Abstract

An alternative method for digital holography using a quadrature phase-shifting interferometer for high-speed measurement is presented. We show that it has image quality equal to the four-bucket method. In addition, it requires fewer imaging devices. Two quadrature phase-shifting fringe patterns are acquired in each state of an object changed temporally. The phase calculation method with these four fringe patterns gives the phase distribution of the hologram. This digital phase hologram is reconstructed to yield an object image by the Fresnel transform using digital convolutions with the fast Fourier transform algorithm. Verification results of simulations and experiments are given.

© 2009 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2008 (2)

2007 (1)

2006 (3)

2005 (1)

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

2004 (3)

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]

2003 (1)

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

2002 (1)

2000 (2)

T. Kim and T. C. Poon, “Three-dimensional matching by use of phase-only holographic information and the Wigner distribution,” J. Opt. Soc. Am. A 17, 2520-2528 (2000).
[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]

1997 (1)

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).

1995 (1)

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

1994 (1)

1987 (1)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124-1132 (1987).

1984 (1)

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-365 (1984).

1982 (1)

1972 (1)

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

1969 (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The kinoform : a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Almazan-Cuellar, S.

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

Awatsuji, Y.

Bertaux, N.

Brock, N.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

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]

Bruning, J. 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]

Creath, K.

K. Creath, J. Schmit, and J. C. Wyant, “Optical metrology of diffuse surfaces,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 783-801.

Doh, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

Frauel, Y.

Hayes, J.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

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]

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]

Hirsch, P. M.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The kinoform : a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Ida, T.

Ina, H.

Javidi, B.

Jordan, J. A.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The kinoform : a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Kaneko, A.

Kemao, Q.

Kiire, T.

T. Kiire, S. Nakadate, and S. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787-4792 (2008).
[CrossRef] [PubMed]

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).

Kim, T.

Kobayashi, S.

Koyama, T.

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]

Kronrod, M.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Kubota, T.

Lesem, L. B.

L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The kinoform : a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

Lett., Opt.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).

Malacara-Hernandez, D.

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

Matoba, O.

Merzlyakov, N.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Millerd, J.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

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]

Mills, G. A.

Moore, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-365 (1984).

Morris, M. N.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Murata, S.

Nakadate, S.

T. Kiire, S. Nakadate, and S. Shibuya, “Simultaneous formation of four fringes by using a polarization quadrature phase-shifting interferometer with wave plates and a diffraction grating,” Appl. Opt. 47, 4787-4792 (2008).
[CrossRef] [PubMed]

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).

Naughton, T. J.

Nishio, K.

Nitanai, E.

Nomura, T.

North-Morris, M.

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]

Novak, M.

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]

Numata, T.

Onural, L.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124-1132 (1987).

Poon, T. C.

Poon, T.-C.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

Saif, B.

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Sasada, M.

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

Schilling, B.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

Schmit, J.

K. Creath, J. Schmit, and J. C. Wyant, “Optical metrology of diffuse surfaces,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 783-801.

Schnars, U.

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]

Scott, P. D.

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124-1132 (1987).

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).

Shibuya, S.

Shinoda, K.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

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).

Smythe, R.

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-365 (1984).

Soon, S. Hock

Suzuki, Y.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

Tahara, T.

Takeda, M.

Ura, S.

Wu, M.

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[CrossRef]

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]

K. Creath, J. Schmit, and J. C. Wyant, “Optical metrology of diffuse surfaces,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 783-801.

Yamaguchi, I.

Yamamoto, K.

Yamashita, K.

Yaroslavskii, L.

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Yokota, M.

Zhang, T.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).

Appl. Opt. (6)

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]

IBM J. Res. Dev. (1)

L. B. Lesem, P. M. Hirsch, and J. A. Jordan Jr., “The kinoform : a new wavefront reconstruction device,” IBM J. Res. Dev. 13, 150-155 (1969).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

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. (5)

L. Onural and P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124-1132 (1987).

R. Smythe and R. Moore, “Instantaneous phase measuring interferometry,” Opt. Eng. 23, 361-365 (1984).

T.-C. Poon, K. Doh, B. Schilling, M. Wu, K. Shinoda, and Y. Suzuki, “Three-dimensional microscopy by optical scanning holography,” Opt. Eng. 34, 1338-1344 (1995).
[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]

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

Opt. Lett. (1)

Proc. SPIE (2)

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]

M. N. Morris, J. Millerd, N. Brock, J. Hayes, and B. Saif, “Dynamic phase-shifting electronic speckle pattern interferometer,” Proc. SPIE 5869, 58691B (2005).
[CrossRef]

Sov. Phys. Tech. Phys. (1)

M. Kronrod, N. Merzlyakov, and L. Yaroslavskii, “Reconstruction of a hologram with computer,” Sov. Phys. Tech. Phys. 17, 333-334 (1972).

Other (3)

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

K. Creath, J. Schmit, and J. C. Wyant, “Optical metrology of diffuse surfaces,” in Optical Shop Testing, 3rd ed., D. Malacara, ed. (Wiley, 2007), pp. 783-801.

I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268-1270 (1997).

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Figures (11)

Fig. 1
Fig. 1

Ideal optical setup for the digital holography with a quadrature phase-shifted interferometer, which records quadrature phase-shifting holograms simultaneously.

Fig. 2
Fig. 2

Characters for objects: (a) letter “A” at the distance z of 3 and (b) letter “B” at the distance z of 5.

Fig. 3
Fig. 3

Phase distributions of holograms calculated by (a) QPI and (b) four-bucket methods.

Fig. 4
Fig. 4

Object images reconstructed from the digital phase holograms. (a), (b) Reconstructed using the phase in Fig. 2a by the QPI method at the distances z of 3 and 5, respectively. (c), (d) Reconstructed using the phase in Fig. 2b by four-bucket method at the distances z of 3 and 5, respectively.

Fig. 5
Fig. 5

Histogram of phase difference between phase holograms calculated by QPI and four-bucket methods.

Fig. 6
Fig. 6

Image reconstructed with a phase hologram by the QPI method as the object is moved by 5 pixels between two sets of quadrature interferograms.

Fig. 7
Fig. 7

Contrast of image reconstructed versus object moving distance between two sets of quadrature interferograms, where the image is reconstructed with a phase hologram calculated by the QPI method.

Fig. 8
Fig. 8

Experimental setup for verifying of hologram on the CCD plane by QPI.

Fig. 9
Fig. 9

Phase holograms transformed to images of 512 × 512 pixels, which are calculated by (a) the QPI method and (b) the four-bucket method.

Fig. 10
Fig. 10

Reconstruction images (a) and (b) [QPI] and (c) and (d) [four-bucket] are calculated with phase holograms, which are reconstructed at the distances z of 2.3 and 2.5, respectively, and focused on the respective letters “p” and “t”. The reconstruction image by QPI method has almost the same contrast as that in four-bucket method.

Fig. 11
Fig. 11

Images reconstructed by QPI with phase holograms as the object moved in parallel to the CCD plane between two sets of quadrature interferograms, where the amounts of object movement are (a) 3, (b) 6, and (c)  9 μm with no bias phase and (d) 0, (e) 6, and (f)  9 μm with the bias phase of 180 ° , respectively.

Equations (11)

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

G = ( I 1 I 3 ) + ( I 2 I 4 ) = 2 2 B sin φ 2 cos ( θ + φ 2 π 4 ) ,
H = ( I 1 I 3 ) ( I 2 I 4 ) = 2 2 B sin φ 2 sin ( θ + φ 2 π 4 ) .
J = G 2 H 2 = 8 B 2 sin 2 ( φ 2 ) sin ( 2 θ + φ ) ,
K = 2 G H = 8 B 2 sin 2 ( φ 2 ) cos ( 2 θ + φ ) .
ξ = ( I 1 I 2 ) cos 2 ( 2 θ + φ ) = 2 B cos 2 ( 2 θ + φ ) cos ( θ π 4 ) ,
η = [ ( I 1 I 2 ) sin ( 2 θ + φ ) ( I 3 I 4 ) ] cos ( 2 θ + φ ) = 2 B cos 2 ( 2 θ + φ ) sin ( θ π 4 ) .
C = ξ cos ( π 4 ) η sin ( π 4 ) = 2 B cos 2 ( 2 θ + φ ) cos θ ,
S = η cos ( π 4 ) + ξ sin ( π 4 ) = 2 B cos 2 ( 2 θ + φ ) sin θ .
θ = tan 1 ( S C ) .
u ( x 0 , y 0 ) = exp ( i k z ) i λ z u ( x 1 , y 1 ) exp { i k 2 z [ ( x 0 x 1 ) 2 + ( y 0 y 1 ) 2 ] } d x 1 d y 1 ,
u ( x 0 , y 0 ) = exp ( i k z ) i λ z exp [ i k 2 z ( x 0 2 + y 0 2 ) ] { u ( x 1 , y 1 ) exp [ i k 2 z ( x 1 2 + y 1 2 ) ] } exp [ i 2 π λ z ( x 0 x 1 + y 0 y 1 ) ] d x 1 d y 1 .

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