Abstract

An improved illumination system is proposed for creating a temporally coherent and spatially incoherent extended source to be used for spatial coherence control and reconstruction of a coherent hologram. Taking into account the fact that a rotating ground glass does not behave as an ideal Lambertian diffuser, the new illumination system tailors the directivity of the scattered lights to direct the lights efficiently into an interferometer so that a spatial coherence function can be better controlled and detected with higher fidelity. Experimental results are presented that demonstrate improved performance of the proposed system.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
  3. J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39 , 4107-4111(2000).
    [CrossRef]
  4. M. Kuechel, “ Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,804,011 (22 January 2002).
  5. L. L. Deck, D. Stephenson, E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,643,024 (3 May 2001).
  6. W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verification,” Appl. Opt. 41, 1962-1970 (2002).
    [CrossRef] [PubMed]
  7. Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
    [CrossRef]
  8. M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
    [CrossRef]
  9. E. Baleine and A. Dogariu, “Variable coherence tomography,” Opt. Lett. 29, 1233-1235 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  11. V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30, 224-226 (2005).
  12. M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629-9635 (2005).
    [CrossRef] [PubMed]

2005 (2)

V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30, 224-226 (2005).

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629-9635 (2005).
[CrossRef] [PubMed]

2004 (2)

2003 (1)

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
[CrossRef]

2002 (2)

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verification,” Appl. Opt. 41, 1962-1970 (2002).
[CrossRef] [PubMed]

2000 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

1972 (1)

Baleine, E.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Deck, L. L.

L. L. Deck, D. Stephenson, E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,643,024 (3 May 2001).

Dogariu, A.

Duan, Z.

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629-9635 (2005).
[CrossRef] [PubMed]

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Flournoy, P. A.

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Gokhler, M.

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

Gratix, E.

L. L. Deck, D. Stephenson, E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,643,024 (3 May 2001).

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Ishii, N.

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

Kozaki, H.

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verification,” Appl. Opt. 41, 1962-1970 (2002).
[CrossRef] [PubMed]

Kuechel, M.

M. Kuechel, “ Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,804,011 (22 January 2002).

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Lobachev, M.

V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30, 224-226 (2005).

V. Ryabukho, D. Lyakin, and M. Lobachev, “Influence of longitudinal spatial coherence on the signal of a scanning interferometer,” Opt. Lett. 29, 667-669 (2004).
[CrossRef] [PubMed]

Lyakin, D.

V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30, 224-226 (2005).

V. Ryabukho, D. Lyakin, and M. Lobachev, “Influence of longitudinal spatial coherence on the signal of a scanning interferometer,” Opt. Lett. 29, 667-669 (2004).
[CrossRef] [PubMed]

McClure, R. W.

Miyamoto, Y.

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Rosen, J.

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verification,” Appl. Opt. 41, 1962-1970 (2002).
[CrossRef] [PubMed]

J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39 , 4107-4111(2000).
[CrossRef]

Ryabukho, V.

V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30, 224-226 (2005).

V. Ryabukho, D. Lyakin, and M. Lobachev, “Influence of longitudinal spatial coherence on the signal of a scanning interferometer,” Opt. Lett. 29, 667-669 (2004).
[CrossRef] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Stephenson, D.

L. L. Deck, D. Stephenson, E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,643,024 (3 May 2001).

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Takeda, M.

M. Takeda, W. Wang, Z. Duan, and Y. Miyamoto, “Coherence holography,” Opt. Express 13, 9629-9635 (2005).
[CrossRef] [PubMed]

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
[CrossRef]

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

W. Wang, H. Kozaki, J. Rosen, and M. Takeda, “Synthesis of longitudinal coherence functions by spatial modulation of an extended light source: a new interpretation and experimental verification,” Appl. Opt. 41, 1962-1970 (2002).
[CrossRef] [PubMed]

J. Rosen and M. Takeda, “Longitudinal spatial coherence applied for surface profilometry,” Appl. Opt. 39 , 4107-4111(2000).
[CrossRef]

Wang, W.

Wyntjes, G.

Zanoni, C. A.

L. L. Deck, D. Stephenson, E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,643,024 (3 May 2001).

Appl. Opt. (3)

Opt. Eng. (1)

M. Gokhler, Z. Duan, J. Rosen, and M. Takeda, “Spatial coherence radar applied for tilted surface profilometry,” Opt. Eng. 42, 830-836 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (2)

Proc. SPIE (1)

Z. Duan, M. Gokhler, J. Rosen, H. Kozaki, N. Ishii, and M. Takeda, “Synthesis spatial coherence function for optical tomography and profilometry: simultaneous realization of longitudinal coherence scan and phase shift,” Proc. SPIE 4777, 110-177 (2002).
[CrossRef]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science 254, 1178-1181 (1991).
[CrossRef] [PubMed]

Other (3)

M. Kuechel, “ Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,804,011 (22 January 2002).

L. L. Deck, D. Stephenson, E. Gratix, and C. A. Zanoni, “Apparatus and method(s) for reducing the effect of coherent artifacts in an interferometer,” U.S. patent 6,643,024 (3 May 2001).

V. Ryabukho, D. Lyakin, and M. Lobachev, “Longitudinal pure spatial coherence of a light field with wide frequency and angular spectra,” Opt. Lett. 30, 224-226 (2005).

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Figures (6)

Fig. 1
Fig. 1

Optical setup for coherence control.

Fig. 2
Fig. 2

Typical scattering characteristic of a ground glass.

Fig. 3
Fig. 3

Illumination system.

Fig. 4
Fig. 4

Experimental setup.

Fig. 5
Fig. 5

Longitudinal spatial coherence function.

Fig. 6
Fig. 6

Interferograms for the distances between the reference and test mirrors being (a)  0 mm , (b)  1.5 mm , and (c)  2.5 mm .

Equations (9)

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u ( x , y , z ) = u s ( x s , y s ) j λ f P ( θ ) × exp [ j 2 π ( z + 2 f ) λ j 2 π λ f ( x s x + y s y ) j π z λ f 2 ( x s 2 + y s 2 ) ] ,
x t = x s a a f · b s b .
θ = x x t f ,
b = s ,
θ = r f = x 2 + y 2 f .
u ( x , y , z ) = u s ( x s , y s ) j λ f p ( x 2 + y 2 f ) × exp [ j 2 π ( z + 2 f ) λ j 2 π λ f ( x s x + y s y ) j π z λ f 2 ( x s 2 + y s 2 ) ] .
I ( x , y , L ) = [ p ( x 2 + y 2 f ) ] 2 | u s ( x s , y s ) j λ f × exp [ j 2 π ( L + 2 f ) λ j 2 π λ f ( x s x + y s y ) j π L λ f 2 ( x s 2 + y s 2 ) ] + u s ( x s , y s ) j λ f × exp [ j 2 π ( L + 2 Δ z + 2 f ) λ j 2 π λ f ( x s x + y s y ) j π ( L + 2 Δ z ) λ f 2 ( x s 2 + y s 2 ) ] | 2 d x s d y s ,
D ZP = 2 f tan [ arccos ( 1 N λ 2 t ) ] 2 f N λ t = 11.54 mm ,
d = 2 ( D L 3 2 l A G + f l A G × D ZP 2 ) = 28.0 mm ,

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