Abstract

A signal-processing method is proposed in the fully interferometric three-dimensional (3D) imaging spectrometry. This processing computes a 3D interferogram, in which recorded fringe patterns do not directly reflect wavefront forms propagated from a polychromatic light source under measurement. This paper presents a procedure for signal processing including a synthesis of the 3D interferogram and retrieval of a set of spectral components of 3D images. We demonstrate retrieving 3D images for spectral components of two planar light sources by means of the proposed method. The procedure to synthesize the 3D interferogram in this method suggests the possibility of direct measurement of the 3D interferogram.

© 2013 Optical Society of America

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2013 (1)

2012 (4)

2011 (3)

2010 (2)

T. Nomura and M. Imbe, “Single-exposure phase-shifting digital holography using a random-phase reference wave,” Opt. Lett. 35, 2281–2283 (2010).
[CrossRef]

T. Tahara, Y. Awatsuji, K. Noshio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[CrossRef]

2009 (2)

M. Sasamoto and K. Yoshimori, “First experimental report on fully passive interferometric three-dimensional imaging spectrometry,” Jpn. J. Appl. Phys. 48, 09LB03 (2009).
[CrossRef]

M.-L. Cruz, A. Castro, and V. Arrizón, “Phase shifting digital holography implemented with a twisted-nematic liquid-crystal display,” Appl. Opt. 48, 6907–6912 (2009).
[CrossRef]

2008 (4)

2007 (1)

2006 (2)

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[CrossRef]

K. Yoshimori, “Passive digital multispectral holography based on synthesis of coherence function,” Proc. SPIE 6252, 625221 (2006).
[CrossRef]

2004 (1)

2001 (1)

2000 (2)

H. Arimoto, K. Yoshimori, and K. Itoh, “Interferometric three-dimensional imaging based on retrieval of generalized radiance distribution,” Opt. Rev. 7, 25–33 (2000).
[CrossRef]

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3920, 48–55 (2000).
[CrossRef]

1999 (2)

1997 (1)

1996 (1)

1990 (1)

1986 (1)

Arimoto, H.

H. Arimoto, K. Yoshimori, and K. Itoh, “Interferometric three-dimensional imaging based on retrieval of generalized radiance distribution,” Opt. Rev. 7, 25–33 (2000).
[CrossRef]

H. Arimoto, K. Yoshimori, and K. Itoh, “Retrieval of the cross-spectral density propagating in free space,” J. Opt. Soc. Am. A 16, 2447–2452 (1999).
[CrossRef]

Arrizón, V.

Awatsuji, Y.

Brady, D. J.

Brooker, G.

Castro, A.

Cho, S.-W.

Cruz, M.-L.

Fetterman, M.

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3920, 48–55 (2000).
[CrossRef]

Földesy, P.

Fujii, A.

Gopinathan, U.

Hahn, J.

Hashimoto, T.

T. Hashimoto and K. Yoshimori, “Fully interferometric three-dimensional imaging spectrometry using hyperbolic-type volume interferogram,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DWC38.

Ichioka, Y.

Imbe, M.

Inoue, T.

Itoh, K.

Kakue, T.

Kaneno, A.

Kiire, T.

Kim, H.

Koyama, T.

Kubota, T.

Lee, B.

Lin, M.

Marks, D. L.

Matoba, O.

Nakadate, S.

Nishio, K.

Nitta, K.

Nomura, T.

Noshio, K.

T. Tahara, Y. Awatsuji, K. Noshio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[CrossRef]

Ohtsuka, Y.

Osten, W.

Pedrini, G.

Rosen, J.

Ryle, J. P.

Sasamoto, M.

M. Sasamoto and K. Yoshimori, “Three-dimensional imaging spectrometry by fully passive interferometry,” Opt. Rev. 19, 29–33 (2012).
[CrossRef]

M. Sasamoto and K. Yoshimori, “First experimental report on fully passive interferometric three-dimensional imaging spectrometry,” Jpn. J. Appl. Phys. 48, 09LB03 (2009).
[CrossRef]

Sheridan, J. T.

Shibuya, M.

Shimozato, Y.

Situ, G.

Stack, R. A.

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3920, 48–55 (2000).
[CrossRef]

D. L. Marks, R. A. Stack, and D. J. Brady, “Three-dimensional coherence imaging in the Fresnel domain,” Appl. Opt. 38, 1332–1342 (1999).
[CrossRef]

Tahara, T.

Teeranutranont, S.

Tiziani, H. J.

Tumbar, R.

Ura, S.

Yamaguchi, I.

Yariv, A.

Yatagai, T.

Yonesaka, R.

Yoshida, T.

Yoshimori, K.

S. Teeranutranont and K. Yoshimori, “Digital holographic three-dimensional imaging spectrometry,” Appl. Opt. 52, A388–A396 (2013).
[CrossRef]

M. Sasamoto and K. Yoshimori, “Three-dimensional imaging spectrometry by fully passive interferometry,” Opt. Rev. 19, 29–33 (2012).
[CrossRef]

M. Sasamoto and K. Yoshimori, “First experimental report on fully passive interferometric three-dimensional imaging spectrometry,” Jpn. J. Appl. Phys. 48, 09LB03 (2009).
[CrossRef]

K. Yoshimori, “Passive digital multispectral holography based on synthesis of coherence function,” Proc. SPIE 6252, 625221 (2006).
[CrossRef]

K. Yoshimori, “Interferometric spectral imaging for three-dimensional objects illuminated by a natural light source,” J. Opt. Soc. Am. A 18, 765–770 (2001).
[CrossRef]

H. Arimoto, K. Yoshimori, and K. Itoh, “Interferometric three-dimensional imaging based on retrieval of generalized radiance distribution,” Opt. Rev. 7, 25–33 (2000).
[CrossRef]

H. Arimoto, K. Yoshimori, and K. Itoh, “Retrieval of the cross-spectral density propagating in free space,” J. Opt. Soc. Am. A 16, 2447–2452 (1999).
[CrossRef]

K. Yoshimori, “Digital holographic three-dimensional imaging spectrometry,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DW1C.1.

T. Hashimoto and K. Yoshimori, “Fully interferometric three-dimensional imaging spectrometry using hyperbolic-type volume interferogram,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DWC38.

Zhang, T.

Zhang, Y.

Appl. Opt. (11)

Y. Awatsuji, A. Fujii, T. Kubota, and O. Matoba, “Parallel three-step phase shifting digital holography,” Appl. Opt. 45, 2995–3002 (2006).
[CrossRef]

R. Tumbar, D. L. Marks, and D. J. Brady, “Robust, common path, phase shifting interferometer and optical profilometer,” Appl. Opt. 47, B32–B43 (2008).
[CrossRef]

G. Situ, J. P. Ryle, U. Gopinathan, and J. T. Sheridan, “Generalized in-line digital holographic technique based on intensity measurements at two different planes,” Appl. Opt. 47, 711–717 (2008).
[CrossRef]

J. Hahn, H. Kim, S.-W. Cho, and B. Lee, “Phase-shifting interferometry with genetic algorithm-based twin image noise elimination,” Appl. Opt. 47, 4068–4076 (2008).
[CrossRef]

Y. Awatsuji, T. Tahara, A. Kaneno, T. Koyama, K. Nishio, S. Ura, T. Kubota, and O. Matoba, “Parallel two-step phase-shifting digital holography,” Appl. Opt. 47, D183–D189(2008).
[CrossRef]

M.-L. Cruz, A. Castro, and V. Arrizón, “Phase shifting digital holography implemented with a twisted-nematic liquid-crystal display,” Appl. Opt. 48, 6907–6912 (2009).
[CrossRef]

T. Kiire, S. Nakadate, M. Shibuya, and T. Yatagai, “Three-dimensional displacement measurement for diffuse object using phase-shifting digital holography with polarization imaging camera,” Appl. Opt. 50, H189–H194 (2011).
[CrossRef]

M. Lin, K. Nitta, O. Matoba, and Y. Awatsuji, “Parallel phase-shifting digital holography with adaptive function using phase-mode spatial light modulator,” Appl. Opt. 51, 2633–2637 (2012).
[CrossRef]

S. Teeranutranont and K. Yoshimori, “Digital holographic three-dimensional imaging spectrometry,” Appl. Opt. 52, A388–A396 (2013).
[CrossRef]

K. Itoh, T. Inoue, T. Yoshida, and Y. Ichioka, “Interferometric supermultispectral imaging,” Appl. Opt. 29, 1625–1630 (1990).
[CrossRef]

D. L. Marks, R. A. Stack, and D. J. Brady, “Three-dimensional coherence imaging in the Fresnel domain,” Appl. Opt. 38, 1332–1342 (1999).
[CrossRef]

J. Opt. Soc. Am. A (4)

Jpn. J. Appl. Phys. (1)

M. Sasamoto and K. Yoshimori, “First experimental report on fully passive interferometric three-dimensional imaging spectrometry,” Jpn. J. Appl. Phys. 48, 09LB03 (2009).
[CrossRef]

Opt. Lett. (7)

Opt. Rev. (4)

T. Tahara, Y. Awatsuji, K. Noshio, S. Ura, T. Kubota, and O. Matoba, “Comparative analysis and quantitative evaluation of the field of view and the viewing zone of single-shot phase-shifting digital holography using space-division multiplexing,” Opt. Rev. 17, 519–524 (2010).
[CrossRef]

T. Kiire, S. Nakadate, M. Shibuya, and T. Yatagai, “Quadrature phase-shifting interferometer using spatial carrier,” Opt. Rev. 18, 103–106 (2011).
[CrossRef]

H. Arimoto, K. Yoshimori, and K. Itoh, “Interferometric three-dimensional imaging based on retrieval of generalized radiance distribution,” Opt. Rev. 7, 25–33 (2000).
[CrossRef]

M. Sasamoto and K. Yoshimori, “Three-dimensional imaging spectrometry by fully passive interferometry,” Opt. Rev. 19, 29–33 (2012).
[CrossRef]

Proc. SPIE (2)

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3920, 48–55 (2000).
[CrossRef]

K. Yoshimori, “Passive digital multispectral holography based on synthesis of coherence function,” Proc. SPIE 6252, 625221 (2006).
[CrossRef]

Other (2)

T. Hashimoto and K. Yoshimori, “Fully interferometric three-dimensional imaging spectrometry using hyperbolic-type volume interferogram,” in Digital Holography and Three-Dimensional Imaging, OSA Techinal Digest (CD) (Optical Society of America, 2011), paper DWC38.

K. Yoshimori, “Digital holographic three-dimensional imaging spectrometry,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (Optical Society of America, 2012), paper DW1C.1.

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of two-wavefront folding interferometer.

Fig. 2.
Fig. 2.

Illustration of the 5D interferogram.

Fig. 3.
Fig. 3.

Example of the hyperbolic-type volume interferogram.

Fig. 4.
Fig. 4.

Front view of S1 and S2.

Fig. 5.
Fig. 5.

Spectral profile of S1 and S2. These spectral profile are measured separately by Fourier transform spectrometry.

Fig. 6.
Fig. 6.

Hyperbolic-type volume interferogram computed by the new selection rule in Eqs. (7). The quarter part of the interferogram is removed to show inner fringe arrangement.

Fig. 7.
Fig. 7.

Spectral profile of the optical field over the observation plane.

Fig. 8.
Fig. 8.

Absolute value image and phase distribution of the cross spectral density (a), (b) at λ=458nm, and (c), (d) at λ=630nm.

Fig. 9.
Fig. 9.

Retrieved images by the proposed method at (a) λ=458nm and z=95mm, (b) λ=630nm and z=82mm, and those by the conventional method, at (c) λ=458nm and z=95mm, and (d) λ=630nm and z=82mm.

Equations (31)

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

Γ(r,r)=Γ(r,t;r,t)=V*(r,t)V(r,t),
I(x,y,x^,y^,Z)=14[Γ(r,r)+Γ(r,r)+Γ(r,r)+Γ*(r,r)],
r=(x,2y^y,z0+Z),
r=(2x^x,y,z0),
x=ξ+x^,
y=η+y^.
I(ξ,η,x^,y^,Z)=14[Γ(r,r)+Γ(r,r)+Γ(r,r)+Γ*(r,r)],
r=(ξ+x^,η+y^,z0+Z),
r=(ξ+x^,η+y^,z0).
ξ=x^,
η=y^.
X=2x^,
Y=2y^,
Γ(X,0,z0;0,Y,z0+Z)=0Wω(X,0,z0;0,Y,z0+Z)dω,
Wω(X,0,z0;0,Y,z0+Z)=Wω(z0)(X,0;0,Y)exp(ikZ),
Wω(z0)(X,0;0,Y)=Sω(rs)exp(ikXxsYysz)exp(ikX2+Y22z)d3rs.
Γ(X,0,z0;0,Y,z0+Z)=c0Wω(z0)(X,0;0,Y)exp(ikZ)dk.
Wω(z0)(X,0;0,Y)=12πcΓ(X,0,z0;0,Y,z0+Z)exp(ikZ)dZ,
Wω(z0)(X,0;0,Y)=Sω(rs)exp[i(kxX+kyY)]exp(ikX2+Y22z)d3rs,
Yω(X,Y,z)=exp(ikX2+Y22z).
Oω(x,y,z)=Wω(z0)(X,0;0,Y)Yω(X,Y,z)exp[i(kxX+kyY)]d3rs,
Wω(r,r)=U*(r,t)U(r,t)=Sω(rs)rrexp[ik(rr)]d3rs,
r=(X,0,z0)
r=(0,Y,z0+Z),
r=(Xxs)2+ys2+(z0zs)2,
r=xs2+(Yys)2+(z0+Zzs)2.
r=z0zs+(Xxs)2+ys22(z0zs),
r=z0+Zzs+xs2+(Yys)22(z0+Zzs).
Wω(r,r)=exp(ikZ)Sω(rs)exp(ikXxsYysz)exp(ikX2+Y22z)d3rs,
Wω(r,r)=Sω(rs)exp(ikXxsYysz)exp(ikX2+Y22z)d3rs.
Wω(r,r)=Wω(r,r)exp(ikZ).

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