Abstract

We present a method for efficiently calculating the interference of complex-valued two-dimensional wave patterns that is useful during the generation of synthetic holograms. These patterns are represented as a special kind of images (textures), and the interference is calculated in a computer graphics rendering process. This enables us to leverage hardware support for holographic imaging that is implemented in many state-of-the-art computer workstations. Using this approach, we gain a speedup of a factor of 60–90 compared with conventional calculation methods for interfering wave patterns. Our method is evaluated numerically, examples are shown, and the program code is outlined.

© 1999 Optical Society of America

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  1. S. A. Benton, “Survey of holographic stereograms,” in Processing and Display of Three-Dimensional Data, J. J. Pearson, ed., Proc. SPIE367, 15–19 (1983).
    [CrossRef]
  2. M. Lucente, “Interactive three-dimensional holographic displays: seeing the future in depth,” ACM (Assoc. Comput. Mach.) Comput. Graphics 31(2), 63–66 (1997).
    [CrossRef]
  3. M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of ACM SIGGRAPH ’95, R. Cook, ed., Annual Conference Series (ACM Press, New York, 1995), pp. 387–394.
    [CrossRef]
  4. M. W. Halle, A. B. Kropp, “Fast computer graphics rendering for full parallax spatial displays,” in Practical Holography XI, S. A. Benton, ed., Proc. SPIE3011, 105–112 (1997).
  5. K. Haines, D. Haines, “Computer graphics for holography,” IEEE Comput. Graphics Appl. 12, 37–46 (1992).
    [CrossRef]
  6. M. J. Kilgard, “Realizing OpenGL: two implementations of one architecture,” in Proceedings of ACM SIGGRAPH/EuroGraphics Workshop on Graphics Hardware, S. Molnar, B.-O. Schneider, eds. (ACM Press, New York, 1997), pp. 45–55.
    [CrossRef]
  7. J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
    [CrossRef]
  8. J. Neider, T. Davis, M. Woo, OpenGL Programming Guide: The Official Guide to Learning OpenGL (Addison-Wesley, Bonn, Germany, 1993).
  9. H. Aagedal, Th. Beth, H. Schwarzer, S. Teiwes, “Design of paraxial diffractive elements with the CAD system DigiOpt,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 50–58 (1994).
    [CrossRef]
  10. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).
  11. A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.
  12. A. Ritter, O. Deussen, H. Wagener, Th. Strothotte, “Holographic imaging of lines: a texture-based approach,” in Proceedings of the International Conference on Information Visualization IV ’97, P. Storms, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 272–278.
  13. J. S. Montrym, D. R. Baum, D. L. Dignam, C. J. Migdal, “InfiniteReality: a real-time graphics system,” in Proceedings of ACM SIGGRAPH ’97, T. Whitted, ed., Annual Conference Series (ACM Press, New York, 1997), 293–302.
  14. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1968).
  15. C. Frère, D. Leseberg, O. Bryngdahl, “Computer-generated holograms of three-dimensional objects composed of line segments,” J. Opt. Soc. Am. A 3, 726–730 (1986).
    [CrossRef]
  16. W. Lauterborn, Th. Kurz, M. Wiesenfeldt, Coherent Optics, Fundamentals and Applications (Springer-Verlag, Berlin, 1995).
  17. D. Leseberg, “Computer generated holograms: cylindrical, conical, and helical waves,” Appl. Opt. 26, 4385–4390 (1987).
    [CrossRef] [PubMed]

1997 (1)

M. Lucente, “Interactive three-dimensional holographic displays: seeing the future in depth,” ACM (Assoc. Comput. Mach.) Comput. Graphics 31(2), 63–66 (1997).
[CrossRef]

1992 (1)

K. Haines, D. Haines, “Computer graphics for holography,” IEEE Comput. Graphics Appl. 12, 37–46 (1992).
[CrossRef]

1987 (1)

1986 (1)

1966 (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Aagedal, H.

H. Aagedal, Th. Beth, H. Schwarzer, S. Teiwes, “Design of paraxial diffractive elements with the CAD system DigiOpt,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 50–58 (1994).
[CrossRef]

Baum, D. R.

J. S. Montrym, D. R. Baum, D. L. Dignam, C. J. Migdal, “InfiniteReality: a real-time graphics system,” in Proceedings of ACM SIGGRAPH ’97, T. Whitted, ed., Annual Conference Series (ACM Press, New York, 1997), 293–302.

Benton, S. A.

S. A. Benton, “Survey of holographic stereograms,” in Processing and Display of Three-Dimensional Data, J. J. Pearson, ed., Proc. SPIE367, 15–19 (1983).
[CrossRef]

Benziger, Th.

A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.

Beth, Th.

H. Aagedal, Th. Beth, H. Schwarzer, S. Teiwes, “Design of paraxial diffractive elements with the CAD system DigiOpt,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 50–58 (1994).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Bryngdahl, O.

Davis, T.

J. Neider, T. Davis, M. Woo, OpenGL Programming Guide: The Official Guide to Learning OpenGL (Addison-Wesley, Bonn, Germany, 1993).

Deussen, O.

A. Ritter, O. Deussen, H. Wagener, Th. Strothotte, “Holographic imaging of lines: a texture-based approach,” in Proceedings of the International Conference on Information Visualization IV ’97, P. Storms, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 272–278.

A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.

Dignam, D. L.

J. S. Montrym, D. R. Baum, D. L. Dignam, C. J. Migdal, “InfiniteReality: a real-time graphics system,” in Proceedings of ACM SIGGRAPH ’97, T. Whitted, ed., Annual Conference Series (ACM Press, New York, 1997), 293–302.

Frère, C.

Galyean, T. A.

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of ACM SIGGRAPH ’95, R. Cook, ed., Annual Conference Series (ACM Press, New York, 1995), pp. 387–394.
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1968).

Haines, D.

K. Haines, D. Haines, “Computer graphics for holography,” IEEE Comput. Graphics Appl. 12, 37–46 (1992).
[CrossRef]

Haines, K.

K. Haines, D. Haines, “Computer graphics for holography,” IEEE Comput. Graphics Appl. 12, 37–46 (1992).
[CrossRef]

Halle, M. W.

M. W. Halle, A. B. Kropp, “Fast computer graphics rendering for full parallax spatial displays,” in Practical Holography XI, S. A. Benton, ed., Proc. SPIE3011, 105–112 (1997).

Kilgard, M. J.

M. J. Kilgard, “Realizing OpenGL: two implementations of one architecture,” in Proceedings of ACM SIGGRAPH/EuroGraphics Workshop on Graphics Hardware, S. Molnar, B.-O. Schneider, eds. (ACM Press, New York, 1997), pp. 45–55.
[CrossRef]

Kropp, A. B.

M. W. Halle, A. B. Kropp, “Fast computer graphics rendering for full parallax spatial displays,” in Practical Holography XI, S. A. Benton, ed., Proc. SPIE3011, 105–112 (1997).

Kurz, Th.

W. Lauterborn, Th. Kurz, M. Wiesenfeldt, Coherent Optics, Fundamentals and Applications (Springer-Verlag, Berlin, 1995).

Lauterborn, W.

W. Lauterborn, Th. Kurz, M. Wiesenfeldt, Coherent Optics, Fundamentals and Applications (Springer-Verlag, Berlin, 1995).

Leseberg, D.

Lucente, M.

M. Lucente, “Interactive three-dimensional holographic displays: seeing the future in depth,” ACM (Assoc. Comput. Mach.) Comput. Graphics 31(2), 63–66 (1997).
[CrossRef]

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of ACM SIGGRAPH ’95, R. Cook, ed., Annual Conference Series (ACM Press, New York, 1995), pp. 387–394.
[CrossRef]

Migdal, C. J.

J. S. Montrym, D. R. Baum, D. L. Dignam, C. J. Migdal, “InfiniteReality: a real-time graphics system,” in Proceedings of ACM SIGGRAPH ’97, T. Whitted, ed., Annual Conference Series (ACM Press, New York, 1997), 293–302.

Montrym, J. S.

J. S. Montrym, D. R. Baum, D. L. Dignam, C. J. Migdal, “InfiniteReality: a real-time graphics system,” in Proceedings of ACM SIGGRAPH ’97, T. Whitted, ed., Annual Conference Series (ACM Press, New York, 1997), 293–302.

Neider, J.

J. Neider, T. Davis, M. Woo, OpenGL Programming Guide: The Official Guide to Learning OpenGL (Addison-Wesley, Bonn, Germany, 1993).

Ritter, A.

A. Ritter, O. Deussen, H. Wagener, Th. Strothotte, “Holographic imaging of lines: a texture-based approach,” in Proceedings of the International Conference on Information Visualization IV ’97, P. Storms, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 272–278.

A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.

Schwarzer, H.

H. Aagedal, Th. Beth, H. Schwarzer, S. Teiwes, “Design of paraxial diffractive elements with the CAD system DigiOpt,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 50–58 (1994).
[CrossRef]

Strothotte, Th.

A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.

A. Ritter, O. Deussen, H. Wagener, Th. Strothotte, “Holographic imaging of lines: a texture-based approach,” in Proceedings of the International Conference on Information Visualization IV ’97, P. Storms, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 272–278.

Teiwes, S.

H. Aagedal, Th. Beth, H. Schwarzer, S. Teiwes, “Design of paraxial diffractive elements with the CAD system DigiOpt,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 50–58 (1994).
[CrossRef]

Wagener, H.

A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.

A. Ritter, O. Deussen, H. Wagener, Th. Strothotte, “Holographic imaging of lines: a texture-based approach,” in Proceedings of the International Conference on Information Visualization IV ’97, P. Storms, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 272–278.

Waters, J. P.

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

Wiesenfeldt, M.

W. Lauterborn, Th. Kurz, M. Wiesenfeldt, Coherent Optics, Fundamentals and Applications (Springer-Verlag, Berlin, 1995).

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

Woo, M.

J. Neider, T. Davis, M. Woo, OpenGL Programming Guide: The Official Guide to Learning OpenGL (Addison-Wesley, Bonn, Germany, 1993).

ACM (Assoc. Comput. Mach.) Comput. Graphics (1)

M. Lucente, “Interactive three-dimensional holographic displays: seeing the future in depth,” ACM (Assoc. Comput. Mach.) Comput. Graphics 31(2), 63–66 (1997).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. P. Waters, “Holographic image synthesis utilizing theoretical methods,” Appl. Phys. Lett. 9, 405–407 (1966).
[CrossRef]

IEEE Comput. Graphics Appl. (1)

K. Haines, D. Haines, “Computer graphics for holography,” IEEE Comput. Graphics Appl. 12, 37–46 (1992).
[CrossRef]

J. Opt. Soc. Am. A (1)

Other (12)

W. Lauterborn, Th. Kurz, M. Wiesenfeldt, Coherent Optics, Fundamentals and Applications (Springer-Verlag, Berlin, 1995).

S. A. Benton, “Survey of holographic stereograms,” in Processing and Display of Three-Dimensional Data, J. J. Pearson, ed., Proc. SPIE367, 15–19 (1983).
[CrossRef]

M. J. Kilgard, “Realizing OpenGL: two implementations of one architecture,” in Proceedings of ACM SIGGRAPH/EuroGraphics Workshop on Graphics Hardware, S. Molnar, B.-O. Schneider, eds. (ACM Press, New York, 1997), pp. 45–55.
[CrossRef]

M. Lucente, T. A. Galyean, “Rendering interactive holographic images,” in Proceedings of ACM SIGGRAPH ’95, R. Cook, ed., Annual Conference Series (ACM Press, New York, 1995), pp. 387–394.
[CrossRef]

M. W. Halle, A. B. Kropp, “Fast computer graphics rendering for full parallax spatial displays,” in Practical Holography XI, S. A. Benton, ed., Proc. SPIE3011, 105–112 (1997).

J. Neider, T. Davis, M. Woo, OpenGL Programming Guide: The Official Guide to Learning OpenGL (Addison-Wesley, Bonn, Germany, 1993).

H. Aagedal, Th. Beth, H. Schwarzer, S. Teiwes, “Design of paraxial diffractive elements with the CAD system DigiOpt,” in Diffractive and Holographic Optics Technology II, I. Cindrich, S. H. Lee, eds., Proc. SPIE2404, 50–58 (1994).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980).

A. Ritter, Th. Benziger, O. Deussen, Th. Strothotte, H. Wagener, “Synthetic holograms of splines,” in 3D Image Analysis and Synthesis ’97, H.-P. Seidel, B. Girod, H. Niemann, eds., (infix Verlag, Sankt Augustin, Germany, 1997), pp. 11–18.

A. Ritter, O. Deussen, H. Wagener, Th. Strothotte, “Holographic imaging of lines: a texture-based approach,” in Proceedings of the International Conference on Information Visualization IV ’97, P. Storms, ed. (IEEE Computer Society Press, Los Alamitos, Calif., 1997), pp. 272–278.

J. S. Montrym, D. R. Baum, D. L. Dignam, C. J. Migdal, “InfiniteReality: a real-time graphics system,” in Proceedings of ACM SIGGRAPH ’97, T. Whitted, ed., Annual Conference Series (ACM Press, New York, 1997), 293–302.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1968).

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Figures (6)

Fig. 1
Fig. 1

Textures representing wave patterns of point sources: (a)–(d) together form a single complex texture: red channel (positive real part), green channel (negative real part), blue channel (positive imaginary part), and alpha channel (negative imaginary part) are shown as gray-scale images. (e) The Fresnel zone plate that is obtained by interference of the complex texture with a plane wave.

Fig. 2
Fig. 2

Generation of a hologram: A geometric object is transformed into a set of complex textures. These textures are interfered to generate the hologram.

Fig. 3
Fig. 3

Construction of a hologram from a set of points: (a) input object, (b) result obtained by superposition of gray-scale textures, (c) interference of complex textures for point sources with random phase, (d) reconstruction of (c) including typical speckles.

Fig. 4
Fig. 4

Off-axis reconstruction: (a) hologram of point sources, with the reference wave parallel to the virtual holographic plate; (b) an inclined wave was chosen.

Fig. 5
Fig. 5

Holographic image of a surface: (a) input object assembled out of 144 points, (b) corresponding hologram with random phase, (c) reconstruction of (b), (d) reconstruction of a hologram of the same object with points in phase.

Fig. 6
Fig. 6

Holograms of lines: (a) cylindrical wave originating from a line, (b) conical wave pattern of an inclined line generated by transformation of the texture, (c) input object assembled from lines; (d) hologram of (c) with cylindrical and conical wave patterns.

Tables (1)

Tables Icon

Table 1 Time Consumed for Calculating Holograms of Different Input Complexity (Number of Points) and Size (512 × 512, 1024 × 1024, 5120 × 5120 Pixels) in Seconds and Speedup of the Texture-Based Approach Compared with the Traditional Method

Equations (6)

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

Ep=1iλpS Ep1r exp2πirλcosαdS,
Ep=1iλiN Ei1r exp2πirλcosα.
Ep=1r exp2πirλ,
s=z/z01/2.
A=|Ep|=ReE2+ImE21/2,
I=A2=ReE2+ImE2.

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