Abstract

We show experimental results for image processing using an acousto-optic light modulator (AOLM) where the image can be edge enhanced with respect to the input object. We can select which edges are enhanced and the degree to which they are enhanced by changing the amplitude of the acoustic wave of the AOLM. We relate this technique to the fractional Hilbert transform and the fractional derivative image-processing operations and discuss its application to phase-only input images.

© 2002 Optical Society of America

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References

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  1. A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional Hilbert transform,” Opt. Lett. 21, 281–283 (1996).
    [CrossRef] [PubMed]
  2. A. W. Lohmann, E. Tepichin, J. G. Ramirez, “Optical implementation of the fractional Hilbert transform for two-dimensional objects,” Appl. Opt. 36, 6620–6626 (1997).
    [CrossRef]
  3. J. A. Davis, D. E. McNamara, D. M. Cottrell, “Analysis of the fractional Hilbert transform,” Appl. Opt. 37, 6911–6913 (1998).
    [CrossRef]
  4. J. A. Davis, D. E. McNamara, D. M. Cottrell, “Image processing with the radial Hilbert transform: theory and experiments,” Opt. Lett. 25, 99–101 (2000).
    [CrossRef]
  5. E. Tajahuerce, T. Szoplik, J. Lancis, V. Climent, M. Fernandez-Alonso, “Phase object fractional differentiation using Fourier plane filters,” Pure Appl. Opt. 6, 481–490 (1977).
    [CrossRef]
  6. H. Kasprzak, “Differentiation of a noninteger order and its optical implementation,” Appl. Opt. 21, 3287–3291 (1982).
    [CrossRef] [PubMed]
  7. T. Szoplik, V. Climent, E. Tajahuerce, J. Lancis, M. Fernandez-Alonso, “Phase-change visualization in two-dimensional phase objects with a semiderivative real filter,” Appl. Opt. 37, 5472–5478 (1998).
    [CrossRef]
  8. J. Lancis, T. Szoplik, E. Tajahuerce, V. Climent, M. Fernandez-Alonso, “Fractional derivative Fourier plane filter for phase-change visualization,” Appl. Opt. 36, 7461–7464 (1997).
    [CrossRef]
  9. J. A. Davis, D. A. Smith, D. E. McNamara, D. M. Cottrell, J. Campos, “Fractional derivatives—analysis and experimental implementation,” Appl. Opt. 40, 5943–5948 (2001).
    [CrossRef]
  10. J. Xia, D. B. Dunn, T.-C. Poon, P. P. Banerjee, “Image edge enhancement by Bragg diffraction,” Opt. Commun. 128, 1–7 (1996).
    [CrossRef]
  11. 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]
  12. 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]
  13. T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing with Matlab (Elsevier Science, New York, 2001), Chap. 7.
  14. R. B. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1986), Chap. 12.
  15. W. R. Klein, B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
    [CrossRef]

2001 (1)

2000 (1)

1998 (3)

1997 (3)

1996 (2)

A. W. Lohmann, D. Mendlovic, Z. Zalevsky, “Fractional Hilbert transform,” Opt. Lett. 21, 281–283 (1996).
[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]

1982 (1)

1977 (1)

E. Tajahuerce, T. Szoplik, J. Lancis, V. Climent, M. Fernandez-Alonso, “Phase object fractional differentiation using Fourier plane filters,” Pure Appl. Opt. 6, 481–490 (1977).
[CrossRef]

1967 (1)

W. R. Klein, B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[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]

T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing with Matlab (Elsevier Science, New York, 2001), Chap. 7.

Bracewell, R. B.

R. B. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1986), Chap. 12.

Campos, J.

Cao, D.

Climent, V.

Cook, B. D.

W. R. Klein, B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

Cottrell, D. M.

Davis, J. A.

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]

Fernandez-Alonso, M.

Kasprzak, H.

Klein, W. R.

W. R. Klein, B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

Lancis, J.

Lohmann, A. W.

McNamara, D. E.

Mendlovic, D.

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]

T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing with Matlab (Elsevier Science, New York, 2001), Chap. 7.

Ramirez, J. G.

Smith, D. A.

Szoplik, T.

Tajahuerce, E.

Tepichin, E.

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]

Zalevsky, Z.

Appl. Opt. (8)

IEEE Trans. Sonics Ultrason. (1)

W. R. Klein, B. D. Cook, “Unified approach to ultrasonic light diffraction,” IEEE Trans. Sonics Ultrason. SU-14, 123–134 (1967).
[CrossRef]

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. Lett. (2)

Pure Appl. Opt. (1)

E. Tajahuerce, T. Szoplik, J. Lancis, V. Climent, M. Fernandez-Alonso, “Phase object fractional differentiation using Fourier plane filters,” Pure Appl. Opt. 6, 481–490 (1977).
[CrossRef]

Other (2)

T.-C. Poon, P. P. Banerjee, Contemporary Optical Image Processing with Matlab (Elsevier Science, New York, 2001), Chap. 7.

R. B. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1986), Chap. 12.

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Figures (6)

Fig. 1
Fig. 1

One-dimensional view of (a) input rectangle function and (b) its first derivative.

Fig. 2
Fig. 2

Values for cos(α/2) and sinc(α/2) versus α.

Fig. 3
Fig. 3

Experimental setup.

Fig. 4
Fig. 4

AOLM diffracted intensity versus voltage at two wavelengths.

Fig. 5
Fig. 5

Output with a one-dimensional slit used as the input object. The left pattern shows the zero order in each case, and the right pattern shows to the first order. The AOLM voltage controls the phase delay and corresponds to (a) α = 0 (we can see the image of the input), (b) α = 0.7π (the right edge is emphasized), (c) α = π (both edges are emphasized), (d) α = 1.4π (the left edge is emphasized).

Fig. 6
Fig. 6

Output with a letter used as the input object. The left image shows the zero order in each case, and the right image shows to the first order. The AOLM voltage controls the phase delay and corresponds to (a) α = 0 (we can see the image of the input), (b) α = 0.7π (the right edge is emphasized), (c) α = π (both edges are emphasized), (d) α = 1.4π (the left edge is emphasized).

Equations (6)

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H0p; L=expjp2L/2k0-pQΛ0/4π ×cospQΛ0/4π2+α/221/2 +jpQΛ0/4πsincpQΛ0/4π2+α/221/2,
H1p; L=expjp2L/2k0+pQΛ0/4π-jα/2×sincpQΛ0/4π2+α/221/2.
|pmaxQΛ0/4π|  α/2.
H0p=cosα/2+jpQΛ0/4πsincα/2=A+jBp.
FGpH0p=FAGp±ipBGp=Agx±Bgx/x.
pmax=2π sin θ/λ=2π/w  2πα/QΛ0.

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