Abstract

A novel technique for synthesizing a hologram of three-dimensional objects from multiple orthographic projection view images is proposed. The three-dimensional objects are captured under incoherent white illumination and their orthographic projection view images are obtained. The orthographic projection view images are multiplied by the corresponding phase terms and integrated to form a Fourier or Fresnel hologram. Using simple manipulation of the orthographic projection view images, it is also possible to shift the three-dimensional objects by an arbitrary amount along the three axes in the reconstruction space or invert their depths with respect to the given depth plane. The principle is verified experimentally.

© 2009 Optical Society of America

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References

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2008

2007

2006

2005

2004

2003

1967

1966

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

Abookasis, D.

Baasantseren, G.

Choi, H.

Itoh, M.

Jung, S.

Kang, J.-M.

Kim, J.

Kim, M.-S.

Kim, N.

Kim, Y.

Lee, B.

Lohmann, A. W.

Mishina, T.

Okano, F.

Okui, M.

Paris, D. P.

Park, G.

Park, J.-H.

Rosen, J.

Sando, Y.

Shaked, N. T.

Stern, A.

Vincent, A.

L. Zhang, D. Wang, and A. Vincent, "Adaptive reconstruction of intermediate views from stereoscopic images," IEEE Trans. Circuits Syst. Video Technol. 16, 102-113 (2006).
[CrossRef]

Wang, D.

L. Zhang, D. Wang, and A. Vincent, "Adaptive reconstruction of intermediate views from stereoscopic images," IEEE Trans. Circuits Syst. Video Technol. 16, 102-113 (2006).
[CrossRef]

Waters, J. P.

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

Yatagai, T.

Zhang, L.

L. Zhang, D. Wang, and A. Vincent, "Adaptive reconstruction of intermediate views from stereoscopic images," IEEE Trans. Circuits Syst. Video Technol. 16, 102-113 (2006).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

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

IEEE Trans. Circuits Syst. Video Technol.

L. Zhang, D. Wang, and A. Vincent, "Adaptive reconstruction of intermediate views from stereoscopic images," IEEE Trans. Circuits Syst. Video Technol. 16, 102-113 (2006).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Korea

Opt. Express

Opt. Lett.

Other

J. W. Goodman, Introduction to Foureir Optics, 2nd ed., (McGraw-Hill, New York, 1996), Chaps. 4-5, p. 66-105.

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Figures (12)

Fig. 1.
Fig. 1.

Projection geometry

Fig. 2.
Fig. 2.

Orthographic image acquisition using a lens array

Fig. 3.
Fig. 3.

Fourier hologram generation from the orthographic projection images

Fig. 4.
Fig. 4.

Fresnel hologram generation from orthographic projection images

Fig. 5.
Fig. 5.

Modification of orthographic images for manipulating 3D object (a)Lateral shift by (δx, δy), (b) depth shift by δz, and (c) depth inversion

Fig. 6.
Fig. 6.

Experimental setup to capture the elemental images

Fig. 7.
Fig. 7.

Captured elemental images

Fig. 8.
Fig. 8.

Generated orthographic images

Fig. 9.
Fig. 9.

Amplitude (upper figure) and phase (lower figure) of the generated Fourier hologram (a) without lateral and depth shift or inversion (b) with lateral shift by 10mm along x and y axis and depth shift of -20mm, (c) with depth inversion and depth shift of 80mm

Fig. 10.
Fig. 10.

Numerical reconstruction of the generated Fourier hologram (a) without lateral and depth shift or inversion (b) with lateral shift by 10mm along x and y axis and depth shift by -20mm, (c) with depth inversion and depth shift by 80mm

Fig. 11.
Fig. 11.

Amplitude (upper figure) and phase (lower figure) of the generated Fresnel hologram (a) without lateral and depth shift or inversion (b) with lateral shift by 10mm along x and y axis and depth shift by -20mm, (c) with depth inversion and depth shift by 80mm

Fig. 12.
Fig. 12.

Numerical reconstruction of the generated Fresnel hologram (a) without lateral and depth shift or inversion (b) with lateral shift by 10mm along x and y axis and depth shift by -20mm, (c) with depth inversion and depth shift by 80mm

Equations (34)

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x p = x cos φ z sin φ ,
y p = y cos θ z sin θ cos φ x sin φ sin θ .
x p = x o ( x x o ) f / z ,
y p = y o ( y y o ) f / z ,
x p = x + z tan φ = x + z s / l ,
y p = y + z tan θ = y + z t / l ,
H ( s , t ) = P s t ( x p , x p ) exp [ j 2 π b ( x p s + y p t ) ] d x p d y p ,
H ( u , v ) = O ( x , y , z ) exp [ j π λ f ( z f u 2 + z f v 2 2 x u 2 y v ) ] d x d y d z ,
P s t S S P ( x p , y p ) = O ( x , y , z ) δ ( x p x s z l , y p y t z l ) Δ x Δ y Δ z ,
H S S P ( s , t ) = O ( x , y , z ) δ ( x p x s z l , y p y t z l ) Δ x Δ y Δ z
× exp [ j 2 π b ( x p s + y p t ) ] d x p d y p
= O ( x , y , z ) exp [ j 2 πb ( x p + y s + z l s 2 + z l t 2 ) ] Δ x Δ y Δ z
H ( s , t ) = H S S P ( s , t ) d x d y d z
= O ( x , y , z ) exp [ j 2 πb ( x s + y s + z l s 2 + z l t 2 ) ] d x d y d z .
H ( u , v ) = O ( x , y , z ) exp [ j 2 π b M ( x u + y v + z l M u 2 + z l M v 2 ) ] d x d y d z ,
M = 2 f l , b = 2 λ l .
H s , t ( u , v ) = P s , t ( u c s D l , v c t D l ) exp { j 2 π b [ ( s l ) 2 + ( t l ) 2 ] } ,
H ( u . v ) = s , t H s , t ( u , v ) .
H ( u , v ) = 1 j λ ( D + z ) O ( x , y , z ) exp { j π λ ( D + z ) [ ( u x ) 2 + ( v y ) 2 ] } d x d y d z ,
H ( u , v ) = P s , t ( u c s D l , v c t D l ) exp { j 2 π b [ ( s l ) 2 + ( t l ) 2 ] } dsdt .
H SSP ( u , v ) = P s , t SSP ( u c s D l , v c t D l ) exp { j 2 π b [ ( s l ) 2 + ( t l ) 2 ] } dsdt
= O ( x , y , z ) δ ( u c s D l x s z l , v c t D l y t z l )
× Δ x Δ y Δ z exp { j 2 π b [ ( s l ) 2 + ( t l ) 2 ] } d s d t
= l 2 ( c D + z ) 2 O ( x , y , z ) exp { j 2 π b ( c D + z ) 2 [ ( u x ) 2 + ( v y ) 2 ] } Δ x Δ y Δ z
H ( u , v ) = H SSP ( u , v ) d x d y d z
= l 2 ( c D + z ) 2 O ( x , y , z ) exp [ j 2 π b ( c D + z ) 2 [ ( u x ) 2 + ( v y ) 2 ] ] d x d y d z .
H ( u , v ) = 1 c D + 2 z O ( x , y , z ) exp { j 2 π b c D ( c D + 2 z ) [ ( u x ) 2 + ( v y ) 2 ] } d x d y d z
b = 2 D λ , c = 2 .
x ' p = x p + δ x = ( x + δ x ) + z s / l ,
y ' p = y p + δ y = ( y + δ y ) + z t / l ,
x ' p = x p + δ z s / l = x + ( z + δ z ) s / l ,
y ' p = y p + δ z t / l = y + ( z + δ z ) t / l ,
x ' p = x z s / l ,
y ' p = y z t / l ,

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