Abstract

A fully interferometric technique for obtaining hypermultispectral components of three-dimensional (3D) images has been tested for a polychromatic object that consists of spatially incoherent, planar light sources of different shapes. Each planar source has different continuous spectra, located at different 3D positions. The method is based on measurement of a five-dimensional (5D) interferogram. By applying synthetic aperture technique and spectral decomposition to that 5D interferogram, one obtains a set of complex holograms of different spectral components. From these holograms, 3D images of multiple spectral components have been retrieved. A decomposed continuous spectrum of each planar light source is also shown to demonstrate the potential applicability to identify materials of a particular part of an object under illumination by white light.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  9. 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]
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    [CrossRef]
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  13. K. Yoshimori, “Digital holographic three-dimensional imaging spectrometry,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2012), paper DW1C.1.
  14. M. Sasamoto and K. Yoshimori, “First experimental report on fully passive interferometric three-dimensional imaging spectrometry,” Jpn. J. Appl. Phys. 48, 09LB03-1-4 (2009).
    [CrossRef]
  15. M. Sasamoto and K. Yoshimori, “Three-dimensional imaging spectrometry by fully passive interferometry,” Opt. Rev. 19, 29–33 (2012).
    [CrossRef]

2012 (1)

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

2009 (1)

M. Sasamoto and K. Yoshimori, “First experimental report on fully passive interferometric three-dimensional imaging spectrometry,” Jpn. J. Appl. Phys. 48, 09LB03-1-4 (2009).
[CrossRef]

2006 (1)

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

2001 (1)

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]

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 3020, 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]

Brady, D. J.

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3020, 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]

Fetterman, M.

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3020, 48–55 (2000).
[CrossRef]

Ichioka, T.

Inoue, T.

Itoh, K.

Marks, D. L.

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3020, 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]

Ohtsuka, Y.

Rosen, J.

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, 09LB03-1-4 (2009).
[CrossRef]

K. Yoshimori and M. Sasamoto, “Experimental report on fully interferometric three-dimensional imaging spectroscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWB34.

Stack, R. A.

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3020, 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]

Teeranutranont, S.

S. Teeranutranont and K. Yoshimori, “Application of digital holographic three-dimensional imaging spectrometry to a spatially incoherent, polychromatic object,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DWB36.

Yariv, A.

Yoshida, T.

Yoshimori, K.

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, 09LB03-1-4 (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 and K. Itoh, “Interferometry and radiometry,” J. Opt. Soc. Am. A 14, 3379–3387 (1997).
[CrossRef]

K. Yoshimori and M. Sasamoto, “Experimental report on fully interferometric three-dimensional imaging spectroscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWB34.

S. Teeranutranont and K. Yoshimori, “Application of digital holographic three-dimensional imaging spectrometry to a spatially incoherent, polychromatic object,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DWB36.

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

Appl. Opt. (2)

J. Opt. Soc. Am A (1)

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]

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, 09LB03-1-4 (2009).
[CrossRef]

Opt. Rev. (2)

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

Proc. SPIE (2)

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

D. L. Marks, M. Fetterman, R. A. Stack, and D. J. Brady, “Spectral tomography from spatial coherence measurements,” Proc. SPIE 3020, 48–55 (2000).
[CrossRef]

Other (3)

K. Yoshimori and M. Sasamoto, “Experimental report on fully interferometric three-dimensional imaging spectroscopy,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2009), paper DWB34.

S. Teeranutranont and K. Yoshimori, “Application of digital holographic three-dimensional imaging spectrometry to a spatially incoherent, polychromatic object,” in Digital Holography and Three-Dimensional Imaging, OSA Technical Digest (CD) (Optical Society of America, 2011), paper DWB36.

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

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Figures (14)

Fig. 1.
Fig. 1.

Schematic of the two-wavefront folding interferometer. The optical axes of the interferometer are indicated by solid lines that intersect at the center of the apexes of the right-angle prisms. The Cartesian coordinate system, fixed on the object, is shown by broken lines.

Fig. 2.
Fig. 2.

Example of an entire interference data set as the 5D interferogram: position on each 2D elemental interference image (ξ, η), x, y position of P, P apex (x^, y^), and optical path difference along the z-direction (Z).

Fig. 3.
Fig. 3.

Example of the reduced-volume interferogram for monochromatic point source located at the origin of the Cartesian coordinate system.

Fig. 4.
Fig. 4.

Continuous spectral profile of each light source: (a) S1, (b) S2, and (c) S3.

Fig. 5.
Fig. 5.

Shape of the measured light sources: S1 (down), S2 (left-up), and S3 (right-up).

Fig. 6.
Fig. 6.

Reduced-volume (3D) interferogram for the spatially incoherent light source distribution. The center of the volume interferogram shows the inner interference fringe.

Fig. 7.
Fig. 7.

One-dimensional interferogram of intensity profile plotted with respect to Z along center line of the volume interferogram.

Fig. 8.
Fig. 8.

Continuous spectral profile recorded on the observation plane. This is obtained by taking Fourier transform of the reduced-volume interferogram with respect to Z.

Fig. 9.
Fig. 9.

(a) Phase distribution and (b) absolute value of the cross-spectral density at spectral peak λ=630nm. (c) In-focus images over xy plane at z=50mm.

Fig. 10.
Fig. 10.

(a) Phase distribution and (b) absolute value of the cross-spectral density at spectral peak λ=504nm. (c) In-focus images over xy plane at z=61mm.

Fig. 11.
Fig. 11.

(a) Phase distribution and (b) absolute value of the cross-spectral density at spectral peak λ=448nm. (c) In-focus images over xy plane at z=70mm.

Fig. 12.
Fig. 12.

Intensity profiles of the retrieved images along the z axis: (a) S1, (b) S2, and (c) S3.

Fig. 13.
Fig. 13.

Retrieved in-focus spectral images of the three planar light sources for multiple spectral bands. The object depths are as follows: (a) 70 mm for λ=403.2458.2nm, (b) 61 mm for λ=480.0560.0nm, and (c) 50 mm for λ=593.0720.0nm.

Fig. 14.
Fig. 14.

Decomposed spectral profiles of the three planar light sources at the particular 3D spatial positions on the 3D images of those: (a) z=50mm, (b) z=61mm, and (c) z=70mm.

Tables (1)

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Table 1. Specification of Planar Light Sources

Equations (27)

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i(x,y,x^,y^,z)=14{Γ(r,r)+Γ(r,r)+Γ(r,r)+Γ*(r,r)},
Γ(r,r)=Sω(rs)exp(ik(rr))d3rsdω,
rz+Z+(xxs)2+(y2y^ys2)2z,
rz+(x2x^xs)2+(yys2)2z,
rrZ+2x^(xxs)2y^(yys)z+(2x^)2+(2y^)22z.
Γ(x2x^,y,z0;x,y2y^,z0+Z)=Sω(rs)exp(ikZ)exp[2x^(xxs)2y^(yys)z]exp[(2x^)2+(2y^)22z]d3rsdω.
ξ=xx^,
η=yy^.
Γ(x^+ξ,y^+η,z0;x^+ξ,y^+η,z0+Z)=Sω(rs)exp(ikZ)exp[ik2x^(ξxs)2y^(ηys)z]d3rsdω.
ξ=x^,
η=y^.
X=2x^,
Y=2y^,
Γ(0,0,z0;X,Y,z0+Z)=Sω(rs)exp(ikZ)exp(ikxX+ikyY)exp[ikX2+Y22z]d3rsdω,
Γ(r,r;τ)=V*(r,t)V(r,t+τ)=0Wω(r,r)exp(iωτ)dω,
Γ(r,r)=0Wω(r,r)dω.
Γ(R0,R0+ρ)=0Wω(R0,R0+ρ)dω
Wω(R0,R0+ρ)=Sω(rs)exp(ikZ)exp(ikxX+ikyY)exp[ikX2+Y22z]d3rs.
Wω(R0,R0+ρ)=exp(ikZ)Wω(R0,R0+ρ).
Γ(R0,R0+ρ)=0Wω(R0,R0+ρ)exp(ikZ)dω.
Wω(R0,R0+ρ)=12πΓ(R0,R0+ρ)exp(ikZ)dZ.
Wω(z0)(ρ)=Wω(R0,R0+ρ)=Sω(rs)exp(ikxX+ikyY)exp[ikX2+Y22z]d3rs.
Wω(z0)(ρ)=Wω(0,0,z0;ρ,z0)=Uω*(0,0,z0)Uω(ρ,z0).
W˜ω(z0)(k)=12πWω(z0)(ρ)exp(ik·ρ)d2ρ=Uω*(0,0,z0)U˜ω(k,z0),
W˜ω(z0z)(k)=exp(ikzz)W˜ω(z0)(k),
Wω(z0z)(ρ)=12πW˜ω(z0)(k)exp(i(k·ρkzz))d2ρ=Uω*(0,0,z0)Uω(ρ,z0z).
|Wω(z0z)(ρ)|=|Uω*(0,0,z0)Uω(ρ,z0z)||Uω(ρ,z0z)|.

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