Abstract

Diffracted image patterns from volume holograms that are used in volume holographic imaging systems (VHISs) are investigated. It is shown that, in VHISs, prior information about the shape and spectral properties of the diffracted patterns is important not only to determine the curvature and field of view of the image, but also for image registration and noise removal. A new methodology to study numerically and analytically the dependence of VHIS diffraction patterns with the hologram construction parameters and the readout wavelength is described. Modeling and experimental results demonstrate that, in most cases, VHIS diffracted shapes can be accurately represented by hyperbolas.

© 2011 Optical Society of America

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  1. O. Momtahan, C. R. Hsieh, A. Karbaschi, A. Adibi, M. E. Sullivan, and D. J. Brady, “Spherical beam volume holograms for spectroscopic applications: modeling and implementation,” Appl. Opt. 43, 6557–6567 (2004).
    [CrossRef]
  2. C. Hsieh, O. Momtahan, A. Karbaschi, and A. Adibi, “Compact Fourier-transform volume holographic spectrometer for diffuse source spectroscopy,” Opt. Lett. 30, 836–838(2005).
    [CrossRef] [PubMed]
  3. A. Sinha, W. Sun, T. Shih, and G. Barbastathis, “Volume holographic imaging in transmission geometry,” Appl. Opt. 43, 1533–1551 (2004).
    [CrossRef] [PubMed]
  4. Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
    [CrossRef]
  5. W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856(2002).
    [CrossRef]
  6. Y. Luo, P. J. Gelsinger, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ-PMMA for spectral-spatial filters,” Opt. Lett. 3, 66–568 (2008).
    [CrossRef]
  7. P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
    [CrossRef]
  8. A. Sinha and G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43, 5214–5221 (2004).
    [CrossRef] [PubMed]
  9. P. Wissmann, S. B. Oh, and G. Barbastathis, “Simulation and optimization of volume holographic imaging systems in Zemax,” Opt. Express 16, 7516–7524 (2008).
    [CrossRef] [PubMed]
  10. Y. Lou, J. M. Castro, J. Barton, R. K. Kostuk, and G. Barbastathis, “Simulation and experiment of non-uniform multiplexed gratings in volume holographic imaging systems,” Opt. Express 18, 19273–19285 (2010).
    [CrossRef]
  11. S. B. Oh, J. M. Watson, and G. Barbastathis, “Theoretical analysis of curved Bragg diffraction images from plane reference volume holograms,” Appl. Opt. 48, 5984–5996(2009).
    [CrossRef] [PubMed]
  12. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
  13. L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981).
  14. M. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  15. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  16. J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).
  17. W. K. Maeda, “Edge-illumination gratings in PQ-doped PMMA for OCDMA applications,” Master’s thesis (The University of Arizona, 2005).
  18. “Conics Section,” in http://en.wikipedia.org/wiki/Conic_section.
  19. “Rotation matrix,” in http://en.wikipedia.org/wiki/Rotation_matrix.

2010

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

Y. Lou, J. M. Castro, J. Barton, R. K. Kostuk, and G. Barbastathis, “Simulation and experiment of non-uniform multiplexed gratings in volume holographic imaging systems,” Opt. Express 18, 19273–19285 (2010).
[CrossRef]

2009

2008

2005

2004

2002

1983

1981

1969

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Adibi, A.

Barbastathis, G.

Barton, J.

Barton, J. K.

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

Y. Luo, P. J. Gelsinger, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ-PMMA for spectral-spatial filters,” Opt. Lett. 3, 66–568 (2008).
[CrossRef]

Bearman, G.

Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
[CrossRef]

Brady, D. J.

Castro, J. M.

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

Y. Lou, J. M. Castro, J. Barton, R. K. Kostuk, and G. Barbastathis, “Simulation and experiment of non-uniform multiplexed gratings in volume holographic imaging systems,” Opt. Express 18, 19273–19285 (2010).
[CrossRef]

Cooke, D. J.

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981).

Gaylord, T. K.

Gelsinger, P. J.

Gelsinger-Austin, P. J.

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Hsieh, C.

Hsieh, C. R.

Johnson, W. R.

Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
[CrossRef]

Karbaschi, A.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

Kostuk, R. K.

Li, Z.

Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
[CrossRef]

Liu, W.

Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
[CrossRef]

W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856(2002).
[CrossRef]

Lou, Y.

Luo, Y.

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

Y. Luo, P. J. Gelsinger, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ-PMMA for spectral-spatial filters,” Opt. Lett. 3, 66–568 (2008).
[CrossRef]

Maeda, W. K.

W. K. Maeda, “Edge-illumination gratings in PQ-doped PMMA for OCDMA applications,” Master’s thesis (The University of Arizona, 2005).

Moharam, M. G.

Momtahan, O.

Oh, S. B.

Psaltis, D.

Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
[CrossRef]

W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856(2002).
[CrossRef]

Shih, T.

Sinha, A.

Solymar, L.

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981).

Sullivan, M. E.

Sun, W.

Watson, J. M.

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

S. B. Oh, J. M. Watson, and G. Barbastathis, “Theoretical analysis of curved Bragg diffraction images from plane reference volume holograms,” Appl. Opt. 48, 5984–5996(2009).
[CrossRef] [PubMed]

Wissmann, P.

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).

J. Opt. Soc. Am.

Opt. Eng

P. J. Gelsinger-Austin, Y. Luo, J. M. Watson, R. K. Kostuk, G. Barbastathis, J. K. Barton, and J. M. Castro, “Optical design for a spatial-spectral volume holographic imaging system,” Opt. Eng 49, 043001 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Proc. SPIE

Z. Li, D. Psaltis, W. Liu, W. R. Johnson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33 (2005).
[CrossRef]

Other

L. Solymar and D. J. Cooke, Volume Holography and Volume Gratings (Academic, 1981).

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

W. K. Maeda, “Edge-illumination gratings in PQ-doped PMMA for OCDMA applications,” Master’s thesis (The University of Arizona, 2005).

“Conics Section,” in http://en.wikipedia.org/wiki/Conic_section.

“Rotation matrix,” in http://en.wikipedia.org/wiki/Rotation_matrix.

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Figures (5)

Fig. 1
Fig. 1

Basic layout of S 2 -VHIS showing the objective lens ( L o ), the collector lens ( L c ), and the hologram (HOE).

Fig. 2
Fig. 2

Experiment layout used to measure crescent shape of the diffracted beam. The Z axis is normal to the hologram and screen. The angles θ i and θ represent the incident and diffracted beam angles, respectively. The distance from the hologram to the screen is denoted by d and the radius of curvature of the resulting pattern is denoted by R.

Fig. 3
Fig. 3

Measured diffractive patterns form a VHOE using two wavelengths. Curve fitting to a hyperbolic shape are indicated by dotted curves. Construction parameters of the VHOE are indicated in Section 2.

Fig. 4
Fig. 4

Modeled diffractive traces compared with curve fitting of Fig. 1.

Fig. 5
Fig. 5

Sample images: (a) before segmentation and without any imaging processing; (b) after segmentation and spatial filtering. In both cases, images from holograms with curved fringes ( z = 50 μm ) are on the left side.

Equations (28)

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u d = ( u x i K x ) x + ( u y i K y ) y + u z d z , u d = u x d x + u y d y + u z d z ,
u z d = k 2 2 | u x d | 2 | u y d | 2 ,
K = K x x + K y y + K z z = 2 π n 2 λ c [ r s ] ,
u d = k 2 [ sin θ cos ϕ , sin θ sin ϕ , cos θ ] ,
DE = sin 2 ( ν 2 + ξ 2 ) 1 + ξ 2 ν 2 ,
ν = π Δ n t H λ c r c s ,
ϑ = 2 ( u i · K ) | K | 2 2 k 2 ,
ξ = ϑ t H 2 c s ,
R = d tan θ , x = R cos ϕ , y = R sin ϕ ,
tan θ = n 2 tan θ cos θ cos θ .
2 ( u d · K ) = | K | 2 .
K = | K | [ sin γ , 0 , cos γ ] ,
sin γ sin θ cos ϕ + cos γ cos θ + q = 0 ,
q = | K | 2 k 2 = λ 2 n 2 Λ .
sin γ tan θ cos ϕ + cos γ = q cos θ .
sin γ tan θ cos ϕ + n 2 cos θ cos θ cos γ = n 2 q cos θ = n 2 q 1 + tan 2 θ .
( sin 2 γ cos 2 ϕ ( n 2 q ) 2 ) tan 2 θ + n 2 cos θ cos θ sin 2 γ cos ϕ tan θ + ( n 2 cos θ cos θ cos γ ) 2 ( n 2 q ) 2 = 0 .
x 2 ( sin 2 γ ( n 2 q ) 2 d 2 ) ( n 2 q d ) 2 y 2 + n 2 sin 2 γ d x + ( n 2 cos γ ) 2 ( n 2 q ) 2 = 0 .
Ellipse :     sin 2 γ ( n 2 q ) 2 < 0 , Parabola :     sin 2 γ ( n 2 q ) 2 = 0 , Hyperbola :     sin 2 γ ( n 2 q ) 2 > 0 .
A x 2 B y 2 = C .
q = λ 2 Λ n 2 sin 80 ° n 2 0.66 .
± sin 2 γ ( n 2 q ) 2 ( n 2 q ) 2 .
| K | = 2 2 π λ c sin ( θ i ) ,
q = λ 2 n 2 Λ = 0.482.
A = sin 2 γ ( n 2 q ) 2 d 2 = 5.78 E 5 mm 2 ,
B = ( n 2 q d ) 2 = 6.37 E 5 mm 2 ,
C = ( n 2 q ) 2 = 0.524.
A = 1 , B = 1.1.

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