
Fig. 6.

Light diffraction and transition through the second DIC module.

Fig. 7.
Fig. 7.

Configuration of analyzer with respect to vibration planes of the incoming waves.

Fig. 8.
Fig. 8.

Transmission curve of the band-pass filter.

Fig. 9.
Fig. 9.

Effect of adding blur and noise to the simulated image: diagonal profile of the modeled “ideal” image (dashed blue line), and diagonal profile of the modeled image after convolution with low-pass filter with added Gaussian white noise, N (0, 0.0003) (solid red line).

Fig. 10.
Fig. 10.

Recorded (left) and simulated (center) DIC images of 82 μm sphere with no bias: (a)–(c) in focus, (d)–(f) 20 μm above focus, (g)–(i) 40 μm above focus, and (j)–(l) 20 μm below focus. The condenser aperture is closed to maximal position; the images are processed for the system noise; the right column shows the comparison of the diagonal profile of the recorded (dashed blue line) and simulated (solid red line) images.

Fig. 11.
Fig. 11.

Diagonal profiles of (a) recorded DIC images and (b) simulated DIC images at different distances above focus; no bias retardation. Solid red, dotted black, and angled dashed blue lines represent 10, 20, and 40 μm above focus level, respectively. The dashed black line represents the profile of the 20 μm above focus simulated image following removal of the ringing effect.

Fig. 12.
Fig. 12.

Recorded (left) and simulated (center) DIC images of 82 μm sphere with bias retardation: (a)–(c) in focus, (d)–(f) 20 μm above focus, (g)–(i) 40 μm above focus, and (j)–(i) 20 μm below focus. The condenser aperture is closed to maximal position; the images are processed for the system noise. The right column shows a comparison of the diagonal profile of the recorded (dashed blue line) and simulated (solid red line) images.

Tables (4)

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Table 1. Summary of the Experimental Setup of the DIC Microscope and the Microspheres Viewed

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Table 2. Summary of Image Formation Model Parameters, Corresponding to the Experimental Setup

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Table 3. Run Times for Mie Series Computations, in hh:mm:ss

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Table 4. Run Times for Fresnel Integral Computations, in hh:mm:ss

Equations (29)

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Ei(r)=E0exp(ike^z·riωt),
Ei(r)=E0exp(ike^z·r)e^φ,
E1(x)(r)=12E0exp(ike^z+·r)e^x,E1(y)(r)=12E0exp(ike^z·r)e^y.
E1(x)(r)=12E0exp(ike^z·r)e^x,E1(y)(r)=12E0exp(i(ke^z·(r+δr))e^y.
E1(x)(r)=12E0exp(ike^z·r)e^x,E1(y)(r)=12E0exp(i(ke^z·(r+δr)+ϕbias))e^y.
B⃗t+×E⃗=0,D⃗t×H⃗=J⃗,
B⃗=μH⃗D⃗=εE⃗,
E3(u,v)=TlE2(u,v),
Tl(u,v)=exp[ik(u2+v2)2f]P(u,v),
1f=1zo+1zi,
P(u,v)={1,u2+v2R2,0,otherwise,
E4(ξ,η)=eikziiλziE3(u,v)exp(ik[(uξ)2+(vη)2]2zi)dudv,
E4(x)(ξ,η)=E4(x)i(ξ,η)+E4(x)s(ξ,η),
E4(y)(ξ,η)=E4(y)i(ξ,η)+E4(y)s(ξ,η),
E5(ξ,η)=(E4(x)cos(π/4)+E4(y)cos(3π/4))e^φ,
E5(ξ,η)=0p(ω)E5(ξ,η,ω)dω.
I(ξ,η)=|E|2=|E5(x)(ξ,η)|2+|E5(y)(ξ,η)|2+|E5(z)(ξ,η)|2.
E1(x)(r)=Ei(kr)=E0exp[ike^z·r]e^x,
Ei(kr)=n=1En[Mo1n(1)iNe1n(1)],Eint(mkr)=n=1En[cnMo1n(1)idnNe1n(1)],Es(kr)=n=1En[ianNe1n(3)bnMo1n(3)],
En=in(2n+1)[n(n+1)]E0.
Mo1n(1,3)(r,θ,φ)=cosφπn(cosθ)zn(1,3)(ρ)e^θsinφτn(cosθ)zn(1,3)(ρ)e^φ,Ne1n(1,3)(r,θ,φ)=cosφn(n+1)sinθπn(cosθ)zn(1,3)(ρ)ρe^r+cosφτn(cosθ)[ρzn(1,3)(ρ)]ρe^θsinφπn(cosθ)[ρzn(1,3)(ρ)]ρe^θ,
πn=Pn1(cosθ)sinθ,τn=dPn1(cosθ)dθ,
jn(ρ)=(π2ρ)0.5Jn+1/2(ρ),
hn(1)(ρ)=jn(ρ)+iyn(ρ),
yn(ρ)=(π2ρ)0.5Yn+1/2(ρ),
(Ei+EsEint)×e^r=0,
ψn(ρ)=ρjn(ρ),ξn(ρ)=ρhn(1)(ρ),
an=mψn(mkr)ψn(kr)ψn(kr)ψn(mkr)mψn(mkr)ξn(kr)ξn(kr)ψn(mkr),bn=ψn(mkr)ψn(kr)mψn(kr)ψn(mkr)ψn(mkr)ξn(kr)mξn(kr)ψn(mkr),cn=mξn(mkr)ψn(mkr)mξn(mkr)ψn(mkr)ψn(mkr)ξn(kr)mξn(kr)ψn(mkr),dn=mξn(mkr)ψn(mkr)mξn(mkr)ψn(mkr)mψn(mkr)ξn(kr)ξn(kr)ψn(mkr).
nc=x+4.05x1/3+2,

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