Abstract

We present a new methodology for ray–tracing analysis of volume holographic imaging (VHI) systems. Using the k–sphere formulation, we apply geometrical relationships to describe the volumetric diffraction effects imposed on rays passing through a volume hologram. We explain the k–sphere formulation in conjunction with ray tracing process and describe its implementation in a Zemax ®UDS (User Defined Surface). We conclude with examples of simulation and optimization results and show proof of consistency and usefulness of the proposed model.

© 2008 Optical Society of America

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References

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  1. A. Sinha, W. Sun, T. Shih, and G. Barbastathis, "Volume Holographic Imaging in Transmission Geometry," Appl. Opt. 43, 1533-1551 (2004).
    [CrossRef] [PubMed]
  2. www.zemax.com.
  3. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, 1996).
  4. W. Sun, K. Tian, and G. Barbastathis, "Hyper-spectral imaging with volume holographic lenses," in Conference on Laser and Electro-Optics (CLEO), Paper CFP2 (2005).
  5. W. Liu, D. Psaltis, and G. Barbastathis, "Real-time spectral imaging in three spatial dimensions," Opt. Lett. 27, 854-856 (2002).
    [CrossRef]
  6. G. Barbastathis, "The transfer function of volume holographic optical systems" in Photorefractive Materials and Their Applications (Springer-Verlag, 2007) Vol. 3.
    [CrossRef]
  7. A. Sinha and G. Barbastathis, "Volume holographic telescope," Opt. Express 27, 1690-1692 (2002).
  8. G. Barbastathis, M. Balberg and D. J. Brady, "Confocal microscopywith a volume holographic filter," Opt. Lett. 24, 811-813 (1999).
    [CrossRef]
  9. G. Barbastathis and D. Psaltis, "Volume Holographic Multiplexing Methods," in Holographic Data Storage (Springer, 2000).
  10. C. Kitel, Introduction to Solid-State Physics, 6th ed. (John Wiley, 1986).
  11. F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, 1976).
  12. J. R. Meyer-Arendt, Introduction to Classical and Modern Optics, 4th ed. (Prentice-Hall, 1989).
  13. R. K. Kostuk, Multiple grating reflection volume holograms with application to optical interconnects, Ph. D. Thesis, (Stanford University, 1986)
    [PubMed]
  14. R. R. A. Syms and L. Solymar, "Analysis of Volume Holographic Cylindrical Lenses," J. Opt. Soc. Am. 72, 179-186 (1982)
    [CrossRef]

2004

2002

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

A. Sinha and G. Barbastathis, "Volume holographic telescope," Opt. Express 27, 1690-1692 (2002).

1999

1982

Balberg, M.

Barbastathis, G.

Brady, D. J.

Liu, W.

Psaltis, D.

Shih, T.

Sinha, A.

Solymar, L.

Sun, W.

Syms, R. R. A.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Express

A. Sinha and G. Barbastathis, "Volume holographic telescope," Opt. Express 27, 1690-1692 (2002).

Opt. Lett.

Other

www.zemax.com.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw Hill, 1996).

W. Sun, K. Tian, and G. Barbastathis, "Hyper-spectral imaging with volume holographic lenses," in Conference on Laser and Electro-Optics (CLEO), Paper CFP2 (2005).

G. Barbastathis and D. Psaltis, "Volume Holographic Multiplexing Methods," in Holographic Data Storage (Springer, 2000).

C. Kitel, Introduction to Solid-State Physics, 6th ed. (John Wiley, 1986).

F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, 1976).

J. R. Meyer-Arendt, Introduction to Classical and Modern Optics, 4th ed. (Prentice-Hall, 1989).

R. K. Kostuk, Multiple grating reflection volume holograms with application to optical interconnects, Ph. D. Thesis, (Stanford University, 1986)
[PubMed]

G. Barbastathis, "The transfer function of volume holographic optical systems" in Photorefractive Materials and Their Applications (Springer-Verlag, 2007) Vol. 3.
[CrossRef]

Supplementary Material (1)

» Media 1: AVI (1393 KB)     

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Figures (6)

Fig. 1.
Fig. 1.

Geometric construction of volumetric diffraction using the k-sphere

Fig. 2.
Fig. 2.

Layouts of several VHI systems with different volume hologram. Note that images are produced by Zemax ®) with a realistic bi–convex lens (BK7, f=30 mm). d r and d s are distances from a volume hologram to point sources. They are used to specify the origin of spherical wavefronts.

Fig. 3.
Fig. 3.

Schematic of volume hologram UDS implementation in Zemax ®, where K g is the local grating vector and η 0 is the local diffraction efficiency at (x,y,z), k p and k d are k-vectors of the incident and diffracted ray, respectively. k d is computed by the k–sphere formulation. The intensity I of the diffracted ray is η 0×η, where η is computed by Eq. (10).

Fig. 4.
Fig. 4.

Longitudinal PSF of a 4–f VHI system (see text for parameters)

Fig. 5.
Fig. 5.

Longitudinal PSFs with paraxial and aberrated lens. (f 1=50.2 mm, L=2 mm, θ s=23.1°, λ f=λ p=532 nm)

Fig. 6.
Fig. 6.

Diffraction image, lens shape and ray fan. (1.4MB) [Media 1]

Tables (1)

Tables Icon

Table 1. Optimization of 4–f and VHI system using the default merit function. The last column is computed by the IMAE operand in the merit function.

Equations (12)

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K g = k s k f .
k d · x ̂ = ( k p + K g ) · x ̂ ,
k d · y ̂ = ( k p + K g ) · y ̂ , and
k d = 2 π λ p .
η sinc 2 ( L ( k p + K g k d ) · z ̂ 2 π ) = sinc 2 ( L δ k d · z ̂ 2 π ) ,
δ k d k p + K g k d
k p = ( m n l ) 2 π λ p .
k d = ( k p , x + K g , x k p , y + K g , y ( 2 π λ p ) 2 k p , x + K g , x 2 k p , y + K g , y 2 )
δ k d = k p + K g k d .
rel _ surf _ tran = η 0 ( x , y , z ) sinc 2 ( L δ k d · z ̂ 2 π ) ,
q = R 1 + R 2 R 1 R 2 ,
q min . SA = 2 ( n 2 1 ) n + 2 ,

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