Abstract

We present a new type of quadrature phase-shifting interferometer, which utilizes wave plates, a diffraction grating, and two lasers with different wavelengths, in order to acquire two sets of two quadrature fringe patterns in each wavelength formed on a single image sensor. This method for calculating with four phase-shifted fringe patterns gives us the phase sum and difference distributions between the phases in two wavelengths. This is also substantiated by results of our experiments.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. J. P. van Haasteren and H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33, 4137-4142 (1994).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  9. Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069-1071(2004).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2007 (2)

2006 (1)

2005 (1)

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

2004 (4)

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407-412 (2004).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069-1071(2004).
[CrossRef]

M. B. North-Morris, J. E. Millerd, N. J. Brock, and J. B. Hayes, “Phase-shifting multi-wavelength dynamic interferometer,” Proc. SPIE 5531, 64-75 (2004).
[CrossRef]

2003 (1)

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524-3531 (2003).
[CrossRef]

2000 (1)

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960-966 (2000).
[CrossRef]

1997 (1)

1995 (1)

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74-86 (1995).

1994 (2)

A. J. P. van Haasteren and H. J. Frankena, “Real-time displacement measurement using a multicamera phase-stepping speckle interferometer,” Appl. Opt. 33, 4137-4142 (1994).
[CrossRef]

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610-622 (1994).
[CrossRef]

1990 (1)

1985 (1)

1984 (1)

1982 (1)

1974 (1)

Almazan-Cuellar, S.

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524-3531 (2003).
[CrossRef]

Awatsuji, Y.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069-1071(2004).
[CrossRef]

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Brangaccio, D. J.

Brock, N.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Brock, N. J.

M. B. North-Morris, J. E. Millerd, N. J. Brock, and J. B. Hayes, “Phase-shifting multi-wavelength dynamic interferometer,” Proc. SPIE 5531, 64-75 (2004).
[CrossRef]

Bruning, J. H.

Cai, L. Z.

Cheng, Y. Y.

Dong, G. Y.

Frankena, H. J.

Gallagher, J. E.

Hayes, J.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Hayes, J. B.

M. B. North-Morris, J. E. Millerd, N. J. Brock, and J. B. Hayes, “Phase-shifting multi-wavelength dynamic interferometer,” Proc. SPIE 5531, 64-75 (2004).
[CrossRef]

He, X.

Herriott, D. R.

Hettwer, A.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960-966 (2000).
[CrossRef]

Ina, H.

Isshiki, M.

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74-86 (1995).

Kameyama, T.

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610-622 (1994).
[CrossRef]

Kemao, Q.

Kerr, D.

Kiire, T.

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407-412 (2004).

Kimbrough, B.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

Kobayashi, S.

Kranz, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960-966 (2000).
[CrossRef]

Kubota, T.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069-1071(2004).
[CrossRef]

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Malacara-Hernandez, D.

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524-3531 (2003).
[CrossRef]

Meng, X. F.

Millerd, J.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Millerd, J. E.

M. B. North-Morris, J. E. Millerd, N. J. Brock, and J. B. Hayes, “Phase-shifting multi-wavelength dynamic interferometer,” Proc. SPIE 5531, 64-75 (2004).
[CrossRef]

Nakadate, S.

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407-412 (2004).

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74-86 (1995).

S. Nakadate and H. Saito, “Fringe scanning speckle-pattern interferometry,” Appl. Opt. 24, 2172-2180 (1985).
[CrossRef] [PubMed]

North-Morris, M.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

North-Morris, M. B.

M. B. North-Morris, J. E. Millerd, N. J. Brock, and J. B. Hayes, “Phase-shifting multi-wavelength dynamic interferometer,” Proc. SPIE 5531, 64-75 (2004).
[CrossRef]

Novak, M.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Onuma, K.

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610-622 (1994).
[CrossRef]

Rosenfeld, D. P.

Saito, H.

Santoyo, F. Mendoza

Sasada, M.

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069-1071(2004).
[CrossRef]

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

Schreiber, H.

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), pp. 547-666.
[CrossRef]

Schwider, J.

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960-966 (2000).
[CrossRef]

Shen, X. X.

Shibuya, M.

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407-412 (2004).

Shiozawa, K.

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407-412 (2004).

Soon, S. Hock

Takeda, M.

Tsukamoto, K.

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610-622 (1994).
[CrossRef]

Tyrer, J. R.

van Haasteren, A. J. P.

Wang, Y. R.

White, A. D.

Wyant, J.

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

Wyant, J. C.

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

Y. Y. Cheng and J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539-4543 (1984).
[CrossRef] [PubMed]

Xu, X. F.

Yamaguchi, I.

Yang, F.

Yang, X. L.

Zhang, T.

Appl. Opt. (5)

Appl. Phys. Lett. (1)

Y. Awatsuji, M. Sasada, and T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85, 1069-1071(2004).
[CrossRef]

J. Cryst. Growth (1)

K. Onuma, T. Kameyama, and K. Tsukamoto, “In situ study of surface phenomena by real time phase shift interferometry,” J. Cryst. Growth 137, 610-622 (1994).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Jpn. J. Opt. (1)

S. Nakadate, T. Kiire, K. Shiozawa, and M. Shibuya, “Phase-shifting interferometer using two phase-shifted fringe patterns in quadrature,” Jpn. J. Opt. 33, 407-412 (2004).

Opt. Eng. (2)

S. Almazan-Cuellar and D. Malacara-Hernandez, “Two-step phase-shifting algorithm,” Opt. Eng. 42, 3524-3531 (2003).
[CrossRef]

A. Hettwer, J. Kranz, and J. Schwider, “Three channel phase-shifting interferometer using polarization-optics and a diffraction grating,” Opt. Eng. 39, 960-966 (2000).
[CrossRef]

Opt. Lett. (3)

Proc. SPIE (4)

N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 5875F (2005).

J. Millerd, N. Brock, J. Hayes, M. North-Morris, M. Novak, and J. C. Wyant, “Pixelated phase-mask dynamic interferometer,” Proc. SPIE 5531, 304-314 (2004).
[CrossRef]

S. Nakadate and M. Isshiki, “Real-time fringe pattern processing and its applications,” Proc. SPIE 2544, 74-86 (1995).

M. B. North-Morris, J. E. Millerd, N. J. Brock, and J. B. Hayes, “Phase-shifting multi-wavelength dynamic interferometer,” Proc. SPIE 5531, 64-75 (2004).
[CrossRef]

Other (2)

H. Schreiber and J. H. Bruning, “Phase shifting interferometry,” in Optical Shop Testing, 3rd ed., D.Malacara, ed. (Wiley, 2007), pp. 547-666.
[CrossRef]

M. Sasada, Y. Awatsuji, and T. Kubota, “Parallel quasi-phase-shifting digital holography implemented by simple optical set up and effective use of image-sensor pixels,” in Technical Digest of 2004 ICO International Conference Optics and Photonics in Technology Frontier (International Commission for Optics, 2004), pp. 357-358.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of two wavelength quadrature phase-shifting interferometer with wave plates and a diffraction grating.

Fig. 2
Fig. 2

Simultaneous formation of four fringe patterns that are separated spatially by orthogonal polarization directions and by wavelengths of light.

Fig. 3
Fig. 3

Quadrature phase-shifting interferograms. Two interferograms on the left-hand side are phase-shifted fringes in quadrature for wavelength λ 1 ( = 612 nm ) , and those on the right-hand side are the same ones for wavelength λ 2 ( = 633 nm ) .

Fig. 4
Fig. 4

Interferograms in phase for use in image matching, which are acquired under the same condition shown in Fig. 3 without the λ / 8 wave plate.

Fig. 5
Fig. 5

Interferograms changed in the region selected from Fig. 3, where each picture size is 140 × 140 pixels. Two interferograms (a) and (b) are phase-shifted fringes in quadrature for wavelength λ 1 ( = 612 nm ) , and (c) and (d) are the same ones for wavelength λ 2 ( 633 nm ) .

Fig. 6
Fig. 6

Phase distributions calculated with fringe patterns shown in Figs. 5a, 5b, 5c, 5d: (a) phase sum of θ 1 + θ 2 ; (b) phase difference of θ 2 θ 1 .

Fig. 7
Fig. 7

Line profiles of (a) unwrapped phase sum and (b) wrapped phase difference in the 36th horizontal line from the top of the image shown in Fig. 6.

Equations (16)

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

I 1 = A + B cos θ 1 ,
I 2 = A B sin θ 1 .
I 3 = A + B cos θ 2 ,
I 4 = A B sin θ 2 .
C = I 1 I 4 = 2 B cos ( ψ 2 π 4 ) cos ( φ 2 π 4 ) ,
S = I 2 I 3 = 2 B cos ( ψ 2 π 4 ) sin ( φ 2 π 4 ) ,
E = C 2 S 2 = 4 B 2 cos 2 ( ψ 2 π 4 ) sin φ ,
F = 2 C S = 4 B 2 cos 2 ( ψ 2 π 4 ) cos φ .
φ = tan 1 ( E F ) .
G = ( I 1 I 3 ) + ( I 2 I 4 ) = 2 2 B sin ( φ 2 ) cos ( ψ 2 π 4 ) ,
H = ( I 1 I 3 ) ( I 2 I 4 ) = 2 2 B sin ( φ 2 ) sin ( ψ 2 π 4 ) .
J = G 2 H 2 = 8 B 2 sin 2 ( φ 2 ) sin ψ ,
K = 2 G H = 8 B 2 sin 2 ( φ 2 ) cos ψ .
ψ = tan 1 ( J K ) .
λ H = λ 1 λ 2 λ 1 + λ 2 ,
λ L = λ 1 λ 2 | λ 1 λ 2 | .

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