Abstract

We describe a simple method for visualization of phase objects. The phase object is placed between a printed two-dimensional periodic pattern and a CCD camera. The ray deflection that is due to the phase object distorts the image of the pattern. This image is subtracted from a reference image and then, by squaring and low-pass filtering, a measurement of the two-dimensional refractive-index changes is obtained. Because the optical system does not require special alignment or illumination, the method presented has potential application for detection of gas leaks in industrial environments.

© 2000 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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1999

1998

E. M. Frins, W. Dultz, J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

1997

1996

1982

Donahue, J. E.

Dubra, A.

Dultz, W.

E. M. Frins, W. Dultz, J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Ferrari, J. A.

J. A. Ferrari, E. M. Frins, D. Perciante, A. Dubra, “Robust one-beam interferometer with phase-delay control,” Opt. Lett. 24, 1272–1274 (1999).
[CrossRef]

E. M. Frins, W. Dultz, J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Frins, E. M.

J. A. Ferrari, E. M. Frins, D. Perciante, A. Dubra, “Robust one-beam interferometer with phase-delay control,” Opt. Lett. 24, 1272–1274 (1999).
[CrossRef]

E. M. Frins, W. Dultz, J. A. Ferrari, “Polarization-shifting method for step interferometry,” Pure Appl. Opt. 7, 53–60 (1998).
[CrossRef]

Ina, H.

Kobayashi, S.

Massig, J. H.

Peale, R. E.

Perciante, D.

Ruffin, A. B.

Summers, P. L.

Takeda, M.

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Figures (2)

Fig. 1
Fig. 1

Sketch of the experimental setup.

Fig. 2
Fig. 2

(a) Image of the reference pattern, (b) image distorted by a column of butane gas flowing out from a tube, shown at the bottom, (c) result of subtraction of images (a) and (b) after squaring and filtering by use of a Gaussian spatial low-pass filter.

Equations (4)

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

Ix, y=1+sinωxsin(ωy),
Idx, y=1+sinωx+ϕxsinωy+ϕy,
Ix, y-Idx, y2cosωxsinωyϕx + cosωysin(ωx) ϕy2.
LPFI-Id2=14ϕx2+ϕx2=14 |Δϕ|2,

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