Abstract

A new method for obtaining digital Fourier holograms, under spatially incoherent white-light illumination and in a single camera shot, is presented. Multiple projections of the 3-D scene are created in the image plane of a microlens array, and a digital camera acquires the entire projections in a single shot. Then, each projection is computer processed to yield a single point in a Fourier hologram. The new method, designated as integral holography, is proved for the general case and demonstrated experimentally for a simple case.

© 2007 Optical Society of America

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References

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  1. B. W. Schilling, T. -C. Poon, G. Indebetouw, B. Storrie, K. Shinoda, Y. Suzuki, and M. H. Wu, "Three-dimensional holographic fluorescence microscopy," Opt. Lett. 22, 1506 (1997).
    [CrossRef]
  2. J. Rosen and G. Brooker, "Digital spatially incoherent Fresnel holography," Opt. Lett. (to be published).
    [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
  5. B. Lee, S. Jung, and J. H. Park, "Viewing-angle-enhanced integral imaging by lens switching," Opt. Lett. 27, 818-820 (2002).
    [CrossRef]
  6. A. Stern and B. Javidi, "Three dimensional sensing, visualization, and processing using integral imaging," Procs. IEEE 94, 591 (2006).
    [CrossRef]
  7. T. Mishina, M. Okui, and F. Okano, "Calculation of holograms from elemental images captured by integral photography," Appl. Opt. 45, 4026 (2006).
    [CrossRef] [PubMed]
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2006 (2)

A. Stern and B. Javidi, "Three dimensional sensing, visualization, and processing using integral imaging," Procs. IEEE 94, 591 (2006).
[CrossRef]

T. Mishina, M. Okui, and F. Okano, "Calculation of holograms from elemental images captured by integral photography," Appl. Opt. 45, 4026 (2006).
[CrossRef] [PubMed]

2003 (2)

2002 (1)

1997 (1)

Abookasis, D.

Brooker, G.

J. Rosen and G. Brooker, "Digital spatially incoherent Fresnel holography," Opt. Lett. (to be published).
[PubMed]

Indebetouw, G.

Itoh, M.

Javidi, B.

A. Stern and B. Javidi, "Three dimensional sensing, visualization, and processing using integral imaging," Procs. IEEE 94, 591 (2006).
[CrossRef]

Jung, S.

Lee, B.

Mishina, T.

Okano, F.

Okui, M.

Park, J. H.

Poon, T. -C.

Rosen, J.

Sando, Y.

Schilling, B. W.

Shinoda, K.

Stern, A.

A. Stern and B. Javidi, "Three dimensional sensing, visualization, and processing using integral imaging," Procs. IEEE 94, 591 (2006).
[CrossRef]

Storrie, B.

Suzuki, Y.

Wu, M. H.

Yatagai, T.

Supplementary Material (1)

» Media 1: AVI (866 KB)     

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Figures (5)

Fig. 1.
Fig. 1.

The optical system used in the IH recording stage.

Fig. 2.
Fig. 2.

Schematic of the IH processing stage.

Fig. 3.
Fig. 3.

Cross section of part of the optical system shown in Fig. 1.

Fig. 4.
Fig. 4.

Several projections taken from different parts of the MLA image plane captured by the camera (contrast-inverted picture).

Fig. 5.
Fig. 5.

(Contrast-inverted pictures) (a) Magnitude and (b) phase of the Fourier hologram obtained after performing the processing stage on the captured projections; (c) Reconstruction of the hologram at the best focus distance of the letter ‘I’; (d) Reconstruction of the hologram at the best focus distance of the letter ‘H’. [Media 1] The continuous propagation from the plane shown in (c) to the plane shown in (d) is presented in the linked movie.

Equations (12)

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H m , n = p m , n C ( X p c , Y p c ) E m , n ( X p c , Y p c ) dX p c dY p c ,
E m , n ( X p c , Y p c ) = exp [ j ( 2 πb D ) ( mX p c + nY p c ) ] ,
x p = M ( mD + x S ) 1 z s L ; y p = M ( nD + y s ) 1 z s L ,
x p M ( mD + x s + z s mD L + z s x s L ) ; y p M ( nD + y s + z s nD L + z s y s L ) .
x p c M ( x s + z s mD L + z s x s L ) ; y p c M ( y s + z s nD L + z s y s L ) .
H m , n SSP x s y s z s = [ h x s y s z s Δ x s Δ y s Δ z s δ X p c x p c Y p c y p c ] E m , n X p c Y p c dX p c dY p c
= h x s y s z s E m , n x p c y p c Δ x s Δ y s Δ z s ,
H m , n SSP x S y S z S = h x S y S z S exp { j ( 2 πbM D ) [ m ( x S + z S mD L + z S x S L ) + n ( y s + z S nD L + z S y S L ) ] } Δ x S Δ y S Δ z S .
H m , n = H m , n SSP X S Y S Z S dX S dY S dZ S = h X S Y S Z S exp { j ( 2 πbM D ) × [ mX S + nY S + ( Z S D L ) ( m 2 + n 2 ) + ( Z S L ) ( mX S + nY S ) ] } dX S dY S dZ S .
H u v h X s Y s Z s exp { j 2 πbM D 2 [ uX s + vY s + ( Z s L ) ( u 2 + v 2 ) ] } dX s dY s dZ s .
Δ x s = max { 1.22 λL D , p c z 1 ( Mz 2 ) } ; Δ z s = Δ x s L ( KD ) ,
b = D ( MK Δ x s ) .

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