Abstract

A new methodology describing the effects of aperiodic and multiplexed gratings in volume holographic imaging systems (VHIS) is presented. The aperiodic gratings are treated as an ensemble of localized planar gratings using coupled wave methods in conjunction with sequential and non-sequential ray-tracing techniques to accurately predict volumetric diffraction effects in VHIS. Our approach can be applied to aperiodic, multiplexed gratings and used to theoretically predict the performance of multiplexed volume holographic gratings within a volume hologram for VHIS. We present simulation and experimental results for the aperiodic and multiplexed imaging gratings formed in PQ-PMMA at 488nm and probed with a spherical wave at 633nm. Simulation results based on our approach that can be easily implemented in ray-tracing packages such as Zemax® are confirmed with experiments and show proof of consistency and usefulness of the proposed models.

© 2010 OSA

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  1. W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27(10), 854–856 (2002).
    [CrossRef]
  2. 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(4), 043001–043005 (2010).
    [CrossRef]
  3. Y. Luo, S. B. Oh, and G. Barbastathis, “Wavelength-coded multifocal microscopy,” Opt. Lett. 35(5), 781–783 (2010).
    [PubMed]
  4. Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
    [CrossRef]
  5. A. V. Veniaminov, V. G. Goncharov, and A. P. Popov, “Hologram amplification by diffusion destruction of out-of phase periodic structures,” Opt. Spectrosc. 70(4), 505–508 (1991).
  6. Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system,” Opt. Lett. 33(18), 2098–2100 (2008).
    [CrossRef] [PubMed]
  7. A. Sinha and G. Barbastathis, “Volume holographic imaging for surface metrology at long working distances,” Opt. Express 11(24), 3202–3209 (2003).
    [CrossRef] [PubMed]
  8. H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2946 (1969).
  9. G. Moharam and T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73(9), 1105–1112 (1983).
    [CrossRef]
  10. P. Wissmann, S. B. Oh, and G. Barbastathis, “Simulation and optimization of volume holographic imaging systems in Zemax,” Opt. Express 16(10), 7516–7524 (2008).
    [CrossRef] [PubMed]
  11. R. R. A. Syms and L. Solymar, “Localized one-dimensional theory for volume holograms,” Opt. Quantum Electron. 13(5), 415–419 (1981).
    [CrossRef]
  12. R. R. A. Syms and L. Solymar, “Analysis of volume holographic cylindrical lenses,” J. Opt. Soc. Am. 72(2), 179–186 (1982).
    [CrossRef]
  13. A. Sinha and G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43(27), 5214–5221 (2004).
    [CrossRef] [PubMed]
  14. A. Sinha, W. Sun, T. Shih, and G. Barbastathis, “Volume holographic imaging in transmission geometry,” Appl. Opt. 43(7), 1533–1551 (2004).
    [CrossRef] [PubMed]
  15. G. Barbastathis, and D. Psaltis, “Volume holographic multiplexing methods,” in Holographic Data Storage (Springer, 2000).
  16. Y. Luo, P. J. Gelsinger, J. K. Barton, G. Barbastathis, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ-PMMA for spectral-spatial imaging filters,” Opt. Lett. 33(6), 566–568 (2008).
    [CrossRef] [PubMed]
  17. R. K. Kostuk, Multiple grating reflection volume holograms with application to optical interconnects, Ph. D. Thesis at Stanford University, 1986.
  18. Y. Luo, J. M. Russo, R. K. Kostuk, and G. Barbastathis, “Silicon oxide nanoparticles doped PQ-PMMA for volume holographic imaging filters,” Opt. Lett. 35(8), 1269–1271 (2010).
    [CrossRef] [PubMed]
  19. G. Barbastathis and D. Psaltis, “Shift-multiplexed holographic memory using the two-lambda method,” Opt. Lett. 21(6), 432–434 (1996).
    [CrossRef] [PubMed]
  20. W. K. Maeda, “Edge-illumination gratings in PQ-doped PMMA for OCDMA applications,” The University of Arizona, ECE Department, Thesis, 2005.
  21. J. M. Russo, “Temperature dependence of holographic filers in phenanthrenquinone-doped poly(methyl methacrylate),” The University of Arizona, ECE Department, Thesis, 2007.
  22. J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008).
    [CrossRef]

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(4), 043001–043005 (2010).
[CrossRef]

Y. Luo, S. B. Oh, and G. Barbastathis, “Wavelength-coded multifocal microscopy,” Opt. Lett. 35(5), 781–783 (2010).
[PubMed]

Y. Luo, J. M. Russo, R. K. Kostuk, and G. Barbastathis, “Silicon oxide nanoparticles doped PQ-PMMA for volume holographic imaging filters,” Opt. Lett. 35(8), 1269–1271 (2010).
[CrossRef] [PubMed]

2008

2005

Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
[CrossRef]

2004

2003

2002

1996

1991

A. V. Veniaminov, V. G. Goncharov, and A. P. Popov, “Hologram amplification by diffusion destruction of out-of phase periodic structures,” Opt. Spectrosc. 70(4), 505–508 (1991).

1983

1982

1981

R. R. A. Syms and L. Solymar, “Localized one-dimensional theory for volume holograms,” Opt. Quantum Electron. 13(5), 415–419 (1981).
[CrossRef]

1969

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2946 (1969).

Barbastathis, G.

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(4), 043001–043005 (2010).
[CrossRef]

Y. Luo, S. B. Oh, and G. Barbastathis, “Wavelength-coded multifocal microscopy,” Opt. Lett. 35(5), 781–783 (2010).
[PubMed]

Y. Luo, J. M. Russo, R. K. Kostuk, and G. Barbastathis, “Silicon oxide nanoparticles doped PQ-PMMA for volume holographic imaging filters,” Opt. Lett. 35(8), 1269–1271 (2010).
[CrossRef] [PubMed]

Y. Luo, P. J. Gelsinger, J. K. Barton, G. Barbastathis, and R. K. Kostuk, “Optimization of multiplexed holographic gratings in PQ-PMMA for spectral-spatial imaging filters,” Opt. Lett. 33(6), 566–568 (2008).
[CrossRef] [PubMed]

P. Wissmann, S. B. Oh, and G. Barbastathis, “Simulation and optimization of volume holographic imaging systems in Zemax,” Opt. Express 16(10), 7516–7524 (2008).
[CrossRef] [PubMed]

Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system,” Opt. Lett. 33(18), 2098–2100 (2008).
[CrossRef] [PubMed]

A. Sinha and G. Barbastathis, “Broadband volume holographic imaging,” Appl. Opt. 43(27), 5214–5221 (2004).
[CrossRef] [PubMed]

A. Sinha, W. Sun, T. Shih, and G. Barbastathis, “Volume holographic imaging in transmission geometry,” Appl. Opt. 43(7), 1533–1551 (2004).
[CrossRef] [PubMed]

A. Sinha and G. Barbastathis, “Volume holographic imaging for surface metrology at long working distances,” Opt. Express 11(24), 3202–3209 (2003).
[CrossRef] [PubMed]

W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27(10), 854–856 (2002).
[CrossRef]

G. Barbastathis and D. Psaltis, “Shift-multiplexed holographic memory using the two-lambda method,” Opt. Lett. 21(6), 432–434 (1996).
[CrossRef] [PubMed]

Barton, J. K.

Bearman, G.

Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
[CrossRef]

Brooker, G.

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[CrossRef]

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(4), 043001–043005 (2010).
[CrossRef]

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(4), 043001–043005 (2010).
[CrossRef]

Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system,” Opt. Lett. 33(18), 2098–2100 (2008).
[CrossRef] [PubMed]

Goncharov, V. G.

A. V. Veniaminov, V. G. Goncharov, and A. P. Popov, “Hologram amplification by diffusion destruction of out-of phase periodic structures,” Opt. Spectrosc. 70(4), 505–508 (1991).

Johson, W. R.

Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2946 (1969).

Kostuk, R. K.

Li, Z.

Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
[CrossRef]

Liu, W.

Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
[CrossRef]

W. Liu, D. Psaltis, and G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27(10), 854–856 (2002).
[CrossRef]

Luo, Y.

Moharam, G.

Oh, S. B.

Popov, A. P.

A. V. Veniaminov, V. G. Goncharov, and A. P. Popov, “Hologram amplification by diffusion destruction of out-of phase periodic structures,” Opt. Spectrosc. 70(4), 505–508 (1991).

Psaltis, D.

Rosen, J.

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[CrossRef]

Russo, J. M.

Shih, T.

Sinha, A.

Solymar, L.

R. R. A. Syms and L. Solymar, “Analysis of volume holographic cylindrical lenses,” J. Opt. Soc. Am. 72(2), 179–186 (1982).
[CrossRef]

R. R. A. Syms and L. Solymar, “Localized one-dimensional theory for volume holograms,” Opt. Quantum Electron. 13(5), 415–419 (1981).
[CrossRef]

Sun, W.

Syms, R. R. A.

R. R. A. Syms and L. Solymar, “Analysis of volume holographic cylindrical lenses,” J. Opt. Soc. Am. 72(2), 179–186 (1982).
[CrossRef]

R. R. A. Syms and L. Solymar, “Localized one-dimensional theory for volume holograms,” Opt. Quantum Electron. 13(5), 415–419 (1981).
[CrossRef]

Veniaminov, A. V.

A. V. Veniaminov, V. G. Goncharov, and A. P. Popov, “Hologram amplification by diffusion destruction of out-of phase periodic structures,” Opt. Spectrosc. 70(4), 505–508 (1991).

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(4), 043001–043005 (2010).
[CrossRef]

Y. Luo, P. J. Gelsinger-Austin, J. M. Watson, G. Barbastathis, J. K. Barton, and R. K. Kostuk, “Laser-induced fluorescence imaging of subsurface tissue structures with a volume holographic spatial-spectral imaging system,” Opt. Lett. 33(18), 2098–2100 (2008).
[CrossRef] [PubMed]

Wissmann, P.

Appl. Opt.

Bell Syst. Tech. J.

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909–2946 (1969).

J. Opt. Soc. Am.

Nat. Photonics

J. Rosen and G. Brooker, “Non-scanning motionless fluorescence three-dimensional holographic microscopy,” Nat. Photonics 2(3), 190–195 (2008).
[CrossRef]

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(4), 043001–043005 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Quantum Electron.

R. R. A. Syms and L. Solymar, “Localized one-dimensional theory for volume holograms,” Opt. Quantum Electron. 13(5), 415–419 (1981).
[CrossRef]

Opt. Spectrosc.

A. V. Veniaminov, V. G. Goncharov, and A. P. Popov, “Hologram amplification by diffusion destruction of out-of phase periodic structures,” Opt. Spectrosc. 70(4), 505–508 (1991).

Proc. SPIE

Z. Li, D. Psaltis, W. Liu, W. R. Johson, and G. Bearman, “Volume holographic spectral imaging,” Proc. SPIE 5694, 33–40 (2005).
[CrossRef]

Other

G. Barbastathis, and D. Psaltis, “Volume holographic multiplexing methods,” in Holographic Data Storage (Springer, 2000).

R. K. Kostuk, Multiple grating reflection volume holograms with application to optical interconnects, Ph. D. Thesis at Stanford University, 1986.

W. K. Maeda, “Edge-illumination gratings in PQ-doped PMMA for OCDMA applications,” The University of Arizona, ECE Department, Thesis, 2005.

J. M. Russo, “Temperature dependence of holographic filers in phenanthrenquinone-doped poly(methyl methacrylate),” The University of Arizona, ECE Department, Thesis, 2007.

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Figures (10)

Fig. 1
Fig. 1

Reconstruction geometry of a single slanted planar grating with a planar wave of propagation vector k 1 incident with an arbitrary angle and polarization.

Fig. 2
Fig. 2

Construction and reconstruction stages of an aperiodic grating.

Fig. 3
Fig. 3

Setup of multiplexed curved gratings.

Fig. 4
Fig. 4

Construction setup of the angle multiplexed holographic filters.

Fig. 5
Fig. 5

Experimental setup for measuring depth selectivity, diffraction efficiency, and distance changes between the 488nm and 633nm lines.

Fig. 6
Fig. 6

(a) Experimental results of the depth selectivity for the hologram of two gratings at 488nm. η is normalized for easy comparison of the width of PSFz, (b) Experimental results of the depth selectivity for the hologram of two gratings at 633nm. (Similarly normalized.)

Fig. 7
Fig. 7

Experimental results of the relationship between ∆z con and ∆z rec. (a) at the same wavelength of 488nm for both construction and reconstruction. (b) at the wavelength of 488nm for construction and 633nm for reconstruction.

Fig. 8
Fig. 8

(a) Layout of a VHIS produced by Zemax® . (b) Diffraction images (from the first diffracted order of a grating) in logarithm scale on the Zemax® detector plane using a point source with different ∆z recon.

Fig. 9
Fig. 9

(a) Experimental and numerical results of the depth selectivity at 488nm for the hologram of two gratings. (b) Experimental and numerical results of the depth selectivity at 633nm for the hologram of two gratings.

Fig. 10
Fig. 10

(a) Experimental results and numerical analysis for the relationship between ∆z con and ∆z recon (a) at the same wavelength of 488nm. (b) at the wavelength of 488nm for construction and 633nm for reconstruction.

Equations (17)

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

Κ = ( Κ sin φ ) x ^ + ( Κ cos φ ) z ^ ,
Ε i n c = u ^ exp ( j k 1 r ) ,
u ^ = ( cos ψ cos α cos β sin ψ sin β ) x ^ + ( cos ψ cos α sin β + sin ψ cos β ) y ^ ( cos ψ sin α ) z ^ .
Ε 1 = Ε i n c + n R n exp ( j k 1 n r ^ ) ,
Ε 3 = n T n exp ( j k 3 n ( r ^ d z ^ ) ) ,
k n = k x n x ^ + k y n y ^ + k z n z ^ = [ ( k 1 n Κ ) x ^ ] x ^ + [ ( k 1 n Κ ) y ^ ] y ^ + k z n z ^ ,
Ε 2 = n [ S x n ( z ) x ^ + S y n ( z ) y ^ + S z n ( z ) z ^ ] exp ( j σ n r ^ ) ,
Η 2 = ( ε 0 / μ 0 ) n [ U x n ( z ) x ^ + U y n ( z ) y ^ + U z n ( z ) z ^ ] exp ( j σ n r ^ ) ,
× Ε 2 = j ω μ 0 ,
× Η 2 = j ω ε 0 ε ( x , y , z ) Ε 2 ,
E 2 = S 0 ( z ) exp ( j k 1 r ^ ) + S 1 ( z ) exp ( j k d r ^ ) ,
η = ( | c s | / c R ) S 1 S 1 * ,
S 1 = j ( c R / c S ) 1 / 2 exp ( ρ d / c R ) exp ( ξ ) sin ( v 2 ξ 2 ) ( 1 v 2 / ξ 2 ) 1 / 2 ,
v = π Δ n d λ c R c S
ξ = d 2 ( ρ c R ρ c S j ϑ c S ) ,
η t o t a l = ( i N η i ) / N .
η ( % ) = ( P d i f f / P i n c ) × 100 % ,

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