Abstract

A liquid-crystal variable retarder inserted into a differential-interference contrast video microscope switches image highlights into shadows and vice versa in alternate frames. Synchronous computation and display of the difference between alternate frames yield a stream of images with doubled contrast and reduced fixed-position noise because of the automatic background subtraction. The measured signal-to-noise ratio (SNR) peaks when the modulation ±Γ of the retarder equals the phase shift δ of the sample. A Jones calculus model of the central ray in the polarization-modulated differential-interference contrast microscope yields

SNR=sin Γ sin δ1-cos Γ cos δN,
where N is the rms time-dependent photon noise. This expression fits the experiments closely for 1.8° ≤ Γ ≤ 115°.

© 2000 Optical Society of America

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  1. R. D. Allen, G. B. David, G. Z. Nomarski, “The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy,” Wiss. Mikros. Mikroscop. Technol. 69, 193–221 (1960).
  2. S. Inoué, Video Microscopy (Plenum, New York, 1986).
    [CrossRef]
  3. E. D. Salmon, P. Tran, “High-resolution video-enhanced differential interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
    [CrossRef]
  4. T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, San Diego, Calif., 1996).
  5. G. Nomarski, “Microinterferometre differential à ondes polarisées,” J. Phys. Radium Paris 16, 9–13 (1955).
  6. R. D. Allen, N. S. Allen, J. L. Travis, “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy,” Cell Motil. 1, 291–302 (1981).
  7. S. Inoué, “Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy,” J. Cell Biol. 89, 346–356 (1981).
    [CrossRef] [PubMed]
  8. R. D. Allen, N. S. Allen, “Video-enhanced microscopy with a computer frame memory,” J. Microsc. 129, 3–17 (1983).
    [CrossRef] [PubMed]
  9. E. D. Salmon, “VE-DIC light microscopy and the discovery of kinesin,” Trends Cell Biol. 5, 154–158 (1995).
    [CrossRef] [PubMed]
  10. G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
    [CrossRef]
  11. H. Ishiwata, M. Itoh, T. Yatagai, “Retardation modulated differential interference microscope and its application to 3-D shape measurement,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 21–24 (1996).
    [CrossRef]
  12. T. R. Corle, G. S. Kino, “Differential interference contrast imaging on a real-time confocal scanning optical microscope,” Appl. Opt. 29, 3769–3774 (1990).
    [CrossRef] [PubMed]
  13. R. Oldenbourg, “Polarized light microscopy of spindles,” Meth. Cell Biol. 61, 175–208 (1999).
    [CrossRef]
  14. N. J. Bershad, A. J. Rockmore, “On estimating signal-to-noise ratio using the sample correlation coefficient,” IEEE Trans. Inf. Theory 20, 112–113 (1974).
    [CrossRef]
  15. J. Frank, L. Al-Ali, “Signal-to-noise ratio of electron micrographs obtained by cross correlation,” Nature 256, 376–379 (1975).
    [CrossRef] [PubMed]
  16. E. Collett, Polarized Light (Marcel Dekker, New York, 1993), Chap. 10.
  17. D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).
  18. G. C. Holst, CCD Arrays, Cameras, and Displays, 2nd ed., Vol. PM57 of SPIE Monographs and Handbooks Series (SPIE Press, Bellingham, Wash., 1998).
  19. D. Axelrod, “Fluorescence polarization microscopy,” Meth. Cell Biol. 30, 333–352 (1989).
    [CrossRef]
  20. R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
    [CrossRef]
  21. F. Kagalwala, T. Kanade, “Computational model of image formation process in DIC microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V, C. J. Cogswell, J. Conchello, J. M. Lerner, T. T. Lu, T. Wilson, eds., Proc. SPIE3261, 193–204 (1999).

1999

R. Oldenbourg, “Polarized light microscopy of spindles,” Meth. Cell Biol. 61, 175–208 (1999).
[CrossRef]

1998

E. D. Salmon, P. Tran, “High-resolution video-enhanced differential interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

1997

G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
[CrossRef]

1995

E. D. Salmon, “VE-DIC light microscopy and the discovery of kinesin,” Trends Cell Biol. 5, 154–158 (1995).
[CrossRef] [PubMed]

R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
[CrossRef]

1990

1989

D. Axelrod, “Fluorescence polarization microscopy,” Meth. Cell Biol. 30, 333–352 (1989).
[CrossRef]

1983

R. D. Allen, N. S. Allen, “Video-enhanced microscopy with a computer frame memory,” J. Microsc. 129, 3–17 (1983).
[CrossRef] [PubMed]

1981

R. D. Allen, N. S. Allen, J. L. Travis, “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy,” Cell Motil. 1, 291–302 (1981).

S. Inoué, “Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy,” J. Cell Biol. 89, 346–356 (1981).
[CrossRef] [PubMed]

1975

J. Frank, L. Al-Ali, “Signal-to-noise ratio of electron micrographs obtained by cross correlation,” Nature 256, 376–379 (1975).
[CrossRef] [PubMed]

1974

N. J. Bershad, A. J. Rockmore, “On estimating signal-to-noise ratio using the sample correlation coefficient,” IEEE Trans. Inf. Theory 20, 112–113 (1974).
[CrossRef]

1960

R. D. Allen, G. B. David, G. Z. Nomarski, “The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy,” Wiss. Mikros. Mikroscop. Technol. 69, 193–221 (1960).

1955

G. Nomarski, “Microinterferometre differential à ondes polarisées,” J. Phys. Radium Paris 16, 9–13 (1955).

Al-Ali, L.

J. Frank, L. Al-Ali, “Signal-to-noise ratio of electron micrographs obtained by cross correlation,” Nature 256, 376–379 (1975).
[CrossRef] [PubMed]

Allen, N. S.

G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
[CrossRef]

R. D. Allen, N. S. Allen, “Video-enhanced microscopy with a computer frame memory,” J. Microsc. 129, 3–17 (1983).
[CrossRef] [PubMed]

R. D. Allen, N. S. Allen, J. L. Travis, “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy,” Cell Motil. 1, 291–302 (1981).

Allen, R. D.

R. D. Allen, N. S. Allen, “Video-enhanced microscopy with a computer frame memory,” J. Microsc. 129, 3–17 (1983).
[CrossRef] [PubMed]

R. D. Allen, N. S. Allen, J. L. Travis, “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy,” Cell Motil. 1, 291–302 (1981).

R. D. Allen, G. B. David, G. Z. Nomarski, “The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy,” Wiss. Mikros. Mikroscop. Technol. 69, 193–221 (1960).

Axelrod, D.

D. Axelrod, “Fluorescence polarization microscopy,” Meth. Cell Biol. 30, 333–352 (1989).
[CrossRef]

Bershad, N. J.

N. J. Bershad, A. J. Rockmore, “On estimating signal-to-noise ratio using the sample correlation coefficient,” IEEE Trans. Inf. Theory 20, 112–113 (1974).
[CrossRef]

Chipman, R. A.

R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
[CrossRef]

Collett, E.

E. Collett, Polarized Light (Marcel Dekker, New York, 1993), Chap. 10.

Corle, T. R.

T. R. Corle, G. S. Kino, “Differential interference contrast imaging on a real-time confocal scanning optical microscope,” Appl. Opt. 29, 3769–3774 (1990).
[CrossRef] [PubMed]

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, San Diego, Calif., 1996).

David, G. B.

R. D. Allen, G. B. David, G. Z. Nomarski, “The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy,” Wiss. Mikros. Mikroscop. Technol. 69, 193–221 (1960).

Frank, J.

J. Frank, L. Al-Ali, “Signal-to-noise ratio of electron micrographs obtained by cross correlation,” Nature 256, 376–379 (1975).
[CrossRef] [PubMed]

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays, 2nd ed., Vol. PM57 of SPIE Monographs and Handbooks Series (SPIE Press, Bellingham, Wash., 1998).

Holzwarth, G.

G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
[CrossRef]

Inoué, S.

S. Inoué, “Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy,” J. Cell Biol. 89, 346–356 (1981).
[CrossRef] [PubMed]

S. Inoué, Video Microscopy (Plenum, New York, 1986).
[CrossRef]

Ishiwata, H.

H. Ishiwata, M. Itoh, T. Yatagai, “Retardation modulated differential interference microscope and its application to 3-D shape measurement,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 21–24 (1996).
[CrossRef]

Itoh, M.

H. Ishiwata, M. Itoh, T. Yatagai, “Retardation modulated differential interference microscope and its application to 3-D shape measurement,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 21–24 (1996).
[CrossRef]

Kagalwala, F.

F. Kagalwala, T. Kanade, “Computational model of image formation process in DIC microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V, C. J. Cogswell, J. Conchello, J. M. Lerner, T. T. Lu, T. Wilson, eds., Proc. SPIE3261, 193–204 (1999).

Kanade, T.

F. Kagalwala, T. Kanade, “Computational model of image formation process in DIC microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V, C. J. Cogswell, J. Conchello, J. M. Lerner, T. T. Lu, T. Wilson, eds., Proc. SPIE3261, 193–204 (1999).

Kino, G. S.

T. R. Corle, G. S. Kino, “Differential interference contrast imaging on a real-time confocal scanning optical microscope,” Appl. Opt. 29, 3769–3774 (1990).
[CrossRef] [PubMed]

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, San Diego, Calif., 1996).

Kliger, D. S.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Kubinski, D. J.

G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
[CrossRef]

Lewis, J. W.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Nomarski, G.

G. Nomarski, “Microinterferometre differential à ondes polarisées,” J. Phys. Radium Paris 16, 9–13 (1955).

Nomarski, G. Z.

R. D. Allen, G. B. David, G. Z. Nomarski, “The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy,” Wiss. Mikros. Mikroscop. Technol. 69, 193–221 (1960).

Oldenbourg, R.

R. Oldenbourg, “Polarized light microscopy of spindles,” Meth. Cell Biol. 61, 175–208 (1999).
[CrossRef]

Randall, C. E.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

Rockmore, A. J.

N. J. Bershad, A. J. Rockmore, “On estimating signal-to-noise ratio using the sample correlation coefficient,” IEEE Trans. Inf. Theory 20, 112–113 (1974).
[CrossRef]

Salmon, E. D.

E. D. Salmon, P. Tran, “High-resolution video-enhanced differential interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

E. D. Salmon, “VE-DIC light microscopy and the discovery of kinesin,” Trends Cell Biol. 5, 154–158 (1995).
[CrossRef] [PubMed]

Tran, P.

E. D. Salmon, P. Tran, “High-resolution video-enhanced differential interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

Travis, J. L.

R. D. Allen, N. S. Allen, J. L. Travis, “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy,” Cell Motil. 1, 291–302 (1981).

Webb, S. C.

G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
[CrossRef]

Yatagai, T.

H. Ishiwata, M. Itoh, T. Yatagai, “Retardation modulated differential interference microscope and its application to 3-D shape measurement,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 21–24 (1996).
[CrossRef]

Appl. Opt.

Cell Motil.

R. D. Allen, N. S. Allen, J. L. Travis, “Video-enhanced contrast, differential interference contrast (AVEC-DIC) microscopy,” Cell Motil. 1, 291–302 (1981).

IEEE Trans. Inf. Theory

N. J. Bershad, A. J. Rockmore, “On estimating signal-to-noise ratio using the sample correlation coefficient,” IEEE Trans. Inf. Theory 20, 112–113 (1974).
[CrossRef]

J. Cell Biol.

S. Inoué, “Video image processing greatly enhances contrast, quality, and speed in polarization-based microscopy,” J. Cell Biol. 89, 346–356 (1981).
[CrossRef] [PubMed]

J. Microsc.

R. D. Allen, N. S. Allen, “Video-enhanced microscopy with a computer frame memory,” J. Microsc. 129, 3–17 (1983).
[CrossRef] [PubMed]

G. Holzwarth, S. C. Webb, D. J. Kubinski, N. S. Allen, “Improving DIC microscopy with polarization modulation,” J. Microsc. 188, 249–254 (1997).
[CrossRef]

J. Phys. Radium Paris

G. Nomarski, “Microinterferometre differential à ondes polarisées,” J. Phys. Radium Paris 16, 9–13 (1955).

Meth. Cell Biol.

R. Oldenbourg, “Polarized light microscopy of spindles,” Meth. Cell Biol. 61, 175–208 (1999).
[CrossRef]

E. D. Salmon, P. Tran, “High-resolution video-enhanced differential interference contrast (VE-DIC) light microscopy,” Meth. Cell Biol. 56, 153–185 (1998).
[CrossRef]

D. Axelrod, “Fluorescence polarization microscopy,” Meth. Cell Biol. 30, 333–352 (1989).
[CrossRef]

Nature

J. Frank, L. Al-Ali, “Signal-to-noise ratio of electron micrographs obtained by cross correlation,” Nature 256, 376–379 (1975).
[CrossRef] [PubMed]

Opt. Eng.

R. A. Chipman, “Mechanics of polarization ray tracing,” Opt. Eng. 34, 1636–1645 (1995).
[CrossRef]

Trends Cell Biol.

E. D. Salmon, “VE-DIC light microscopy and the discovery of kinesin,” Trends Cell Biol. 5, 154–158 (1995).
[CrossRef] [PubMed]

Wiss. Mikros. Mikroscop. Technol.

R. D. Allen, G. B. David, G. Z. Nomarski, “The Zeiss–Nomarski differential interference equipment for transmitted-light microscopy,” Wiss. Mikros. Mikroscop. Technol. 69, 193–221 (1960).

Other

S. Inoué, Video Microscopy (Plenum, New York, 1986).
[CrossRef]

T. R. Corle, G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic, San Diego, Calif., 1996).

E. Collett, Polarized Light (Marcel Dekker, New York, 1993), Chap. 10.

D. S. Kliger, J. W. Lewis, C. E. Randall, Polarized Light in Optics and Spectroscopy (Academic, New York, 1990).

G. C. Holst, CCD Arrays, Cameras, and Displays, 2nd ed., Vol. PM57 of SPIE Monographs and Handbooks Series (SPIE Press, Bellingham, Wash., 1998).

H. Ishiwata, M. Itoh, T. Yatagai, “Retardation modulated differential interference microscope and its application to 3-D shape measurement,” in International Symposium on Polarization Analysis and Applications to Device Technology, T. Yoshizawa, H. Yokota, eds., Proc. SPIE2873, 21–24 (1996).
[CrossRef]

F. Kagalwala, T. Kanade, “Computational model of image formation process in DIC microscopy,” in Three-Dimensional and Multidimensional Microscopy: Image Acquisition and Processing V, C. J. Cogswell, J. Conchello, J. M. Lerner, T. T. Lu, T. Wilson, eds., Proc. SPIE3261, 193–204 (1999).

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Figures (6)

Fig. 1
Fig. 1

Schematic of the DIC microscope with a retardation modulator installed between the polarizer and the first Wollaston prism.

Fig. 2
Fig. 2

Dependence of the intensity I within a DIC image on the total phase difference between the two arms of the interferometer. The insets on the right-hand side show a phase object whose refractive index is larger than that of the background and the resultant image for Γ = +90°. The image has a highlight at the left-hand edge of the object and a shadow on its right-hand edge. The insets on the left-hand side show the same object and its image intensity for Γ = -90°. The contrast generated by the same object is reversed because the slope of the sine-squared curve changes sign.

Fig. 3
Fig. 3

SNR for PM-DIC images obtained by manual (off-line) subtraction of the DIC images at specific values of +Γ and -Γ. The curve through the data points represents Eq. (11) with I*/(N2¯)1/2= 10.8 and δ = 14°; these values were obtained by a nonlinear least-squares fit of Eq. (11) to the experimental data with I*/(N2¯)1/2 and δ as the adjustable parameters. We used a Zeiss Model Axioplan DIC microscope with a 63× planapo objective (NA = 1.4 and oil immersion), a NA = 1.4 oil condenser, and a 2× Optovar setting. The sample was the diatom Pleurosigma angulatum. The camera was a Sony Model XC7500 analog CCD with 659 × 494 elements, each of dimensions 9.9 µm × 9.9 µm.

Fig. 4
Fig. 4

PM-DIC images of the diatom Pleurosigma angulatum obtained by insertion of an electro-optic modulator in the microscope and the processing of the images continually at 30 fps with a frame processor. Left-hand panel: Γ = 3.6° and a SNR of 7.7. Center panel: Γ = 14.4° and a SNR of 17.7. Right-hand panel: Γ = 90° and a SNR of 4.5. The SNR’s were determined in the same 50 × 100 pixel AOI shown overlaid on each image. The camera was a Sony Model XC7500. The spacing of the repetitive pattern in the diatom is 620 nm.3

Fig. 5
Fig. 5

SNR of the PM-DIC images processed and displayed immediately in real time at 30 fps. The curve through the data points represents Eq. (11) with I*/(N2¯)1/2= 18.1 and δ = 14°; these values were obtained by a nonlinear least-squares fit of the experimental data to Eq. (11). The microscope, the sample, and the camera were as in Fig. 3, but Γ was modulated at 30 Hz by the variable retarder.

Fig. 6
Fig. 6

SNR for PM-DIC images obtained with a Kodak Model ES 1.0 digital CCD camera with 1000 × 1000 × 10 bits at 15 fps. The images were processed on-line and displayed immediately at 15 fps. The curve through the data points is a nonlinear least squares fit to Eq. (11) with I*/(N2¯)1/2= 43 and δ = 23°. The microscope, the specimen, and the modulator were the same as for Figs. 4 and 5.

Equations (13)

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

SNR=sin Γ sin δ1-cos Γ cos δN,
I=I0 sin2Δ2,
I1=S+N1,  I2=S+N2,
SNR=I1-I1¯I2-I2¯I1-I1¯2I2-I2¯21/2-I1-I1¯I2-I2¯1/2,
|output|=|analyzer||WollastonsampleWollaston||WollastonsampleWollaston||modulatorinput|.
ExEy=00011001          ½½½½expiδ00expiδ½-½-½½cosΓ/2  i sinΓ/2i sinΓ/2  cosΓ/210,
I+=I021+sin Γ sin δ-cos Γ cos δ=I0 sin2Γ+δ2.
I-=I021-sin Γ sin δ-cos Γ cos δ=I0 sin2-Γ+δ2.
I=I+-I-=I0 sin Γ sin δ.
Ī=I021-cos Γ cos δ.
I0=2I*1-cos Γ cos δ.
I=2I* sin Γ sin δ1-cos Γ cos δ.
SNR=2I* sin Γ sin δN2¯1/21-cos Γ cos δ.

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