Abstract

Common path interferometers are widely used for visualizing phase disturbances and fluid flows. They are attractive because of the inherent simplicity and robustness in the setup. A graphic method will be presented for analyzing and optimizing filter parameters in common path interferometers.

© 1998 Optical Society of America

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References

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  1. C. S. Anderson. “Fringe visibility, irradiance, and accuracy in common path interferometers for visualization of phase disturbances,” Appl. Opt. 34,7474–7485 (1995).
    [CrossRef] [PubMed]
  2. H. Kadono et al., “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Comm. 110,391–400 (1994).
    [CrossRef]
  3. J. Glückstad, “Pattern generation by inverse phase contrast-comment,” Opt. Comm. 147,16–19 (1998).
    [CrossRef]
  4. J. Glückstad, “Phase contrast image synthesis,” Opt. Comm. 130,225–230 (1996).
    [CrossRef]
  5. F. Zernike, “How I discovered phase contrast,” Science 121,345–349 (1955).
    [CrossRef] [PubMed]
  6. J. Glückstad et al., “Lossless projection of light,” Opt. Phot. News 8(12), 20–21 (1997).
    [CrossRef]

1998 (1)

J. Glückstad, “Pattern generation by inverse phase contrast-comment,” Opt. Comm. 147,16–19 (1998).
[CrossRef]

1997 (1)

J. Glückstad et al., “Lossless projection of light,” Opt. Phot. News 8(12), 20–21 (1997).
[CrossRef]

1996 (1)

J. Glückstad, “Phase contrast image synthesis,” Opt. Comm. 130,225–230 (1996).
[CrossRef]

1995 (1)

1994 (1)

H. Kadono et al., “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Comm. 110,391–400 (1994).
[CrossRef]

1955 (1)

F. Zernike, “How I discovered phase contrast,” Science 121,345–349 (1955).
[CrossRef] [PubMed]

Anderson, C. S.

Glückstad, J.

J. Glückstad, “Pattern generation by inverse phase contrast-comment,” Opt. Comm. 147,16–19 (1998).
[CrossRef]

J. Glückstad et al., “Lossless projection of light,” Opt. Phot. News 8(12), 20–21 (1997).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Comm. 130,225–230 (1996).
[CrossRef]

Kadono, H.

H. Kadono et al., “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Comm. 110,391–400 (1994).
[CrossRef]

Zernike, F.

F. Zernike, “How I discovered phase contrast,” Science 121,345–349 (1955).
[CrossRef] [PubMed]

Appl. Opt. (1)

Opt. Phot. News (1)

J. Glückstad et al., “Lossless projection of light,” Opt. Phot. News 8(12), 20–21 (1997).
[CrossRef]

Opt. Comm. (3)

H. Kadono et al., “Phase shifting common path interferometer using a liquid-crystal phase modulator,” Opt. Comm. 110,391–400 (1994).
[CrossRef]

J. Glückstad, “Pattern generation by inverse phase contrast-comment,” Opt. Comm. 147,16–19 (1998).
[CrossRef]

J. Glückstad, “Phase contrast image synthesis,” Opt. Comm. 130,225–230 (1996).
[CrossRef]

Science (1)

F. Zernike, “How I discovered phase contrast,” Science 121,345–349 (1955).
[CrossRef] [PubMed]

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Figures (5)

Figure 1
Figure 1

Common path interferometer based on 4-f lens configuration. Filter parameters are given by (A, B. θ) and η indicates the fraction of filter radius measured to the radius of the mainlobe of the zero-order diffracted light From a circular input object aperture.

Figure 2
Figure 2

The new chart introduced in the paper.

Figure 3
Figure 3

Zernike phase contrast with ( K | α ¯ | ,   θ ) = ( 1 ,   π / 2 ) .

Figure 4
Figure 4

Generalized phase contrast with ( K | α ¯ | ,   θ ) = ( 1 / 2 ,   π ) .

Figure 5
Figure 5

Example showing optimization of filter parameters (A, B, θ) for K | α ¯ | = 1 / 2 .

Equations (5)

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I ( x ,   y )     A 2 | exp ( i ϕ ˜ ( x ,   y ) ) + K | α ¯ | ( BA 1 exp ( i θ ) 1 ) | 2
{ α ¯ = ( obj.area ) 1   obj.area exp ( i ϕ ( x ,   y ) ) d x d y = | α ¯ | exp ( i ϕ α ¯ ) ϕ ˜ ( x ,   y ) = ϕ ( x ,   y ) ϕ α ¯ K = η 2 ( 0.61   π ) 2
| α ¯ | = ( 2 | sin ( θ / 2 ) | ) 1
{ B A 1 = 1 2 ( K | α ¯ | ) 1   cos ( ϕ ˜ 0 ) + ( K | α ¯ | ) 2 θ = sin 1   ( ( B A 1   K | α ¯ | ) 1   sin ( ϕ ˜ 0 ) )
| α ¯ | u n i f o r m = | sin c ( ϕ ˜ 0 ) | .

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