Abstract

We describe the design and development of an acousto-optical wideband correlator that we integrated into a digital signal-processing system testbed. We report its measured performance and compare it with various theoretical performance measures, one of which compares the optical system with an equivalent efficient digital correlator. The measured performance of the optical system was 20 to 70 times that of a VAX 6410 computer using a fast-Fourier-transform correlation algorithm and a vector processor, even though the electronic interface system limited the performance of the optical system to less than 0.5% of its potential. We also compare the system with commercially available digital signal-processing boards.

© 1994 Optical Society of America

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References

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  1. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992).
  2. N. J. Berg, J. N. Lee, eds., Acousto-Optic Signal Processing, (Dekker, New York, 1983).
  3. D. P. Casasent, ed., Transition of Optical Processors into Systems 1993, Proc. Soc. Photo-Opt. Instrum. Eng.1958, (1993).
  4. A. D. Whalen, Detection of Signals in Noise (Academic, Orlando, Fla., 1971), Chap. 6, pp. 167–179.
  5. J. N. Lee, ed., Design Issues inOptical Processing (Cambridge U. Press, to be published).
  6. H. H. Szu, B. A. Telfer, A. Lohmann, “Causal analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
    [Crossref]
  7. R. E. Crochiere, L. R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 2, pp. 13–58.
  8. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J.1974), Chap. 13, pp. 209–213.
  9. O. D. Grace, S. P. Pitt, “Sampling and interpolation of bandlimited signals by quadrature methods,” J. Acoust. Soc. Am. 48, 1311–1318 (1969).
    [Crossref]
  10. H. D. Helms, “Fast Fourier transform method of computing difference equations and simulating filters,” IEEE Trans. Audio Electroacoust. AU-15, 85–90 (1967).
    [Crossref]
  11. R. D. Griffin, “System design, implementation, and evaluation of the optical broadband correlator,” NRL Memorandum Rep. 7612 (U.S. Naval Research Laboratory, Washington, D.C., to be published).
  12. E. J. Kelly, R. P. Wishner, “matched-filter theory for high-velocity, accelerating targets,” IEEE Trans. Mil. Electron. ME-9, 56–69 (1965).
    [Crossref]
  13. G. Elston, “Intermodulation products in acousto-optic signal processing systems,” in Proceedings of IEEE Ultrasonics Symposium, B. R. McAvoy, ed. (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 391–397.
  14. D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
    [Crossref]
  15. B. Smith, “Instantaneous companding of quantized signals,” Bell Syst. Tech. J. 36, 653–709 (1957).
  16. M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), Chap. 10, pp. 392–395.
  17. W. A. Struzinski, E. D. Lowe, “The effect of improper normalization on the performance of an automated energy detector,” J. Acoust. Soc. Am. 78, 936–941 (1985).
    [Crossref]
  18. D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
    [Crossref]
  19. R. B. K. Dewar, M. Smosna, Microprocessors: A Programmers View (McGraw-Hill, New York, 1990), Chap. 8, pp. 229–264.

1992 (1)

H. H. Szu, B. A. Telfer, A. Lohmann, “Causal analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
[Crossref]

1985 (1)

W. A. Struzinski, E. D. Lowe, “The effect of improper normalization on the performance of an automated energy detector,” J. Acoust. Soc. Am. 78, 936–941 (1985).
[Crossref]

1977 (2)

D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
[Crossref]

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
[Crossref]

1969 (1)

O. D. Grace, S. P. Pitt, “Sampling and interpolation of bandlimited signals by quadrature methods,” J. Acoust. Soc. Am. 48, 1311–1318 (1969).
[Crossref]

1967 (1)

H. D. Helms, “Fast Fourier transform method of computing difference equations and simulating filters,” IEEE Trans. Audio Electroacoust. AU-15, 85–90 (1967).
[Crossref]

1965 (1)

E. J. Kelly, R. P. Wishner, “matched-filter theory for high-velocity, accelerating targets,” IEEE Trans. Mil. Electron. ME-9, 56–69 (1965).
[Crossref]

1957 (1)

B. Smith, “Instantaneous companding of quantized signals,” Bell Syst. Tech. J. 36, 653–709 (1957).

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J.1974), Chap. 13, pp. 209–213.

Crochiere, R. E.

R. E. Crochiere, L. R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 2, pp. 13–58.

Curry, T. J.

D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
[Crossref]

Dewar, R. B. K.

R. B. K. Dewar, M. Smosna, Microprocessors: A Programmers View (McGraw-Hill, New York, 1990), Chap. 8, pp. 229–264.

Elston, G.

G. Elston, “Intermodulation products in acousto-optic signal processing systems,” in Proceedings of IEEE Ultrasonics Symposium, B. R. McAvoy, ed. (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 391–397.

Francis, J. T.

D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
[Crossref]

Grace, O. D.

O. D. Grace, S. P. Pitt, “Sampling and interpolation of bandlimited signals by quadrature methods,” J. Acoust. Soc. Am. 48, 1311–1318 (1969).
[Crossref]

Griffin, R. D.

R. D. Griffin, “System design, implementation, and evaluation of the optical broadband correlator,” NRL Memorandum Rep. 7612 (U.S. Naval Research Laboratory, Washington, D.C., to be published).

Gupta, D. V.

D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
[Crossref]

Hecht, D. L.

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
[Crossref]

Helms, H. D.

H. D. Helms, “Fast Fourier transform method of computing difference equations and simulating filters,” IEEE Trans. Audio Electroacoust. AU-15, 85–90 (1967).
[Crossref]

Kelly, E. J.

E. J. Kelly, R. P. Wishner, “matched-filter theory for high-velocity, accelerating targets,” IEEE Trans. Mil. Electron. ME-9, 56–69 (1965).
[Crossref]

Lohmann, A.

H. H. Szu, B. A. Telfer, A. Lohmann, “Causal analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
[Crossref]

Lowe, E. D.

W. A. Struzinski, E. D. Lowe, “The effect of improper normalization on the performance of an automated energy detector,” J. Acoust. Soc. Am. 78, 936–941 (1985).
[Crossref]

Pitt, S. P.

O. D. Grace, S. P. Pitt, “Sampling and interpolation of bandlimited signals by quadrature methods,” J. Acoust. Soc. Am. 48, 1311–1318 (1969).
[Crossref]

Rabiner, L. R.

R. E. Crochiere, L. R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 2, pp. 13–58.

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), Chap. 10, pp. 392–395.

Smith, B.

B. Smith, “Instantaneous companding of quantized signals,” Bell Syst. Tech. J. 36, 653–709 (1957).

Smosna, M.

R. B. K. Dewar, M. Smosna, Microprocessors: A Programmers View (McGraw-Hill, New York, 1990), Chap. 8, pp. 229–264.

Struzinski, W. A.

W. A. Struzinski, E. D. Lowe, “The effect of improper normalization on the performance of an automated energy detector,” J. Acoust. Soc. Am. 78, 936–941 (1985).
[Crossref]

Szu, H. H.

H. H. Szu, B. A. Telfer, A. Lohmann, “Causal analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
[Crossref]

Telfer, B. A.

H. H. Szu, B. A. Telfer, A. Lohmann, “Causal analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
[Crossref]

VanderLugt, A.

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

Vetelino, J. F.

D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
[Crossref]

Whalen, A. D.

A. D. Whalen, Detection of Signals in Noise (Academic, Orlando, Fla., 1971), Chap. 6, pp. 167–179.

Wishner, R. P.

E. J. Kelly, R. P. Wishner, “matched-filter theory for high-velocity, accelerating targets,” IEEE Trans. Mil. Electron. ME-9, 56–69 (1965).
[Crossref]

Bell Syst. Tech. J. (1)

B. Smith, “Instantaneous companding of quantized signals,” Bell Syst. Tech. J. 36, 653–709 (1957).

IEEE Trans. Aerosp. Electron. Syst. (1)

D. V. Gupta, J. F. Vetelino, T. J. Curry, J. T. Francis, “An adaptive threshold system for nonstationary noise backgrounds,” IEEE Trans. Aerosp. Electron. Syst. AES-13, 11–16 (1977).
[Crossref]

IEEE Trans. Audio Electroacoust. (1)

H. D. Helms, “Fast Fourier transform method of computing difference equations and simulating filters,” IEEE Trans. Audio Electroacoust. AU-15, 85–90 (1967).
[Crossref]

IEEE Trans. Mil. Electron. (1)

E. J. Kelly, R. P. Wishner, “matched-filter theory for high-velocity, accelerating targets,” IEEE Trans. Mil. Electron. ME-9, 56–69 (1965).
[Crossref]

IEEE Trans. Sonics Ultrason. (1)

D. L. Hecht, “Multifrequency acoustooptic diffraction,” IEEE Trans. Sonics Ultrason. SU-24, 7–18 (1977).
[Crossref]

J. Acoust. Soc. Am. (2)

O. D. Grace, S. P. Pitt, “Sampling and interpolation of bandlimited signals by quadrature methods,” J. Acoust. Soc. Am. 48, 1311–1318 (1969).
[Crossref]

W. A. Struzinski, E. D. Lowe, “The effect of improper normalization on the performance of an automated energy detector,” J. Acoust. Soc. Am. 78, 936–941 (1985).
[Crossref]

Opt. Eng. (1)

H. H. Szu, B. A. Telfer, A. Lohmann, “Causal analytical wavelet transform,” Opt. Eng. 31, 1825–1829 (1992).
[Crossref]

Other (11)

R. E. Crochiere, L. R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1983), Chap. 2, pp. 13–58.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, N.J.1974), Chap. 13, pp. 209–213.

R. D. Griffin, “System design, implementation, and evaluation of the optical broadband correlator,” NRL Memorandum Rep. 7612 (U.S. Naval Research Laboratory, Washington, D.C., to be published).

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

N. J. Berg, J. N. Lee, eds., Acousto-Optic Signal Processing, (Dekker, New York, 1983).

D. P. Casasent, ed., Transition of Optical Processors into Systems 1993, Proc. Soc. Photo-Opt. Instrum. Eng.1958, (1993).

A. D. Whalen, Detection of Signals in Noise (Academic, Orlando, Fla., 1971), Chap. 6, pp. 167–179.

J. N. Lee, ed., Design Issues inOptical Processing (Cambridge U. Press, to be published).

G. Elston, “Intermodulation products in acousto-optic signal processing systems,” in Proceedings of IEEE Ultrasonics Symposium, B. R. McAvoy, ed. (Institute of Electrical and Electronics Engineers, New York, 1985), pp. 391–397.

R. B. K. Dewar, M. Smosna, Microprocessors: A Programmers View (McGraw-Hill, New York, 1990), Chap. 8, pp. 229–264.

M. I. Skolnik, Introduction to Radar Systems (McGraw-Hill, New York, 1980), Chap. 10, pp. 392–395.

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Figures (10)

Fig. 1
Fig. 1

Basic optical layout for correlation processing.

Fig. 2
Fig. 2

Time compression of a waveform: curve (a), band of the original waveform sampled at a rate f S; curve (b), original waveform shifted by an amount −δf; curve (c), time compression effected by a change of the sample rate to f CLK.

Fig. 3
Fig. 3

Reference and return waveform positions relative to the optical aperture at the beginning of a correlation sweep. Also shown is the effect of overhead on the positions of a second set of waveforms that will produce the next correlation sweep.

Fig. 4
Fig. 4

Comparison of the maximum average number of correlation function samples produced per second, Eq. (9), with the computation rate required of an equivalent digital processor, Eq. (15), as a function of τREF. For this figure, f CLK = 80 MHz, N REF = 1024, and N opt = 8192.

Fig. 5
Fig. 5

Input and output data rates from Eqs. (16) and (17) in samples per second as a function of reference duration for the case f CLK = 80 MHz and τOVR = 0.

Fig. 6
Fig. 6

High-level block diagram of the signal-processing system.

Fig. 7
Fig. 7

Top and side views of the optical layout.

Fig. 8
Fig. 8

Block diagram of the optical correlator system: D/A's, digital-to-analog converters; DET, detector.

Fig. 9
Fig. 9

Comparison of scalar and vector digital processors with the optical correlator as a function of the number of correlation sweeps. Times for the optical correlator include the time required to generate and digitize the correlation function and to upload it to the host computer.

Fig. 10
Fig. 10

Dynamic-range performance of the optical correlator system.

Tables (5)

Tables Icon

Tabel 1 Optimum Values of Fast-Fourier-Transform Size for Correlation or Convolution a

Tables Icon

Table 2 Computation Rates from Eqs. (7), (9), and (15), with f CLK = 80 MHz

Tables Icon

Table 3 Acousto-Optical Cell Parameters

Tables Icon

Table 4 Performance of the Continuously Correlating Diagnostic Subroutine a

Tables Icon

Table 5 Comparison of Optical, Vector, and Scalar Correlators a

Equations (22)

Equations on this page are rendered with MathJax. Learn more.

ɛ = f CLK f S = ( M L ) f CLK f S .
ɛ = W cell W ,
f cell = ɛ f 0 = ɛ ( f 0 δ f ) ,
T COR = ( T RCV T REF ) .
T RCV max = 2 T OA T REF .
T RPT = T RCV + T OVR .
f raw = 2 f CLK N REF .
f avg = 2 f CLK ½ T COR T RPT = f CLK T RCV T REF T RCV + T OVR ,
f avg max = 2 f CLK T OA T REF 2 T OA T REF = 2 f CLK 1 τ REF 2 τ REF ,
τ REF = T REF T OA
η f avg f avg max .
f flops = 4 ɛ f S ( 1 τ REF ) ( 2 τ REF + τ OVR ) N opt ( log 2 N opt + ½ ) ( N opt N REF ) ,
τ OVR = T OVR T OA ,
f flops 2 ɛ f S log 2 N opt = 2 f CLK log 2 N opt ,
f flops max = 4 f CLK ( 1 τ REF ) ( 2 τ REF ) N opt ( log 2 N opt + ½ ) ( N opt N REF ) ,
f IN = f CLK ( T RCV + T REF ) T RCV + T OVR = 2 f CLK 2 τ REF + τ OVR ,
f OUT = f CLK T COR T RPT = 2 f CLK ( 1 τ REF ) 2 τ REF + τ OVR ,
f IN max + f OUT max = 2 f CLK .
f IN f CLK ( 2 τ REF ) N Dplr ( 2 τ REF + τ OVR ) .
f avg max ( Msps )
f flops max ( Gflops )
f avg max

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