Abstract

A novel method for computer-generated rainbow holograms (CGRHs) of full-color objects is proposed. First, a new algorithm for fabricating full-color CGRHs of real-existing objects is proposed based on the interrelationship between coding of a CGRH and reconstruction of the hologram. Second, a color rainbow hologram for a real-existing object is generated by combining the proposed algorithm and computer-generated hologram generating system. Finally, the hologram is outputted by an auto-microfilming system. The principle of the algorithm, the process of hologram calculation, and the hologram generating system for real-existing objects and experimental results are presented. The experimental results demonstrate that the new method is feasible.

© 2009 Optical Society of America

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References

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  1. W. J. Dallas and A. W. Lohmann, “Holography, techniques: computer-generated holograms,” in Encyclopedia of Modern Optics, B. D. Guenther, ed. (Elsevier, 2005), pp. 72-79.
    [CrossRef]
  2. R. Bhatt, S. K. Mishra, and D. Mohan, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
    [CrossRef]
  3. A. G. Poleshchuk, R. K. Nasyrov, and J. M. Asfour, “Combined computer-generated hologram for testing steep aspheric surfaces,” Opt. Express 17, 5420-5425 (2009).
    [CrossRef] [PubMed]
  4. H. Wang, Y. Li, and H. Jin, “Three-dimensional visualization of shape measurement data based on a computer generated hologram,” J. Opt. A: Pure Appl. Opt. 5, 195-199 (2003).
    [CrossRef]
  5. K. Choi, J. Kim, and Y. Lim, “Full parallax viewing-angle enhanced computer generated holographic 3D display system using integral lens array,” Opt. Express 13, 10494-10502(2005).
    [CrossRef] [PubMed]
  6. T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
    [CrossRef]
  7. Y. Sando, M. Itoh, and T. Yatagai, “Fast calculation method for cylindrical computer-generated holograms,” Opt. Express 13, 1418-1423 (2005).
    [CrossRef] [PubMed]
  8. S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986-5995 (2008).
    [CrossRef] [PubMed]
  9. S. Matsuda, F. Tomohiko, and T. Yamaguchi, “Fast generation of computer-generated hologram by graphics processing unit,” Proc. SPIE 7233, 72330I (2009).
    [CrossRef]
  10. R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).
  11. S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545A-1546A (1969).
  12. C. Fan, C. Jiang, and L. Guo, “Analyses of rainbow holography with the line-element hologram,” Acta Opt. Sin. 10, 845-849(1990).
  13. C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
    [CrossRef]

2009 (2)

A. G. Poleshchuk, R. K. Nasyrov, and J. M. Asfour, “Combined computer-generated hologram for testing steep aspheric surfaces,” Opt. Express 17, 5420-5425 (2009).
[CrossRef] [PubMed]

S. Matsuda, F. Tomohiko, and T. Yamaguchi, “Fast generation of computer-generated hologram by graphics processing unit,” Proc. SPIE 7233, 72330I (2009).
[CrossRef]

2008 (2)

R. Bhatt, S. K. Mishra, and D. Mohan, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

S.-C. Kim, J.-H. Yoon, and E.-S. Kim, “Fast generation of three-dimensional video holograms by combined use of data compression and lookup table techniques,” Appl. Opt. 47, 5986-5995 (2008).
[CrossRef] [PubMed]

2007 (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

2005 (2)

2003 (1)

H. Wang, Y. Li, and H. Jin, “Three-dimensional visualization of shape measurement data based on a computer generated hologram,” J. Opt. A: Pure Appl. Opt. 5, 195-199 (2003).
[CrossRef]

1990 (1)

C. Fan, C. Jiang, and L. Guo, “Analyses of rainbow holography with the line-element hologram,” Acta Opt. Sin. 10, 845-849(1990).

1969 (1)

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545A-1546A (1969).

1949 (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
[CrossRef]

Sando, Y.

Asfour, J. M.

Benton, S. A.

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545A-1546A (1969).

Bhatt, R.

R. Bhatt, S. K. Mishra, and D. Mohan, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

Burckhardt, C. B.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Choi, K.

Collier, R. J.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Dallas, W. J.

W. J. Dallas and A. W. Lohmann, “Holography, techniques: computer-generated holograms,” in Encyclopedia of Modern Optics, B. D. Guenther, ed. (Elsevier, 2005), pp. 72-79.
[CrossRef]

Fan, C.

C. Fan, C. Jiang, and L. Guo, “Analyses of rainbow holography with the line-element hologram,” Acta Opt. Sin. 10, 845-849(1990).

Guo, L.

C. Fan, C. Jiang, and L. Guo, “Analyses of rainbow holography with the line-element hologram,” Acta Opt. Sin. 10, 845-849(1990).

Itoh, M.

Jiang, C.

C. Fan, C. Jiang, and L. Guo, “Analyses of rainbow holography with the line-element hologram,” Acta Opt. Sin. 10, 845-849(1990).

Jin, H.

H. Wang, Y. Li, and H. Jin, “Three-dimensional visualization of shape measurement data based on a computer generated hologram,” J. Opt. A: Pure Appl. Opt. 5, 195-199 (2003).
[CrossRef]

Kim, E.-S.

Kim, J.

Kim, S.-C.

Li, Y.

H. Wang, Y. Li, and H. Jin, “Three-dimensional visualization of shape measurement data based on a computer generated hologram,” J. Opt. A: Pure Appl. Opt. 5, 195-199 (2003).
[CrossRef]

Lim, Y.

Lin, L. H.

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

Lohmann, A. W.

W. J. Dallas and A. W. Lohmann, “Holography, techniques: computer-generated holograms,” in Encyclopedia of Modern Optics, B. D. Guenther, ed. (Elsevier, 2005), pp. 72-79.
[CrossRef]

Matsuda, S.

S. Matsuda, F. Tomohiko, and T. Yamaguchi, “Fast generation of computer-generated hologram by graphics processing unit,” Proc. SPIE 7233, 72330I (2009).
[CrossRef]

Mishra, S. K.

R. Bhatt, S. K. Mishra, and D. Mohan, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

Mohan, D.

R. Bhatt, S. K. Mishra, and D. Mohan, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

Nasyrov, R. K.

Okabe, G.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Poleshchuk, A. G.

Shannon, C. E.

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
[CrossRef]

Tomohiko, F.

S. Matsuda, F. Tomohiko, and T. Yamaguchi, “Fast generation of computer-generated hologram by graphics processing unit,” Proc. SPIE 7233, 72330I (2009).
[CrossRef]

Wang, H.

H. Wang, Y. Li, and H. Jin, “Three-dimensional visualization of shape measurement data based on a computer generated hologram,” J. Opt. A: Pure Appl. Opt. 5, 195-199 (2003).
[CrossRef]

Yamaguchi, T.

S. Matsuda, F. Tomohiko, and T. Yamaguchi, “Fast generation of computer-generated hologram by graphics processing unit,” Proc. SPIE 7233, 72330I (2009).
[CrossRef]

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Yatagai, T.

Yoon, J.-H.

Yoshikawa, H.

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Acta Opt. Sin. (1)

C. Fan, C. Jiang, and L. Guo, “Analyses of rainbow holography with the line-element hologram,” Acta Opt. Sin. 10, 845-849(1990).

Appl. Opt. (1)

J. Opt. A: Pure Appl. Opt. (1)

H. Wang, Y. Li, and H. Jin, “Three-dimensional visualization of shape measurement data based on a computer generated hologram,” J. Opt. A: Pure Appl. Opt. 5, 195-199 (2003).
[CrossRef]

J. Opt. Soc. Am. (1)

S. A. Benton, “Hologram reconstructions with extended incoherent sources,” J. Opt. Soc. Am. 59, 1545A-1546A (1969).

Opt. Eng. (1)

T. Yamaguchi, G. Okabe, and H. Yoshikawa, “Real-time image plane full-color and full-parallax holographic video display system,” Opt. Eng. 46, 125801 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lasers Eng. (1)

R. Bhatt, S. K. Mishra, and D. Mohan, “Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: modeling and simulation,” Opt. Lasers Eng. 46, 428-439 (2008).
[CrossRef]

Proc. IRE (1)

C. E. Shannon, “Communication in the presence of noise,” Proc. IRE 37, 10-21 (1949).
[CrossRef]

Proc. SPIE (1)

S. Matsuda, F. Tomohiko, and T. Yamaguchi, “Fast generation of computer-generated hologram by graphics processing unit,” Proc. SPIE 7233, 72330I (2009).
[CrossRef]

Other (2)

R. J. Collier, C. B. Burckhardt, and L. H. Lin, Optical Holography (Academic, 1971).

W. J. Dallas and A. W. Lohmann, “Holography, techniques: computer-generated holograms,” in Encyclopedia of Modern Optics, B. D. Guenther, ed. (Elsevier, 2005), pp. 72-79.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Color cross talk in the reconstruction of a color hologram.

Fig. 2
Fig. 2

Relationship among object point, slit, line-element hologram, and corresponding strip light beam in a rainbow hologram.

Fig. 3
Fig. 3

Reconstruction principle of a color rainbow hologram.

Fig. 4
Fig. 4

Schematic diagram of hologram generating system for real-existing objects.

Fig. 5
Fig. 5

Schematic drawing of the CGH microfilming system.

Fig. 6
Fig. 6

Experiment results: (a) image of original color 3D object, (b) partly enlarged color CGRH, (c) and (d) photos of reconstructed image in two viewing points.

Tables (2)

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Table 1 Performance Parameters of the 3D Scanner

Tables Icon

Table 2 Parameters of Calculation and Hologram

Equations (28)

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z r = z C z O r z R z O r z R + z C ( z R z O r ) , x r = x C z O r z R + z C ( x O r z R x R z O r ) z O r z R + z C ( z R z O r ) , y r = y C z O r z R + z C ( y O r z R y R z O r ) z O r z R + z C ( z R z O r ) ,
z g = z C z O g z R z O g z R + μ g z C ( z R z O g ) , x g = x C z O g z R + μ g z C ( x O g z R x R z O g ) z O g z R + μ g z C ( z R z O g ) , y g = y C z O g z R + μ g z C ( y O g z R y R z O g ) z O g z R + μ g z C ( z R z O g ) ,
z b = z C z O b z R z O b z R + μ b z C ( z R z O b ) , x b = x C z O b z R + μ b z C ( x O b z R x R z O b ) z O b z R + μ b z C ( z R z O b ) , y b = y C z O b z R + μ b z C ( y O b z R y R z O b ) z O b z R + μ b z C ( z R z O b ) ,
z r = z O r , z g = z O g μ g , z g = z O b μ b , x r = x O r , z g = z O g , z b = z O b , y r = y O r , y g = tan θ y R z O g ( 1 μ g 1 ) + y O g , y b = tan θ y R z O b ( 1 μ b 1 ) + y O b .
z O r = z O , z O g = μ g z O , z O b = μ b z O , x O r = x O , x O g = x O , x O b = x O , y O r = y O , y O g = y O + z O tan θ y R ( μ g 1 ) , y O b = y O + z O tan θ y R ( μ b 1 ) .
z S r = z e , z S g = μ g z e , z S b = μ b z e , x S r = 0 , x S g = 0 , x S b = 0 , y S r = 0 , y S g = z e tan θ y R ( μ g 1 ) , y S b = z e tan θ y R ( μ b 1 ) .
U oijl ( x slit , y slit ) = a oijl exp ( i k x oi j l 2 + y oi j l 2 2 z oi j l ) exp ( i k x slit 2 + y slit 2 2 z oijl ) exp ( i k x oijl x slit + y oi j l y slit z oi j l ) ,
U oijl ( x , y ) = a oijl Σ exp ( i k x oijl 2 + y oijl 2 2 z oijl ) exp ( i k x slit 2 + y slit 2 2 z oijl ) exp ( i k x oijl x slit + y oijl y slit z oijl ) exp ( i k x 2 + y 2 2 z e ) exp ( i k x slit 2 + y slit 2 2 z e ) exp ( i k x x slit + y y slit z e ) d x slit d y slit ,
U oijl ( x , y ) = a oijl exp ( i k x oijl 2 + y oijl 2 2 z oijl ) exp ( i k x 2 + y 2 2 z e ) Σ exp [ i k ( 1 2 z e 1 2 z oijl ) ( x slit 2 + y slit 2 ) ] exp { i k [ ( x oijl z oijl x z e ) x slit + ( y oijl z oijl y z e ) y slit ] } d x slit d y slit = a oijl exp ( i k x oijl 2 + y oijl 2 2 z oijl ) exp ( i k x 2 + y 2 2 z e ) a / 2 a / 2 exp [ i k ( 1 2 z e 1 2 z oijl ) x slit 2 ] exp [ i k ( x oijl z oijl x z e ) x slit ] d x slit l / 2 l / 2     exp [ i k ( 1 2 z e 1 2 z oijl ) y slit 2 ] exp [ i k ( y oijl z oijl y z e ) y slit ] d y slit .
U x slit = exp ( i k x oijl 2 2 z oijl ) exp ( i k x 2 2 z e ) a / 2 a / 2 exp [ i k ( 1 2 z e 1 2 z oijl ) x slit 2 ] exp [ i k ( x oijl z oijl x z e ) x slit ] d x slit ,
U y slit = exp ( i k y oijl 2 2 z oijl ) exp ( i k y 2 2 z e ) l / 2 l / 2 exp [ i k ( 1 2 z e 1 2 z oijl ) y slit 2 ] exp [ i k ( y oijl z oijl y z e ) y slit ] d y slit .
U y slit = exp ( i k y oijl 2 2 z oijl ) exp ( i k y 2 2 z e ) exp [ i k ( 1 2 z e 1 2 z oijl ) y slit 2 ] exp [ i k ( y oijl z oijl y z e ) y slit ] d y slit = C exp [ i k y oijl 2 2 ( z oijl z e ) ] exp [ i k y 2 2 ( z oijl z e ) ] exp [ i 2 π λ y oijl y ( z oijl z e ) ] = C exp [ i k ( y oijl y ) 2 2 ( z oijl z e ) ] .
U oijl ( x , y ) = a oijl U x slit ( x oijl , x , z oijl ) U y slit ( y ) a oijl U x slit ( x oijl , x , z oijl ) exp [ i k ( y oijl y ) 2 2 ( z oijl z e ) ] .
O ( x , y ) = i , j , l U oijl ( x , y ) .
U oRijl ( x , y ) = a oRijl U x R slit ( x oRijl , x , z oRijl ) exp [ i k ( y oRijl y ) 2 2 ( z oRijl z e R ) ] , U oGijl ( x , y ) = a oGijl U x G slit ( x oGijl , x , z oGijl ) exp [ i k ( y o G i j l y ) 2 2 ( z o G i j l z e G ) ] , U oBijl ( x , y ) = a oBijl U x B slit ( x oBijl , x , z oBijl ) exp [ i k ( y oBijl y ) 2 2 ( z oBijl z e B ) ] .
O ( x , y ) = i , j , l U oRijl ( x , y ) + i , j , l U oGijl ( x , y ) + i , j , l U oBijl ( x , y ) .
I ( x , y ) = | O ( x , y ) + R ( x , y ) | 2 .
U x slit = exp ( i k x oijl 2 2 z oijl ) exp ( i k x 2 2 z e ) rect ( x slit a ) exp [ i k ( 1 2 z e 1 2 z o i j l ) x slit 2 ] exp [ i k ( x o i j l z o i j l x z e ) x slit ] d x slit = exp ( i k x oijl 2 2 z oijl ) exp ( i k x 2 2 z e ) rect ( x slit a ) exp ( i Z x slit 2 ) exp ( i 2 π f x x slit ) d x slit ,
f x = 1 λ ( x oijl z oijl x z e ) .
f x o = 1 2 π d ( Z x slit 2 ) d x slit = 1 π Z x slit = 1 λ ( 1 z oijl 1 z e ) x slit .
f x o max = 1 2 λ ( 1 z oijl 1 z e ) a .
Δ x slit 1 2 f x o max .
f x max = x o max / ( z e min λ ) + sin θ / λ ,
U y slit ( y ) = exp [ i k ( y oijl y ) 2 2 ( z oijl z e ) ]
f x = x slit Δ x slit 1 a .
x = z e ( x oijl z oijl f x λ ) .
Δ x = x max x min ,
Δ y = ( 1 z e z oijl ) l .

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