Abstract

We propose an approach to generate as many parallax images (PIs) having different viewpoints of a 3-D object as required by use of multiple diffraction gratings (MDG) and confirm its feasibility through theoretical analysis and optical experiments. Here, the PIs generated from the MDG are derived as a convolution integral between the scaled object intensity and each δ-function array of m number of diffraction gratings based on wave-optics, which means the total number of PIs and viewpoints to be generated with the MDG may increase with the mth power of that generated with the single diffraction grating. In addition, optical experiments show that the number of PIs for the case of m=2 has been increased up to the second power of that for the case of m=1, which may validate the theoretical analysis and confirm its feasibility in the practical application.

© 2013 Optical Society of America

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References

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  1. A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
    [CrossRef]
  2. R. Shogenji, Y. Kitamura, K. Yamada, S. Miyatake, and J. Tanida, Opt. Express 12, 1643 (2004).
    [CrossRef]
  3. R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
    [CrossRef]
  4. J.-H. Park, K. Hong, and B. Lee, Appl. Opt. 48, H77 (2009).
    [CrossRef]
  5. J.-I. Ser, J.-Y. Jang, S. Cha, and S.-H. Shin, Appl. Opt. 49, 2429 (2010).
    [CrossRef]
  6. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 114.

2010

2009

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

J.-H. Park, K. Hong, and B. Lee, Appl. Opt. 48, H77 (2009).
[CrossRef]

2006

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

2004

Cha, S.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 114.

Hong, K.

Jang, J.-Y.

Javidi, B.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

Kitamura, Y.

Lee, B.

Martinez-Corral, M.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Martinez-Cuenca, R.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Miyatake, S.

Park, J.-H.

Saavedra, G.

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Ser, J.-I.

Shin, S.-H.

Shogenji, R.

Stern, A.

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

Tanida, J.

Yamada, K.

Appl. Opt.

Opt. Express

Proc. IEEE

A. Stern and B. Javidi, Proc. IEEE 94, 591 (2006).
[CrossRef]

R. Martinez-Cuenca, G. Saavedra, M. Martinez-Corral, and B. Javidi, Proc. IEEE 97, 1067 (2009).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 114.

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Figures (2)

Fig. 1.
Fig. 1.

PIA generation method based on the double diffraction gratings.

Fig. 2.
Fig. 2.

PIAs generated with the SDGs and DDG. (a) PIA with “Grating 1”. (b) PIA with “Grating 2”. (c) PIA from combined gratings of “Gratings 1 and 2”, and “A” a part of the enlarged PIA of (c).

Equations (12)

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g(xe)=S(zO,xe)f(zO,xe)dzO,
h(xe)=R[ze]Q[1f]R[d1]U2(ξ)×R[d2]Q[1zO(d1+d2)]U1(η),
R[α]U(x)=(1iλα)U(x)exp[ik(xx)22α]dxQ[β]U(x)=exp[ikβx22]U(x),
h(xe)=Q[(zO+ze)d1zOzeze2(d1zO)]ν[zOλze(zOd1)]FQ[1d1zO]×U2(ξ)R[d2]Q[1zO(d1+d2)]U1(η).
Q[1d1zO]U2(ξ)R[d2]=U2(ξ)R[d2(d1zO)d1zO+d2]×ν[1+d2d1zO]Q[1d1zO+ze].
h(xe)=Q[1ze2(d1zO)[(zO+ze)d1zOze+zO2d2zO(d1+d2)]]×Fν[λze(zOd1)zO]U2(ξ)ν[λze[zO(d1+d2)]zO]U1(η).
h(xe)=Q[K]{ν[zOλze(zOd1)]FU2(ξ)}{ν[zOλze[zO(d1+d2)]]FU1(η)},
h(xe)|η=zOλze[zO(d1+d2)]U1(η)ej2πzOxeηλze[zO(d1+d2)]dη,
h(xe)|ξ=zOλze(zOd1)U2(ξ)ej2πzOxeξλze(zOd1)dξ,
|h(xe)|2=sin2(2πNczOxeλze(zOd1))sin2(2πczOxeλze(zOd1))sin2(2πNdzOxeλze(zO(d1+d2)))sin2(2πdzOxeλze(zO(d1+d2))).
S(zO,xe)|DDG{n=0Mδ[xenλze(zOd1)2czO]}{n=0Mδ[xenλze[zO(d1+d2)]2dzO]}.
S(zO,xe)|mn=0Mδ(xenX1)n=0Mδ(xenX2)n=0Mδ(xenXm),

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