Abstract

We introduce a single-exposure widefield system of producing phase gradient images by dividing the illumination and detection apertures into two oblique complementary components and encoding them using polarization. A Wollaston prism splits the images formed by the two respective aperture halves to allow both components to be simultaneously imaged by a single camera. By producing images characteristically similar to differential interference contrast while using a darkfield illumination scheme, sensitivity to weak phase gradients is improved.

© 2012 Optical Society of America

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References

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  1. F. Zernike, Z. Tech. Phys. 16, 454 (1935).
  2. G. Nomarski, J. Phys. Radium 16, 9S (1955).
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    [CrossRef]
  9. R. Yi, K. K. Chu, and J. Mertz, Opt. Express 14, 5191(2006).
    [CrossRef]

2009 (1)

2006 (1)

1999 (1)

H. U. Dodt, M. Eder, A. Frick, and W. Zieglgänsberger, Science 286, 110 (1999).
[CrossRef]

1984 (1)

D. K. Hamilton and C. J. R. Sheppard, J. Microsc. 133, 27 (1984).
[CrossRef]

1977 (1)

1976 (1)

1975 (1)

1955 (1)

G. Nomarski, J. Phys. Radium 16, 9S (1955).

1935 (1)

F. Zernike, Z. Tech. Phys. 16, 454 (1935).

Chu, K. K.

Dodd, J. G.

Dodt, H. U.

H. U. Dodt, M. Eder, A. Frick, and W. Zieglgänsberger, Science 286, 110 (1999).
[CrossRef]

Eder, M.

H. U. Dodt, M. Eder, A. Frick, and W. Zieglgänsberger, Science 286, 110 (1999).
[CrossRef]

Frick, A.

H. U. Dodt, M. Eder, A. Frick, and W. Zieglgänsberger, Science 286, 110 (1999).
[CrossRef]

Gross, L.

Hamilton, D. K.

D. K. Hamilton and C. J. R. Sheppard, J. Microsc. 133, 27 (1984).
[CrossRef]

Hoffman, R.

Mehta, S. B.

Mertz, J.

Nomarski, G.

G. Nomarski, J. Phys. Radium 16, 9S (1955).

Sheppard, C. J. R.

S. B. Mehta and C. J. R. Sheppard, Opt. Lett. 34, 1924(2009).
[CrossRef]

D. K. Hamilton and C. J. R. Sheppard, J. Microsc. 133, 27 (1984).
[CrossRef]

Stewart, W. C.

Yi, R.

Zernike, F.

F. Zernike, Z. Tech. Phys. 16, 454 (1935).

Zieglgänsberger, W.

H. U. Dodt, M. Eder, A. Frick, and W. Zieglgänsberger, Science 286, 110 (1999).
[CrossRef]

Appl. Opt. (2)

J. Microsc. (1)

D. K. Hamilton and C. J. R. Sheppard, J. Microsc. 133, 27 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Radium (1)

G. Nomarski, J. Phys. Radium 16, 9S (1955).

Opt. Express (1)

Opt. Lett. (1)

Science (1)

H. U. Dodt, M. Eder, A. Frick, and W. Zieglgänsberger, Science 286, 110 (1999).
[CrossRef]

Z. Tech. Phys. (1)

F. Zernike, Z. Tech. Phys. 16, 454 (1935).

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Figures (5)

Fig. 1.
Fig. 1.

Setup diagram of CAP, equivalent to two concurrent GFM setups encoded by polarization. The Wollaston prism splits the two polarizations onto two separate fields of view on the camera. Planes labeled xn to match equivalent planes in GFM.

Fig. 2.
Fig. 2.

A 90 μm polystyrene bead as seen through the two fields of view produced by the Wollaston prism, LS, and RS, respectively.

Fig. 3.
Fig. 3.

(a) CAP difference image of one lens from a Shack–Hartmann lenslet array with area outside imaging aperture removed. Dashed line indicates line profile section in (b), shown with linear fit.

Fig. 4.
Fig. 4.

Phase gradient shifts in detection aperture illustrated for the RS side of CAP and brightfield/oblique technique. Black: not illuminated. Gray: illuminated but blocked. White: illuminated and transmitted. (a) No phase gradient in sample. No light passed in CAP, maximum light passed in brightfield. (b) Phase gradient causing Δα rightward shift. Positive contrast in CAP, negative contrast in brightfield.

Fig. 5.
Fig. 5.

SNR for CAP and brightfield implementation of phase gradient imaging compared by plotting Eqs. (5) and (6).

Equations (7)

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I3(x3)=(Ke(x3+x1c,x1d)Tr(x1c,x1d)±Ko(x3+x1c,x1d)Ti(x1c,x1d))dx1cdx1d.
T(x1c,x1d)=t(x1c12x1d)t*(x1c+12x1d),
T(x1c,x1d)|t(x1c)|2[1+ix1dϕ(x1c)].
ΣI3(x3)=I3L(x3)+I3R(x3)=2Ke(x3+x1c,x1d)|t(x1c)|2dx1cdx1d,
ΔI3(x3)=I3L(x3)I3R(x3)=2Ko(x3+x1c,x1d)|t(x1c)|2x1dϕ(x1c)dx1cdx1d.
SNRCAP=(N0|Δα/αmax|)1/2.
SNRbright=(N0(Δα/αmax)22|Δα/αmax|)1/2.

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