Abstract

We propose modified hologram cells (or macropixels) for the computer-generated double-phase holograms (DPHs), based on pixelated phase-only spatial light modulators (SLMs). Such modified DPHs exhibit a substantially improved signal-to-noise ratio, in comparison with the conventional ones. The modified macropixels are formed by arrays of either 1 × 2 or 2 × 2 SLM pixels.

© 2002 Optical Society of America

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References

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  1. K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlaton,” in Optical Pattern Recognition VIII, D. P. Casasent, T. H. Chao, eds., Proc. SPIE3073, 170–177 (1997).
    [CrossRef]
  2. C. K. Hsueh, A. A. Sawchuck, “Computer-generated double phase holograms,” Appl. Opt. 17, 3874–3883 (1978).
    [CrossRef] [PubMed]
  3. J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed, Proc. SPIE1558, 487–498, 1991.
    [CrossRef]
  4. D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
    [CrossRef]
  5. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [CrossRef]
  6. B. R. Brown, A. W. Lohmann, “Complex spatial filtering with binary masks,” Appl. Opt. 5, 967–968 (1966).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. D. C. Chu, J. W. Goodmann, “Spectrum shaping with parity sequences,” Appl. Opt. 11, 1716–1724 (1972).
    [CrossRef] [PubMed]
  9. J. N. Mait, K. H. Brenner, “Dual-phase holograms: improved design,” Appl. Opt. 26, 4883–4892 (1987).
    [CrossRef] [PubMed]
  10. J. Bucklew, N. C. Gallagher, “Comprehensive error models and a comparative study of some detour-phase holograms,” Appl. Opt. 18, 2861–2869 (1979).
    [CrossRef] [PubMed]

1999 (1)

1997 (1)

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
[CrossRef]

1987 (1)

1979 (1)

1978 (1)

1972 (2)

1966 (1)

Bauchert, K. A.

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlaton,” in Optical Pattern Recognition VIII, D. P. Casasent, T. H. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Brenner, K. H.

Brown, B. R.

Bucklew, J.

Campos, J.

Chu, D. C.

Cottrell, D. M.

Culver, B. C.

Davis, J. A.

Florence, J. M.

J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed, Proc. SPIE1558, 487–498, 1991.
[CrossRef]

Gallagher, N. C.

Goodmann, J. W.

Haskell, R. E.

Hsueh, C. K.

Juday, R. D.

J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed, Proc. SPIE1558, 487–498, 1991.
[CrossRef]

Levi, U.

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
[CrossRef]

Lohmann, A. W.

Mait, J. N.

Maron, E.

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
[CrossRef]

McKnight, D. J.

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlaton,” in Optical Pattern Recognition VIII, D. P. Casasent, T. H. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Mendlovic, D.

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
[CrossRef]

Moreno, I.

Sawchuck, A. A.

Serati, S. A.

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlaton,” in Optical Pattern Recognition VIII, D. P. Casasent, T. H. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Shabtay, G.

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
[CrossRef]

Sharp, G. D.

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlaton,” in Optical Pattern Recognition VIII, D. P. Casasent, T. H. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

Yzuel, M. J.

Zalevsky, Z.

D. Mendlovic, G. Shabtay, U. Levi, Z. Zalevsky, E. Maron, “Encoding technique for design of zero-order (on-axis) Fraunhofer computer-generated holograms,” Appl. Opt. 32, 8427–8434 (1997).
[CrossRef]

Appl. Opt. (8)

Other (2)

J. M. Florence, R. D. Juday, “Full-complex spatial filtering with a phase mostly DMD,” in Wave Propagation and Scattering in Varied Media II, V. K. Varadan, ed, Proc. SPIE1558, 487–498, 1991.
[CrossRef]

K. A. Bauchert, S. A. Serati, G. D. Sharp, D. J. McKnight, “Complex phase/amplitude spatial light modulator advances and use in a multispectral optical correlaton,” in Optical Pattern Recognition VIII, D. P. Casasent, T. H. Chao, eds., Proc. SPIE3073, 170–177 (1997).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Pixelated structure of a phase-only SLM considered for implementation of a DPH.

Fig. 2
Fig. 2

Pixelated structure of the complex modulation to be holographically encoded with the phase-only SLM shown in Fig. 1.

Fig. 3
Fig. 3

(a) One pixel of the spatially quantized complex modulation and (b) its corresponding double-phase holographic macropixel.

Fig. 4
Fig. 4

(a) Modulus and (b) phase of the real-only filter c(x, y) for the synthesis of an annular field.

Fig. 5
Fig. 5

Normalized power spectrum of the filter c(x, y) considered in Fig. 4.

Fig. 6
Fig. 6

(a) Phase modulation of the conventional DPH (based on the macro-pixel structure in Fig. 3) for encoding the filter c(x, y) considered in Fig. 4, and (b) corresponding DPH power spectrum.

Fig. 7
Fig. 7

First modified macropixel for the double-phase holographic code.

Fig. 8
Fig. 8

(a) Phase modulation of the first modified DPH for encoding the filter c(x, y) considered in Fig. 4, and (b) corresponding DPH power spectrum.

Fig. 9
Fig. 9

Distribution of signal and noise in the reconstruction plane of the second modified DPH.

Fig. 10
Fig. 10

Binary object whose complex Fourier spectrum t(x, y) is intended to be encoded with the discussed DPHs.

Fig. 11
Fig. 11

Power spectrum of the pixelated complex function c(x, y), designed to synthesize the object considered in Fig. 10.

Fig. 12
Fig. 12

Power spectrum generated by the (a) conventional DPH, (b) first modified DPH, and (c) second modified DPH, encoding the complex function c(x, y) considered in Fig. 11.

Fig. 13
Fig. 13

(a) Phase modulation of the third modified DPH for encoding the filter c(x, y) considered in Fig. 11, and (b) corresponding DPH power spectrum.

Fig. 14
Fig. 14

Transmittance of the conventional macropixel (a) is equal to the sum of the complex pixel transmittance (b) and the macro-pixel noise transmittance (c).

Fig. 15
Fig. 15

Transmittance of the first modified macropixel (a), with four different phases, is equal to the sum of the complex pixel transmittance (b) and the macro-pixel noise transmittance (c).

Equations (34)

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cx, y=n,m cnmwcx-2nα, y-mβ,
wcx, y=rectx/2αrecty/β,
hnmx, y=expiϕnm1whx-znα+αz, y-mβ+expiϕnm2whx-znα-αz, y-mβ,
whx, y=rectx/arecty/b,
hx, y=n,m hnmx, y.
ϕnm1=ϕnm-Δnm,
ϕ2nm=ϕnm+Δnm,
Δnm=cos-1|cnm|.
Cu, v=ECu, vn,m cnm exp-i2π2nαu+mβv,
ECu, v=2αβ sinc2αusincβv.
Hu, v=2Whu, vn,mcosΔnm-παuexpiϕnm×exp-i2π2nαu+mβv,
Hu, v=HSu, v+HNu, v,
HSu, v=ESu, vn,mcosΔnmexpiϕnm×exp-i2π2nαu+mβv,
HNu, v=ENu, vn,msinΔnmexpiϕnm×exp-i2π2nαu+mβv.
ESu, v=2ab sincausincbvcosπαu,
ENu, v=2ab sincausincbvsinπαu.
η2=abαβ2|cx, y|2dxdy|hx, y|2dxdy=abNMαβn,m|Cnm|2,
SNR=D|HSu, v|2dudvD|HSu, v-RHu, v|2dudv,
R=D|HSu, v|2dudvD|Hu, v|2dudv.
tx, y=Ax2+y21/4J02πx2+y2sx, y,
cx, y=n,m cnmwcx-2nα, y-2mβ,
wcx, y=rectxzαrectyzβ.
hnmx, y=expiϕnm1whx-2nα+α/2, y-2mβ-β/2+whx-2nα-α/2, y-2mβ+β/2+expiϕnm2whx-2nα-α/2, y-2mβ-β/2+whx-2nα+α/2, y-2mβ+β/2,
Cu, v=ECu, vn,m cnmexp-i2π2nαu+2mβv,
ECu, v=4αβ sinc2αusinc2βv.
HSu, v=ESu, vn,mcosΔnmexpiϕnm×exp-i2π2nαu+2mβv,
HNu, v=ENu, vn,msinΔnmexpiϕnm×exp-i2π2nαu+2mβv,
ESu, v=4ab sincausincbvcosπαucosπβv,
ENu,v=-4iab sincausincbv×sinπαusinπβv.
Δnm=-1n+m cos-1|cnm|.
Δnm=Bnm cos-1|cnm|,
cnm=12expiϕnm1+expiϕnm2.
Δnm=±cos-1|cnm|.
cnm=14expiϕnm1+expiϕnm2+expiϕnm3+expiϕnm4.

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