Abstract

Various effects associated with using a random phase mask in holographic data storage are analyzed. It is shown that the nonlinear nature of recording a phase hologram coupled with the highly nonuniform profile of the object beam is the major source of interpixel cross talk. It is also shown that, although the nonlinear effects are reduced by an increase in the reference-to-object beam ratio, the scattering noise is increased. Thus an optimal beam ratio must be used to maximize the signal-to-noise ratio. It is demonstrated as well that the interpixel interference noise can be suppressed effectively by use of a multilevel pseudorandom phase mask, which also significantly reduces the nonlinear noise. These findings are supported by experimental results that show the signal-to-noise ratio and efficiency are improved significantly by use of a six-level pseudorandom phase mask.

© 1997 Optical Society of America

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References

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  1. C. B. Burkhardt, “Use of a random phase mask for the recording of Fourier transform holograms of data masks,” Appl. Opt. 9, 695–700 (1969).
    [CrossRef]
  2. Y. Takeda, Y. Oshida, Y. Miyamura, “Random phase shifters for Fourier transformed holograms,” Appl. Opt. 11, 818–822 (1972).
    [CrossRef] [PubMed]
  3. Y. Nakayama, M. Kato, “Diffuser with a pseudorandom phase sequence,” J. Opt. Soc. Am. 69, 1367–1372 (1979).
    [CrossRef]
  4. C. Gu, J. Hong, I. McMichael, R. Saxena, “Cross-talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  5. J. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, New York, 1995), p. 116.
  6. D. Meyerhofer, “Phase holograms in dichromated gelatin,” RCA Rev. 33, 111–129 (1972).
  7. J. Hong, I. McMichael, J. Ma, “Influence of phase masks on cross talk in holographic memory,” Opt. Lett. 21, 1694–1696 (1996).
    [CrossRef] [PubMed]
  8. M. P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, M. Quintanilla, “Effects of multilevel phase masks on interpixel cross talk in digital holographic storage,” Appl. Opt. 36, 3107–3115 (1997).
    [CrossRef] [PubMed]
  9. A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), p. 48.
  10. G. Burr, “Volume holographic storage using the 90 geometry,” Ph.D. dissertation (Caltech, Pasadena, Calif., 1996), p. 244.

1997 (1)

1996 (1)

1992 (1)

1979 (1)

1972 (2)

1969 (1)

Bernal, M. P.

Burkhardt, C. B.

Burr, G.

G. Burr, “Volume holographic storage using the 90 geometry,” Ph.D. dissertation (Caltech, Pasadena, Calif., 1996), p. 244.

Burr, G. W.

Coufal, H.

Goodman, J.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, New York, 1995), p. 116.

Grygier, R. K.

Gu, C.

Hoffnagle, J. A.

Hong, J.

Jefferson, C. M.

Kato, M.

Ma, J.

McMichael, I.

Meyerhofer, D.

D. Meyerhofer, “Phase holograms in dichromated gelatin,” RCA Rev. 33, 111–129 (1972).

Miyamura, Y.

Nakayama, Y.

Oesterschulze, E.

Oshida, Y.

Quintanilla, M.

Saxena, R.

Shelby, R. M.

Sincerbox, G. T.

Takeda, Y.

Yariv, A.

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), p. 48.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

RCA Rev. (1)

D. Meyerhofer, “Phase holograms in dichromated gelatin,” RCA Rev. 33, 111–129 (1972).

Other (3)

A. Yariv, Optical Electronics, 4th ed. (Saunders, Philadelphia, Pa., 1991), p. 48.

G. Burr, “Volume holographic storage using the 90 geometry,” Ph.D. dissertation (Caltech, Pasadena, Calif., 1996), p. 244.

J. Goodman, Introduction to Fourier Optics, 3rd ed. (McGraw-Hill, New York, 1995), p. 116.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of a 4f holographic digital memory system. Obj, object; Ref, reference.

Fig. 2
Fig. 2

Parameters A1 and A2 plotted versus the focal length (Δz = 1 mm, f = 60 mm, N = 1024, P = 50 µm) for no phase mask (— 0A1 and ----- 0A2), for a random phase mask (-·-·-· 2A1 and ····· 2A2), and for a six-level pseudorandom phase mask (---- 6A1 and -··-··- 6A2).

Fig. 3
Fig. 3

Parameters A1 and A2 plotted versus the focal length (Δz = 1 mm) for no phase mask (— 0A1 and ----- 0A2), for a random phase mask (-·-·-· 2A1 and ····· 2A2), and for a six-level pseudorandom phase mask (---- 6A1 and -··-··- 6A2).

Fig. 4
Fig. 4

Parameters A1 and A2 plotted versus the hologram size H [normalized to (λf)/P, with dz = 1 mm] for no phase mask (— 0A1 and ----- 0A2), for a random phase mask (-·-·-· 2A1 and ····· 2A2), and for a six-level pseudorandom phase mask (---- 6A1 and -··-··- 6A2).

Fig. 5
Fig. 5

Parameters A1 and A2 plotted versus the pixel for no phase mask, P = 50 µm, f = 60 mm, and dz = 1 mm. The image degradation near the edges becomes more significant as the focal length becomes shorter and the amount of defocusing is increased.

Fig. 6
Fig. 6

Parameter A0 plotted versus the hologram size H [normalized to (λf)/P, with a focal length of f = 60 mm and dz = 1 mm] for no phase mask (— 0A0), for a random phase mask (-·-·-· 2A0), and for a six-level pseudorandom phase mask (---- 6A0).

Fig. 7
Fig. 7

SNR calculated from Eq. (22) plotted as a function of the beam-intensity ratio r2 for different values of A2 from 0 to 0.95 (from left to right, respectively), with dz = 1 mm, f = 60 mm, and P = 50 µm: (—) 0.0, (-----) 0.50, (-·-·-·) 0.60, (·····) 0.70, (----) 0.80, (-··-··-) 0.85, (—) 0.90, and (-----) 0.95.

Fig. 8
Fig. 8

Power spectra of (a) a six-level phase mask, pseudorandom, (b) a six-level phase mask, random, (c) and no phase mask but shifted a distance away from the focal plane such that the image area is kept the same as in the pseudorandom direction.

Fig. 9
Fig. 9

Peak intensity (normalized to the intensity at the focal point) versus the distance away from the focal point (a) in front of the focal and (b) after the focal point.

Fig. 10
Fig. 10

SNR plotted versus the beam-intensity ratio for a six-level phase mask (▲) and for 1.5-mm defocusing alone (■).

Fig. 11
Fig. 11

Playback image of a hologram with a SNR of 15.2, with the phase mask.

Fig. 12
Fig. 12

Histogram of the bright and dark pixel distributions for the image of Fig. 11. The bright pixels with an intensity greater than 255 are saturated by the autogain function of the CCD camera.

Equations (26)

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dx0, y0=m=1m=Nn=1n=Namn rectx0/P-mrecty0/P-n,
Uxr, yr, z=Kdx0dy0dx0, y0expjπλff-zf×x02+y02exp-j2πλfx0xr+y0yr,  =K exp-jπλxr2+yr2f-zdx0dy0dx0, y0×expjπλff-zfx0-xrff-z2-y0-yrff-z2,  =K exp-jπλxr2+yr2f-z×f, zdx0, y0,
Ufx, fy=sincfxPsincfyPm=1n=1m=Nn=Namn×exp-j2πmfx+nfyP,
I=R+UR+U*=R2+U2+R*U+RU*,
Prxr, yr=R expjmR2+U2+RU*+R*U,
Prxr, yr=expjmR2+U2×R1+mjRU*-m22RRU*U*×1+mjR*U-m22R*R*UU,
Prxr, yr=expjmR2+U21-m22R2U2×jmR2U=gxr, yrU,
Sx=dxrgxrexp-jπλf1-zf×x+xrff-z2dx0dx0×expjπλf1-zfx0-xrff-z2=-1f, zgxrf, zdx0=exp-jπλf1-zfx2expjπλf×1-zfx2d-x*Gx,
Gx=dxgxrexp-j2πλfxxr.
Pq=Rq expjp=1MmRp2+Up2+RpUp*+Rp*Up,
Pq=expjp=1MmRp2+Up21-m2Rq2Uq2jmRq2Uq,
S=P1+P2 expjϕ*H,
Iϕ=SS*=P1*H2+P2*H2+2 cosϕP1*H×P2*H,
ΔI=I0-Iϕ=21-cosϕP1*HP2*H.
A0=-H/2H/2u2xrdxr,  A1l=-1/21/2dx expjπλff-zfx2×rectxPexp-jπλff-zfx2*dxr exp-j2πλfxxrrectxrHu2xr,  A2l=-1/21/2dxrectxPexp-jπλff-zfx2*dxr exp-j2πλfxxrrectxrHu2xr2,
I1l=-l/2l/2dx-1f, z1+jγ0/ru2xrf, z×rectx0/P2,
C1=IbId1=I1()I1()-I1P=1+γ02/r2γ02/r21-A2,
I2l=-l/2l/2dx-1f, z1-12γ02u2xrf, z×rectx0/P2,
C2=IbId2=I2I2-I2P=1-γ02+γ04/4γ02A1-1+γ021-A2/4.
δϕ=δγ0+δm1I=δγ0+δm1R*Uxr+R2+U2xr.
σ=Ib2δγ0+2δγ1/V2+δγ122+Id21/2,
SNR=Ib-Idσ=1-1/Cδγ0+2δγ1/V2+δγ122+1/C21/2.
U2fx=sinc2fxPsinc2fxNP.
U2=2N+1P2 sinc2fxP,
U2=9N+1+2M=1NN-M+1-12M×cos4πMPfxL2 sinc23fxP.
Hmax=12Δz+z02Δz.

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