Abstract

The optical system configuration and design of a dot matrix holographic printer that can create image grating pixels of variable size, arbitrary pitch, and discretionary angle on a photoresist plate are presented. With the capability to vary spot size, grating orientation, and grating pitch on the fly, this newly developed holographic printer can apply a prespecified color at each specific viewing angle. Diffractive images with various visual effects and the wide color range that are possible by use of this system are examined in detail.

© 2000 Optical Society of America

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  34. R. W. G. Hunt, Measuring Colour (Ellis Horwood, Ashburton, Devon, UK, 1995).
  35. C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
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1998

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

N. Yoshikawa, M. Itoh, T. Yatagai, “Binary computer-generated holograms for security applications from a synthetic double-exposure method by electron-beam lithography,” Opt. Lett. 23, 1483–1485 (1998).
[CrossRef]

1995

1994

U. Schnars, W. P. O. Jüeptner, “Digital recording and reconstruction of holograms in hologram interferometry and shearography,” Appl. Opt. 33, 4373–4377 (1994).
[CrossRef] [PubMed]

R. G. Dorsche, A. W. Lehman, S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated holograms display,” Appl. Opt. 33, 846–875 (1994).

1993

W. Lehman, J. Ojeda-Castaneda, “Computer generated holography: novel procedure,” Opt. Commun. 3, 181–184 (1993).
[CrossRef]

M. J. Verheijen, “E-beam lithography for digital holograms,” J. Mod. Opt. 40, 711–721 (1993).
[CrossRef]

D. M. Newman, R. W. Hawley, D. L. Goeckel, R. D. Crawford, S. Abraham, N. C. Gallagher, “Efficient storage, computation, and exposure of computer-generated holograms by electron-beam lithography,” Appl. Opt. 32, 2555–2565 (1993).
[CrossRef] [PubMed]

1987

F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer holography: object dependent deterministic diffusers,” Opt. Commun. 63, 81–84 (1987).
[CrossRef]

1968

B. Lesem, P. M. Hirsch, A. Jordan, “Computer synthesis of holograms or 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

1966

1964

1949

D. Gabor, “Microscope by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

1948

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Abraham, S.

Benton, S. A.

S. A. Benton, “The reflection alcove hologram: a computer-graphic holographic stereogram,” in Computer-Generated Holography II, S. H. Lee, ed., Proc. SPIE884, 106–113 (1988).
[CrossRef]

Billmeyer, F. W.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology (Wiley, New York, 1981).

Brown, B. R.

Bryngdahl, O.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer holography: object dependent deterministic diffusers,” Opt. Commun. 63, 81–84 (1987).
[CrossRef]

Cai, L.

L. Cai, “Generation of 3D image from computer data with dot array rainbow hologram,” in Holographic Optical Elements and Display, F. S. Lin, D. Xu, eds., Proc. SPIE2885, 17–25 (1996).
[CrossRef]

Chamberlain, M. R.

M. R. Chamberlain, “Elemental analysis of kinematic optically variable devices,” in Optical Security and Counterfeit Deterrence Techniques, R. L. van Renesse, ed., Proc. SPIE2659, 170–180 (1996).
[CrossRef]

Chiang, S. J.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Crawford, R. D.

Davis, F.

F. Davis, “System for making a hologram of an image by manipulating object beam characteristics to reflect image data,” U.S. patent5,822,092 (13October1998).

F. Davis, “Holographic image conversion method for making a controlled holographic grating,” U.S. patent5,262,879 (16November1993).

Dietrich, C.

Dorsche, R. G.

R. G. Dorsche, A. W. Lehman, S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated holograms display,” Appl. Opt. 33, 846–875 (1994).

Drain, L. E.

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

Fan, J.

Fan, S.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Gabor, D.

D. Gabor, “Microscope by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Gallagher, N. C.

Goeckel, D. L.

Hamano, T.

T. Hamano, H. Yoshikawa, “Image-type CGH by means of e-beam printing,” in Practical Holography XII, S. A. Benton, ed., Proc. SPIE3293, 170–180 (1998).

Han, Y. A.

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

Hauck, R.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer holography: object dependent deterministic diffusers,” Opt. Commun. 63, 81–84 (1987).
[CrossRef]

Hawley, R. W.

Hirsch, P. M.

B. Lesem, P. M. Hirsch, A. Jordan, “Computer synthesis of holograms or 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

Hsieh, C. T.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Hsu, C. C.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Huang, J. H.

J. H. Huang, S. L. Yeh, C. K. Lee, T. K. Huang, “Large format grating image hologram based on e-beam lithography,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 117–123 (1996).
[CrossRef]

Huang, T. K.

J. H. Huang, S. L. Yeh, C. K. Lee, T. K. Huang, “Large format grating image hologram based on e-beam lithography,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 117–123 (1996).
[CrossRef]

Hunt, R. W. G.

R. W. G. Hunt, Measuring Colour (Ellis Horwood, Ashburton, Devon, UK, 1995).

Itoh, M.

Iwata, F.

S. Takahashi, T. Toda, F. Iwata, “Method of manufacturing display having diffraction grating patterns,” U.S. patent5,132,812 (21July1992).

Jordan, A.

B. Lesem, P. M. Hirsch, A. Jordan, “Computer synthesis of holograms or 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

Jüeptner, W. P. O.

Kuo, C. W.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Lee, C. K.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

J. H. Huang, S. L. Yeh, C. K. Lee, T. K. Huang, “Large format grating image hologram based on e-beam lithography,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 117–123 (1996).
[CrossRef]

Lee, J. T.

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

Lee, S. H.

Lehman, A. W.

R. G. Dorsche, A. W. Lehman, S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated holograms display,” Appl. Opt. 33, 846–875 (1994).

B. R. Brown, A. W. Lehman, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–969 (1966).
[CrossRef] [PubMed]

Lehman, W.

W. Lehman, J. Ojeda-Castaneda, “Computer generated holography: novel procedure,” Opt. Commun. 3, 181–184 (1993).
[CrossRef]

Leith, E. N.

Lesem, B.

B. Lesem, P. M. Hirsch, A. Jordan, “Computer synthesis of holograms or 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

Li, Y.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Liao, E. H. Z.

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

Lin, C. C.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Lin, S. T.

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Maenner, R.

Mitsuhashi, Y.

M. Nakajima, Y. Mitsuhashi, “Computer-generated polarization holography: automatic hologram making system and the quality of the reconstructed image,” in International Conference on Computer-Generated Holography, S. H. Lee, ed., Proc. SPIE437, 79–88 (1983).
[CrossRef]

Nakajima, M.

M. Nakajima, Y. Mitsuhashi, “Computer-generated polarization holography: automatic hologram making system and the quality of the reconstructed image,” in International Conference on Computer-Generated Holography, S. H. Lee, ed., Proc. SPIE437, 79–88 (1983).
[CrossRef]

Newman, D. M.

Newswanger, C.

C. Newswanger, “Holographic diffraction grating patterns and method for creating the same,” U.S. patent5,291,317 (1March1994).

Noehte, S.

Ojeda-Castaneda, J.

W. Lehman, J. Ojeda-Castaneda, “Computer generated holography: novel procedure,” Opt. Commun. 3, 181–184 (1993).
[CrossRef]

Peng, A. S. T.

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

Saltzman, M.

F. W. Billmeyer, M. Saltzman, Principles of Color Technology (Wiley, New York, 1981).

Schnars, U.

Sinzinger, S.

R. G. Dorsche, A. W. Lehman, S. Sinzinger, “Fresnel ping-pong algorithm for two-plane computer-generated holograms display,” Appl. Opt. 33, 846–875 (1994).

Stephen, R.

R. Stephen, “Enhanced nondestructive holographic reconstruction,” U.S. patent4,953,924 (4September1990).

Stiles, W. S.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Takahashi, S.

S. Takahashi, “Method for producing a display with a diffraction grating pattern and a display produced by the method,” U.S. patent5,058,992 (22October1991).

S. Takahashi, T. Toda, F. Iwata, “Method of manufacturing display having diffraction grating patterns,” U.S. patent5,132,812 (21July1992).

Toda, T.

S. Takahashi, T. Toda, F. Iwata, “Method of manufacturing display having diffraction grating patterns,” U.S. patent5,132,812 (21July1992).

Tu, C. W.

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

Upatnieks, J.

Urquhart, K. S.

van Renesse, R. L.

R. L. van Renesse, Optical Document Security (Artech House, Norwood, Mass., 1994).

Verheijen, M. J.

M. J. Verheijen, “E-beam lithography for digital holograms,” J. Mod. Opt. 40, 711–721 (1993).
[CrossRef]

Wang, T.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Wen, H.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Wu, W. J.

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

Wyrowski, F.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer holography: object dependent deterministic diffusers,” Opt. Commun. 63, 81–84 (1987).
[CrossRef]

Wyszecki, G.

G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

Yang, S.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Yatagai, T.

Yeh, S. L.

J. H. Huang, S. L. Yeh, C. K. Lee, T. K. Huang, “Large format grating image hologram based on e-beam lithography,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 117–123 (1996).
[CrossRef]

Yoshikawa, H.

T. Hamano, H. Yoshikawa, “Image-type CGH by means of e-beam printing,” in Practical Holography XII, S. A. Benton, ed., Proc. SPIE3293, 170–180 (1998).

Yoshikawa, N.

Zaleta, D.

Zhang, E.

Zhang, S.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Appl. Opt.

Commun. ACM

B. Lesem, P. M. Hirsch, A. Jordan, “Computer synthesis of holograms or 3-D display,” Commun. ACM 11, 661–674 (1968).
[CrossRef]

J. Mod. Opt.

M. J. Verheijen, “E-beam lithography for digital holograms,” J. Mod. Opt. 40, 711–721 (1993).
[CrossRef]

J. Opt. Soc. Am.

J. Optoelectron. Laser Suppl.

T. Wang, Y. Li, S. Yang, S. Fan, S. Zhang, H. Wen, “Fractal IFS in laser lithographic hologram,” J. Optoelectron. Laser Suppl. 9, 397–399 (1998).

Nature (London)

D. Gabor, “A new microscope principle,” Nature (London) 161, 777–778 (1948).
[CrossRef]

Opt. Commun.

F. Wyrowski, R. Hauck, O. Bryngdahl, “Computer holography: object dependent deterministic diffusers,” Opt. Commun. 63, 81–84 (1987).
[CrossRef]

W. Lehman, J. Ojeda-Castaneda, “Computer generated holography: novel procedure,” Opt. Commun. 3, 181–184 (1993).
[CrossRef]

Opt. Lett.

Proc. R. Soc. London Ser. A

D. Gabor, “Microscope by reconstructed wave-fronts,” Proc. R. Soc. London Ser. A 197, 454–487 (1949).
[CrossRef]

Other

L. Cai, “Generation of 3D image from computer data with dot array rainbow hologram,” in Holographic Optical Elements and Display, F. S. Lin, D. Xu, eds., Proc. SPIE2885, 17–25 (1996).
[CrossRef]

S. A. Benton, “The reflection alcove hologram: a computer-graphic holographic stereogram,” in Computer-Generated Holography II, S. H. Lee, ed., Proc. SPIE884, 106–113 (1988).
[CrossRef]

R. Stephen, “Enhanced nondestructive holographic reconstruction,” U.S. patent4,953,924 (4September1990).

M. Nakajima, Y. Mitsuhashi, “Computer-generated polarization holography: automatic hologram making system and the quality of the reconstructed image,” in International Conference on Computer-Generated Holography, S. H. Lee, ed., Proc. SPIE437, 79–88 (1983).
[CrossRef]

S. Takahashi, “Method for producing a display with a diffraction grating pattern and a display produced by the method,” U.S. patent5,058,992 (22October1991).

S. Takahashi, T. Toda, F. Iwata, “Method of manufacturing display having diffraction grating patterns,” U.S. patent5,132,812 (21July1992).

F. Davis, “Holographic image conversion method for making a controlled holographic grating,” U.S. patent5,262,879 (16November1993).

C. Newswanger, “Holographic diffraction grating patterns and method for creating the same,” U.S. patent5,291,317 (1March1994).

F. Davis, “System for making a hologram of an image by manipulating object beam characteristics to reflect image data,” U.S. patent5,822,092 (13October1998).

W. J. Wu, C. K. Lee, C. T. Hsieh, S. J. Chiang, S. T. Lin, C. C. Hsu, C. C. Lin, C. W. Kuo, “Methods to create true-color dot matrix holograms,” U.S. patent pending (application filed 25June1997).

L. E. Drain, The Laser Doppler Technique (Wiley, New York, 1980).

R. L. van Renesse, Optical Document Security (Artech House, Norwood, Mass., 1994).

T. Hamano, H. Yoshikawa, “Image-type CGH by means of e-beam printing,” in Practical Holography XII, S. A. Benton, ed., Proc. SPIE3293, 170–180 (1998).

J. H. Huang, S. L. Yeh, C. K. Lee, T. K. Huang, “Large format grating image hologram based on e-beam lithography,” in Practical Holography X, S. A. Benton, ed., Proc. SPIE2652, 117–123 (1996).
[CrossRef]

M. R. Chamberlain, “Elemental analysis of kinematic optically variable devices,” in Optical Security and Counterfeit Deterrence Techniques, R. L. van Renesse, ed., Proc. SPIE2659, 170–180 (1996).
[CrossRef]

National Nano Device Laboratory, http://www.ndl.gov.tw/ (1999).

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G. Wyszecki, W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Wiley, New York, 1982).

R. W. G. Hunt, Measuring Colour (Ellis Horwood, Ashburton, Devon, UK, 1995).

C. W. Tu, Y. A. Han, C. K. Lee, W. J. Wu, A. S. T. Peng, E. H. Z. Liao, J. T. Lee, “Expanding a color presentation range with true-color dot matrix holograms,” in Practical Holography XIII, S. A. Benton, ed., Proc. SPIE3637, 130–140 (1999).
[CrossRef]

Photo Research, Inc., PR-650 Spectra Colorimeter Operating Manual (Photo Research, Inc., Chatsworth, California, 1996).

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Figures (23)

Fig. 1
Fig. 1

Optical layout from the Toppan patent.17

Fig. 2
Fig. 2

Optical layout from the first Davis patent.18

Fig. 3
Fig. 3

Schematic of Applied Holographic’s patent.19

Fig. 4
Fig. 4

Optical layout from the second Davis patent20: OB’s, object beams; RB, reference beam; BS’s, beam splitters.

Fig. 5
Fig. 5

Spot grating image created by two focused beams.

Fig. 6
Fig. 6

Grating pixel diffracting incident beam 1 into an observing direction.

Fig. 7
Fig. 7

Geometric relationship to determine grating pitch and grating orientation.

Fig. 8
Fig. 8

1931 chromaticity diagram showing the color ranges of various methods.

Fig. 9
Fig. 9

Schematic of an asymmetric two-beam interference holographic printer.

Fig. 10
Fig. 10

Shape of an effective grating pixel in (a) a asymmetric and (b) a symmetric optical configurations.

Fig. 11
Fig. 11

Schematic of another two-beam interference holographic printer.

Fig. 12
Fig. 12

Schematic of the newly developed two-beam interference holographic printer Sparkle.

Fig. 13
Fig. 13

Changing grating pitch on the fly with the newly developed Sparkle printer.

Fig. 14
Fig. 14

Changing the light beam convergent angles on the fly by use of a lens pair.

Fig. 15
Fig. 15

Changing the grating pixel spot size on the fly with the newly developed Sparkle printer.

Fig. 16
Fig. 16

Microscopic photos of grating pixels at different resolutions and at different spot sizes: (a) 400 dpi with small spot size, (b) 400 dpi with large spot size, (c) 800 dpi with small spot size, (d) 800 dpi with large spot size.

Fig. 17
Fig. 17

Color composition by use of three extreme points located on the CIE color diagram.

Fig. 18
Fig. 18

Schematic of the experimental setup.

Fig. 19
Fig. 19

Color spectra of the light sources used, where the intensity response is measured in kilowatts per square meter. The intensities of the halogen lamp and the snake light are taken from the left-hand axis; those of the incandescent lamp and fluorescent light, from right-hand axis.

Fig. 20
Fig. 20

Chromaticity coordinates of six color blocks illuminated by using four different light sources.

Fig. 21
Fig. 21

Perspectives of 3D images at three different angles.

Fig. 22
Fig. 22

Grating pixel for a true-color 3D dot matrix hologram.

Fig. 23
Fig. 23

(a) Left and (b) right images of a 3D true-color dot matrix hologram.

Tables (1)

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Table 1 Characteristics of 6 of the 49 Color Blocks When the Incident Angle Equals 30°

Equations (13)

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Ω=φ1-sin-1λc sin γ1,
d=a sinφ2-Ω,
X=380780 PRx¯dλ, Y=380780 PRy¯dλ, Z=380780 PRz¯dλ,
x=X/X+Y+Z,  y=Y/X+Y+Z.
x0=u×x1+v×x2+w×x3,
y0=u×y1+v×y2+w×y3,
A1=M32x2-M10x1-y2+y1/M32-M10,B1=M32A1-x2+y2,
A2=M31x1-M20x2-y3+y2/M31-M20,B2=M31A2-x3+y3,
A3=M21x1-M30x3-y1+y3/M21-M30,B3=M21A3-x1+y1,
dnm=λ/sin θ=380nm/sin 45°.
d=λsin2 γ1+sin2 γ2+2 sin γ1 sin γ2 cos ω1/2,
Ω=sin-1sin ω1+sin2 γ1sin2 γ2+2 cos ω sin γ1sin γ21/2,
ω=tan-1cos β2cos α2+π2,

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