Abstract

The role of acousto-optic (AO) modulators in programmable real-time image processing has recently been demonstrated. For fully investigating the image-processing capabilities of the AO modulator, general techniques to derive spatial transfer functions are needed for a variety of physical situations. We develop a technique to determine the spatial transfer functions numerically for various cases of beam incidence on an AO modulator. Normal incidence and incidence at twice the Bragg angle are investigated as examples for which double-sided and single-sided notch spatial filtering, respectively, are achieved. The observed spatial-filtering characteristics are reconciled with simple intuitive physical arguments.

© 1998 Optical Society of America

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References

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  1. H. K. Liu, J. Davis, R. Lilly, “Optical-data-processing properties of a liquid-crystal television spatial light modulator,” Opt. Lett. 10, 635–637 (1985).
    [CrossRef] [PubMed]
  2. J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
    [CrossRef]
  3. W. E. Ross, D. Psaltis, R. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
    [CrossRef]
  4. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).
  5. P. Das, C. DeCusatis, Acousto-Optic Signal Processing: Fundamentals & Applications (Artech House, New York, 1991).
  6. A. Korpel, Acousto-Optics, 2nd ed. (Artech House, New York, 1997).
  7. J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
    [CrossRef]
  8. P. P. Banerjee, D. Cao, T.-C. Poon, “Basic image-processing operations by use of acousto-optics,” Appl. Opt. 36, 3086–3089 (1997).
    [CrossRef] [PubMed]
  9. D. Cao, P. P. Banerjee, T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37, 3007–3014 (1998).
    [CrossRef]
  10. M. R. Chatterjee, T.-C. Poon, D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–92 (1990).
  11. M. D. McNeill, T.-C. Poon, “Gaussian-beam profile shaping by acousto-optic Bragg diffraction,” Appl. Opt. 33, 4508–4515 (1994).
    [CrossRef] [PubMed]
  12. R. J. Pieper, T.-C. Poon, “System characterization of apodized acousto-optic Bragg cells,” J. Opt. Soc. Am. A 7, 1751–1758 (1990).
    [CrossRef]
  13. P. P. Banerjee, C. W. Tarn, “A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction,” Acustica 74, 181–191 (1991).
  14. R. Alferness, “Analysis of propagation at the second-order Bragg angle of a thick holographic grating,” J. Opt. Soc. Am. 66, 353–362 (1976).
    [CrossRef]
  15. T.-C. Poon, A. Korpel, “High efficiency acousto-optic diffraction into the second Bragg order,” in IEEE Ultrasonics Symposium Proceedings (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 751–754.

1998 (1)

1997 (1)

1996 (1)

J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
[CrossRef]

1994 (1)

1991 (1)

P. P. Banerjee, C. W. Tarn, “A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction,” Acustica 74, 181–191 (1991).

1990 (2)

R. J. Pieper, T.-C. Poon, “System characterization of apodized acousto-optic Bragg cells,” J. Opt. Soc. Am. A 7, 1751–1758 (1990).
[CrossRef]

M. R. Chatterjee, T.-C. Poon, D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–92 (1990).

1985 (1)

1983 (1)

W. E. Ross, D. Psaltis, R. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

1976 (1)

1975 (1)

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Alferness, R.

Anderson, R.

W. E. Ross, D. Psaltis, R. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Banerjee, P. P.

D. Cao, P. P. Banerjee, T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37, 3007–3014 (1998).
[CrossRef]

P. P. Banerjee, D. Cao, T.-C. Poon, “Basic image-processing operations by use of acousto-optics,” Appl. Opt. 36, 3086–3089 (1997).
[CrossRef] [PubMed]

J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
[CrossRef]

P. P. Banerjee, C. W. Tarn, “A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction,” Acustica 74, 181–191 (1991).

Bleha, W.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Boswell, D.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Cao, D.

Chatterjee, M. R.

M. R. Chatterjee, T.-C. Poon, D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–92 (1990).

Das, P.

P. Das, C. DeCusatis, Acousto-Optic Signal Processing: Fundamentals & Applications (Artech House, New York, 1991).

Davis, J.

DeCusatis, C.

P. Das, C. DeCusatis, Acousto-Optic Signal Processing: Fundamentals & Applications (Artech House, New York, 1991).

Dunn, D. B.

J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
[CrossRef]

Fraas, L.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Grinberg, J.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Jacobson, A.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Korpel, A.

A. Korpel, Acousto-Optics, 2nd ed. (Artech House, New York, 1997).

T.-C. Poon, A. Korpel, “High efficiency acousto-optic diffraction into the second Bragg order,” in IEEE Ultrasonics Symposium Proceedings (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 751–754.

Lilly, R.

Liu, H. K.

McNeill, M. D.

Miller, L.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Myer, G.

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

Pieper, R. J.

Poon, T.-C.

D. Cao, P. P. Banerjee, T.-C. Poon, “Image edge enhancement with two cascaded acousto-optic cells with contrapropagating sound,” Appl. Opt. 37, 3007–3014 (1998).
[CrossRef]

P. P. Banerjee, D. Cao, T.-C. Poon, “Basic image-processing operations by use of acousto-optics,” Appl. Opt. 36, 3086–3089 (1997).
[CrossRef] [PubMed]

J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
[CrossRef]

M. D. McNeill, T.-C. Poon, “Gaussian-beam profile shaping by acousto-optic Bragg diffraction,” Appl. Opt. 33, 4508–4515 (1994).
[CrossRef] [PubMed]

M. R. Chatterjee, T.-C. Poon, D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–92 (1990).

R. J. Pieper, T.-C. Poon, “System characterization of apodized acousto-optic Bragg cells,” J. Opt. Soc. Am. A 7, 1751–1758 (1990).
[CrossRef]

T.-C. Poon, A. Korpel, “High efficiency acousto-optic diffraction into the second Bragg order,” in IEEE Ultrasonics Symposium Proceedings (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 751–754.

Psaltis, D.

W. E. Ross, D. Psaltis, R. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Ross, W. E.

W. E. Ross, D. Psaltis, R. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Sitter, D. N.

M. R. Chatterjee, T.-C. Poon, D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–92 (1990).

Tarn, C. W.

P. P. Banerjee, C. W. Tarn, “A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction,” Acustica 74, 181–191 (1991).

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

Xia, J.

J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
[CrossRef]

Acustica (2)

M. R. Chatterjee, T.-C. Poon, D. N. Sitter, “Transfer function formalism for strong acousto-optic Bragg diffraction of light beams with arbitrary profiles,” Acustica 71, 81–92 (1990).

P. P. Banerjee, C. W. Tarn, “A Fourier transform approach to acousto-optic interactions in the presence of propagational diffraction,” Acustica 74, 181–191 (1991).

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

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

Opt. Commun. (1)

J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
[CrossRef]

Opt. Eng. (2)

J. Grinberg, A. Jacobson, W. Bleha, L. Miller, L. Fraas, D. Boswell, G. Myer, “A new real-time non-coherent to coherent light image converter: the hybrid field effect liquid crystal light valve,” Opt. Eng. 14, 217–225 (1975).
[CrossRef]

W. E. Ross, D. Psaltis, R. Anderson, “Two-dimensional magneto-optic spatial light modulator for signal processing,” Opt. Eng. 22, 485–490 (1983).
[CrossRef]

Opt. Lett. (1)

Other (4)

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).

P. Das, C. DeCusatis, Acousto-Optic Signal Processing: Fundamentals & Applications (Artech House, New York, 1991).

A. Korpel, Acousto-Optics, 2nd ed. (Artech House, New York, 1997).

T.-C. Poon, A. Korpel, “High efficiency acousto-optic diffraction into the second Bragg order,” in IEEE Ultrasonics Symposium Proceedings (Institute of Electrical and Electronics Engineers, New York, 1983), pp. 751–754.

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Figures (5)

Fig. 1
Fig. 1

Configuration showing light at normal incidence during AO interaction, along with the diffracted orders.

Fig. 2
Fig. 2

Numerical calculation results for the transfer-function graphs for the case of normal incidence and for Q = 28, Λ = 72 μm, and λ0 = 632.8 nm. Dashed curve, α = 0.8π; solid curve, α = 0.6π. (a) Zeroth order, (b) positive-first diffracted order, and (c) negative-first diffracted order.

Fig. 3
Fig. 3

Comparison between the computed zeroth-order transfer function (dashed curve) and the guessed analytical solution (solid curve) in the case of normal incidence. The parameters are α = 0.8π, Q = 28, Λ = 72 μm, and λ0 = 632.8 nm.

Fig. 4
Fig. 4

Configuration showing light incidence at twice the Bragg angle during AO interaction, along with the diffracted orders.

Fig. 5
Fig. 5

Computed transfer functions for zeroth (solid curve), first (dotted curve), and second (dashed curve) orders for incidence at twice the Bragg angle. The parameters are α = 0.7π, Q = 14, and λ0 = 632.8 nm.

Equations (23)

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2 E t 2 - v 2 2 E = - 0 2 E t 2 ,
E x ,   z ;   t = m Re ψ m x ,   z × exp j ω m t - k mx x - k mz z a ˆ y .
ω m = ω + m Ω ,
ϕ B K 2 k = λ 0 2 Λ n 0 ,     ϕ m ϕ inc + mK / k ,
= 0 C   Re S e x ,   z exp   j Ω t - Kx ,
2 ψ m x 2 - 2 j k mx ψ m x + k mz ψ m z + k 2 C 2 A ψ m - 1   exp - j k m - 1 z - k mz z + A * ψ m + 1   exp - j k m + 1 z - k mz z + 2 ψ m z 2 = 0 .
2 ψ m z 2 k mz ψ m z ,
2 ψ m x 2 - 2 j k mx ψ m x + k mz ψ m z + k 2 C 2 × A ψ m - 1   exp - j k m - 1 z - k mz z + A * ψ m + 1   exp - j k m + 1 z - k mz z = 0 .
ψ ˆ m z = j   k x 2 + 2 k x k mx 2 k mz   ψ ˆ m - jD ψ ˆ m + 1 - jE ψ ˆ m - 1 ,
D = kCA * / 4 exp - jk cos ϕ m + 1 - cos ϕ m z ,
E = kCA / 4 exp - jk cos ϕ m - 1 - cos ϕ m z .
ψ ˆ m k x ,   z = F x ψ m x ,   z = -   ψ m x ,   z exp jk x x d x .
ψ ˆ 0 z = j k x 2 + 2 k x k 0 x 2 k 0 z   ψ ˆ 0 - jE ψ ˆ - 1 ,
ψ ˆ - 1 z = j k x 2 + 2 k x k - 1 x 2 k - 1 z   ψ ˆ - 1 - jD ψ ˆ 0 ,
H 0 k x ,   z = L = exp j k x 2 L 2 k cos k x k 0 x L k 2 + α 2 2 1 / 2 + jk x k 0 x L k sin k x k 0 x L k 2 + α 2 2 1 / 2 k x k 0 x L k 2 + α 2 2 1 / 2 ,
H 1 k x ,   z = L = exp j k x 2 L 2 k - j   α 2 sin k x k 0 x L k 2 + α 2 2 1 / 2 k x k 0 x L k 2 + α 2 2 1 / 2 ,
ψ ˆ 0 z = jk x 2 2 k   ψ ˆ 0 - j α 2 L exp jk δ z ψ ˆ 1 - j α 2 L × exp jk δ z ψ ˆ - 1 ,
ψ ˆ 1 z = j k x 2 + 4 k ϕ B k x 2 k   ψ ˆ 1 - j α 2 L × exp - jk δ z ψ ˆ 0 ,
ψ ˆ - 1 z = j k x 2 - 4 k ϕ B k x 2 k   ψ ˆ - 1 - j α 2 L × exp - jk δ z ψ ˆ 0 ,
| H 0 k x ,   z | = 1 - | H 1 k x - k ϕ B ,   z | 2 - | H - 1 k x + k ϕ B ,   z | 2 1 / 2 ,
ψ ˆ 0 z = j k x 2 - 4 k ϕ B k x 2 k   ψ ˆ 0 - j α 2 L exp - jk δ z ψ ˆ 1 ,
ψ ˆ 1 z = jk x 2 2 k   ψ ˆ 1 - j α 2 L exp jk δ z ψ ˆ 0 + ψ ˆ 2 ,
ψ ˆ 2 z = j k x 2 + 4 ϕ B kk x 2 k   ψ ˆ - 1 - j α 2 L exp - jk δ z ψ ˆ 1 ,

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