Abstract

We develop the general scanning relationships of an acousto-optic system by using both a purely geometric-optics and a physical-optics approach; each approach provides useful insights into the scanning relationships. The diffraction approach reveals that there are four basic scanning configurations: a long or short chirp scanner, either aperture or repetition-rate limited. The throughput rate for a scanner is always maximized if we use the short-chirp-scanning, repetition-rate-limited mode of operation. The maximum rate may be achieved with other configurations, but at the expense of a decrease in some of the other performance parameters. Examples are given of how these design relationships are used.

© 1992 Optical Society of America

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References

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  1. R. Lipnik, A. Reich, G. A. Schoen, “Nonmechanical scanning of light using acoustic waves,” Proc. IEEE 52, 853–854 (1964).
  2. J. S. Gerig, H. Montague, “A simple optical filter for chirp radar,” Proc. IEEE 52, 1753 (1964).
  3. A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).
  4. A. Korpel, R. Adler, P. Desmares, W. Watson, “A television display using acoustic deflection and modulation of coherent light,” Appl. Opt. 5, 1667–1675 (1966).
  5. E. I. Gordon, “A review of acoustooptical deflection and modulation devices,” Appl. Opt. 5, 1629–1639 (1966).
  6. M. B. Schultz, M. G. Holland, L. Davies, “Optical pulse compression using Bragg scattering by ultrasonic waves,” Appl. Phys. Lett. 11, 237–240 (1967).
  7. J. H. Collins, E. G. H. Lean, H. J. Shaw, “Pulse compression by Bragg diffraction of light with microwave sound,” Appl. Phys. Lett. 11, 240–242 (1967).
  8. I. Gorog, J. D. Knox, P. V. Goedertier, “A television-rate laser scanner,” RCA Rev. 33, 623–694 (1972).
  9. L. D. Dickson, “Optical considerations for an acousto-optic deflector,” Appl. Opt. 11, 2196–2202 (1972).
  10. J. H. Eveleth, “High resolution laser beam recorder with self-focusing acousto-optic scanner,” U.S. patent3,851,951 (3December1974).
  11. M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Dekker, New York, 1983).
  12. A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 2, p. 49.
  13. Ref. 12, pp. 35–37.
  14. J. Randolph, J. Morrison, “Rayleigh equivalent resolution of acousto-optic deflection cells,” Appl. Opt. 10, 1453–145450 (1971).

1972 (2)

I. Gorog, J. D. Knox, P. V. Goedertier, “A television-rate laser scanner,” RCA Rev. 33, 623–694 (1972).

L. D. Dickson, “Optical considerations for an acousto-optic deflector,” Appl. Opt. 11, 2196–2202 (1972).

1971 (1)

1967 (2)

M. B. Schultz, M. G. Holland, L. Davies, “Optical pulse compression using Bragg scattering by ultrasonic waves,” Appl. Phys. Lett. 11, 237–240 (1967).

J. H. Collins, E. G. H. Lean, H. J. Shaw, “Pulse compression by Bragg diffraction of light with microwave sound,” Appl. Phys. Lett. 11, 240–242 (1967).

1966 (2)

1965 (1)

A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).

1964 (2)

R. Lipnik, A. Reich, G. A. Schoen, “Nonmechanical scanning of light using acoustic waves,” Proc. IEEE 52, 853–854 (1964).

J. S. Gerig, H. Montague, “A simple optical filter for chirp radar,” Proc. IEEE 52, 1753 (1964).

Adler, R.

A. Korpel, R. Adler, P. Desmares, W. Watson, “A television display using acoustic deflection and modulation of coherent light,” Appl. Opt. 5, 1667–1675 (1966).

A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).

Collins, J. H.

J. H. Collins, E. G. H. Lean, H. J. Shaw, “Pulse compression by Bragg diffraction of light with microwave sound,” Appl. Phys. Lett. 11, 240–242 (1967).

Davies, L.

M. B. Schultz, M. G. Holland, L. Davies, “Optical pulse compression using Bragg scattering by ultrasonic waves,” Appl. Phys. Lett. 11, 237–240 (1967).

Desmares, P.

A. Korpel, R. Adler, P. Desmares, W. Watson, “A television display using acoustic deflection and modulation of coherent light,” Appl. Opt. 5, 1667–1675 (1966).

A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).

Dickson, L. D.

Eveleth, J. H.

J. H. Eveleth, “High resolution laser beam recorder with self-focusing acousto-optic scanner,” U.S. patent3,851,951 (3December1974).

Gerig, J. S.

J. S. Gerig, H. Montague, “A simple optical filter for chirp radar,” Proc. IEEE 52, 1753 (1964).

Goedertier, P. V.

I. Gorog, J. D. Knox, P. V. Goedertier, “A television-rate laser scanner,” RCA Rev. 33, 623–694 (1972).

Gordon, E. I.

Gorog, I.

I. Gorog, J. D. Knox, P. V. Goedertier, “A television-rate laser scanner,” RCA Rev. 33, 623–694 (1972).

Gottlieb, M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Dekker, New York, 1983).

Holland, M. G.

M. B. Schultz, M. G. Holland, L. Davies, “Optical pulse compression using Bragg scattering by ultrasonic waves,” Appl. Phys. Lett. 11, 237–240 (1967).

Ireland, C. L. M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Dekker, New York, 1983).

Knox, J. D.

I. Gorog, J. D. Knox, P. V. Goedertier, “A television-rate laser scanner,” RCA Rev. 33, 623–694 (1972).

Korpel, A.

A. Korpel, R. Adler, P. Desmares, W. Watson, “A television display using acoustic deflection and modulation of coherent light,” Appl. Opt. 5, 1667–1675 (1966).

A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).

Lean, E. G. H.

J. H. Collins, E. G. H. Lean, H. J. Shaw, “Pulse compression by Bragg diffraction of light with microwave sound,” Appl. Phys. Lett. 11, 240–242 (1967).

Ley, J. M.

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Dekker, New York, 1983).

Lipnik, R.

R. Lipnik, A. Reich, G. A. Schoen, “Nonmechanical scanning of light using acoustic waves,” Proc. IEEE 52, 853–854 (1964).

Montague, H.

J. S. Gerig, H. Montague, “A simple optical filter for chirp radar,” Proc. IEEE 52, 1753 (1964).

Morrison, J.

Randolph, J.

Reich, A.

R. Lipnik, A. Reich, G. A. Schoen, “Nonmechanical scanning of light using acoustic waves,” Proc. IEEE 52, 853–854 (1964).

Schoen, G. A.

R. Lipnik, A. Reich, G. A. Schoen, “Nonmechanical scanning of light using acoustic waves,” Proc. IEEE 52, 853–854 (1964).

Schultz, M. B.

M. B. Schultz, M. G. Holland, L. Davies, “Optical pulse compression using Bragg scattering by ultrasonic waves,” Appl. Phys. Lett. 11, 237–240 (1967).

Shaw, H. J.

J. H. Collins, E. G. H. Lean, H. J. Shaw, “Pulse compression by Bragg diffraction of light with microwave sound,” Appl. Phys. Lett. 11, 240–242 (1967).

Smith, T. M.

A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).

VanderLugt, A.

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 2, p. 49.

Watson, W.

Appl. Opt. (4)

Appl. Phys. Lett. (2)

M. B. Schultz, M. G. Holland, L. Davies, “Optical pulse compression using Bragg scattering by ultrasonic waves,” Appl. Phys. Lett. 11, 237–240 (1967).

J. H. Collins, E. G. H. Lean, H. J. Shaw, “Pulse compression by Bragg diffraction of light with microwave sound,” Appl. Phys. Lett. 11, 240–242 (1967).

IEEE J. Quantum Electron. (1)

A. Korpel, R. Adler, P. Desmares, T. M. Smith, “An ultrasonic light deflection system,” IEEE J. Quantum Electron. QE-1, 60–61 (1965).

Proc. IEEE (2)

R. Lipnik, A. Reich, G. A. Schoen, “Nonmechanical scanning of light using acoustic waves,” Proc. IEEE 52, 853–854 (1964).

J. S. Gerig, H. Montague, “A simple optical filter for chirp radar,” Proc. IEEE 52, 1753 (1964).

RCA Rev. (1)

I. Gorog, J. D. Knox, P. V. Goedertier, “A television-rate laser scanner,” RCA Rev. 33, 623–694 (1972).

Other (4)

J. H. Eveleth, “High resolution laser beam recorder with self-focusing acousto-optic scanner,” U.S. patent3,851,951 (3December1974).

M. Gottlieb, C. L. M. Ireland, J. M. Ley, Electro-Optic and Acousto-Optic Scanning and Deflection (Dekker, New York, 1983).

A. VanderLugt, Optical Signal Processing (Wiley, New York, 1992), Chap. 2, p. 49.

Ref. 12, pp. 35–37.

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Figures (8)

Fig. 1
Fig. 1

Relationships among wavelength, spatial frequency, and diffraction angle.

Fig. 2
Fig. 2

Acousto-optic scanner.

Fig. 3
Fig. 3

Linear scanning with chirp waveform.

Fig. 4
Fig. 4

Chirp train and its associated frequency–time relationship.

Fig. 5
Fig. 5

Relationship of scanning action for upchirp signals.

Fig. 6
Fig. 6

High duty cycle scanner.

Fig. 7
Fig. 7

Normalized plots: (a) number of samples per scan, (b) throughput rate.

Fig. 8
Fig. 8

Spot sizes for various illumination profiles.

Tables (2)

Tables Icon

Table 1 Acousto-Optic Scanner Parameters

Tables Icon

Table 2 Examples of Various Scanning Configurations

Equations (72)

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α = 1 / Λ = f / v .
θ = λ / Λ = λ α = λ f / v ,
F + ( ξ , t ) = - f + ( x , t ) exp ( j 2 π λ F ξ x ) d x ,
F + ( ξ , t ) = - L / 2 L / 2 exp [ j 2 π f k ( t - T 2 - x v ) ] exp ( j 2 π λ F ξ x ) d x = exp [ j 2 π f k ( t - T / 2 ) ] sinc [ ( ξ λ F - f k v ) L ] ,
ξ k = ( λ F / v ) f k
ξ = d 0 = λ F / L .
c ( t ) = cos ( 2 π f 1 t + π a t 2 ) ;             0 t T c ,
f i ( t ) = 1 2 π t ( 2 π f 1 t + π a t 2 ) = f 1 + a t ;             0 t T c .
a = W / T c for upchirp signals = - W / T c for downchirp signals .
f b = f e + a T = f e + W T / T c .
θ e = α e λ = λ f e / v .
θ b = α b λ = λ f b v = λ ( f e + W T / T c ) v .
Δ θ = θ b - θ e = λ W T / v T c ,
D = L / Δ θ = v 2 T c / λ W .
v 2 / λ D = W / T c = a .
d 0 = λ / Δ θ = v T c / T W .
ξ ( t ) = - L / 2 + D θ b ( t ) = - L / 2 + D λ ( f e + W t / T c ) v ,
v s = t ξ ( t ) = D λ W v T c .
v s = v 2 T c λ W λ W v T c = v .
L s = v s ( T c - T ) = ( T c / T - 1 ) L ,
M = L s d 0 = v ( T c - T ) v T c / T W = ( 1 - T T c ) T W ,
f ( t ) = c ( t ) * n = - δ ( t - n T r ) = cos ( 2 π f 1 t + π a t 2 ) * n = - δ ( t - n T r ) .
f - ( x , t ) = rect ( x / L ) exp { - j [ 2 π f 1 ( t - T 2 - x v ) + π α ( t - T 2 - x v ) 2 ] } ,             T t T c ,
h ( x ) = exp ( j π λ F x 2 ) ,
r - ( x , t ) = rect ( x / L ) exp { - j [ 2 π f 1 ( t - T 2 - x v ) + π a ( t - T 2 - x v ) 2 ] } exp ( j π λ F x 2 ) ,             T t T c .
F ( ξ , t ) = - r - ( x , t ) exp [ - j π λ D f ( ξ - x ) 2 ] d x .
F ( ξ , t ) = - rect ( x / L ) exp { - j [ 2 π f 1 ( t - T 2 - x v ) + π a ( t - T 2 - x v ) 2 ] } exp ( j π λ F x 2 ) × exp [ - j π λ D f ( ξ - x ) 2 ] d x ,             T t T c .
F ( ξ , t ) = exp [ - j 2 π f 1 ( t - T / 2 ) ] × - rect ( x / L ) exp ( j 2 π f 1 x / v ) × exp { [ - j π v 2 λ D ( t - T 2 - x v ) 2 ] } × exp ( j π λ F x 2 ) exp [ - j π λ D f ( ξ - x ) 2 ] d x = exp ( j ϕ ) - L / 2 L / 2 exp { j π x 2 λ [ 1 F - 1 D - 1 D f ] } × exp { j 2 π x λ [ v ( t - T / 2 ) D + ξ D f + λ f 1 v ] } d x ,             T t ( T c - T ) ,
1 F - 1 D - 1 D f = 0
D f = D F D - F .
F ( ξ , t ) = - L / 2 L / 2 exp { j 2 π x λ [ v ( t - T / 2 ) D + ξ D f + λ f 1 v ] } d x = L sinc [ v ( t - T / 2 ) L λ D + ξ ( D - F ) L λ F D + f 1 L v ] ,             T t T c .
ξ = - λ f 1 D F v ( D - F ) - v ( t - T / 2 ) F D - F ,             T t T c .
ξ b = - λ f 1 D F v ( D - F ) - v ( T / 2 ) F D - F ,
ξ e = - λ f 1 D F v ( D - F ) - v ( T c - T / 2 ) F D - F ,
L s = ξ e - ξ b = | v ( T c - T ) F D - F | .
v s = ξ t = - v F D - F .
c ( t ) = cos ( 2 π f 2 t - π a t 2 ) ,
F = D 1 - v / v s .
d 0 = λ L / D f = λ D F ( D - F ) L .
M = L s d 0 = | v ( T c - T ) L λ D | .
M = ( 1 - T T c ) T W ,
U = min ( T s , T r ) T r = T c - T T r .
R s = v s d 0 = T T c W .
R t = U R s = ( 1 - T T c ) T T r W ,
K eq = K 1 + K 2 - d 12 K 1 K 2 .
F ( ξ , t ) = - L / 2 ( L - L c ) / 2 exp { j 2 π x λ [ v ( t - T / 2 ) D + ξ D f + λ f 1 v ] } d x = L c sinc [ v ( t - T / 2 ) L c λ D + ξ ( D - F ) L c λ F D + f 1 L c v ] ,             T c t ( T - T c ) ,
ξ = - λ f 1 D F v ( D - F ) - v ( t - T / 2 ) F D - F ,             T c t ( T - T c ) .
ξ b = - λ f 1 D F v ( D - F ) - v ( T c / 2 ) F D - F ,
ξ e = - λ f 1 D F v ( D - F ) - v ( T 2 - T c ) F D - F ,
L s = ξ e - ξ b = | v ( T - T c ) F D - F | .
d 0 = λ L c / D f = λ D F ( D - F ) L c ,
M = L s d 0 = | v ( T - T c ) L c λ D | .
M = ( 1 - T c T ) T W .
U = T - T c T r ,
R s = v s d 0 = W ,
R t = U v s d 0 = ( T - T c T r ) W ,
F ( ξ , t ) = - L / 2 - L / 2 + v t exp { j π x 2 λ [ 1 F - 1 D - 1 D f ] } × exp { j 2 π x λ [ v ( t - T / 2 ) D + ξ D f + λ f 1 v ] } d x ,             0 t T c ,
F ( ξ , t = - L / 2 - L / 2 + v t exp { j 2 π x λ [ v ( t - T / 2 ) D + ξ D f + λ f 1 v ] } d x = v t sinc { [ v ( t - T / 2 ) D + ξ D f + λ f 1 v ] v t / λ } ,             0 t T c ,
ξ = - λ f 1 D F v ( D - F ) - v ( t - T / 2 ) F D - F ,             0 t T c ,
ξ b = - λ f 1 D F v ( D - F ) - v ( - T / 2 ) F D - F ,
ξ e = - λ f 1 D F v ( D - F ) - v ( T / 2 ) F D - F .
Δ ξ = d 0 = λ D f v t ,             0 t T c .
L s = ξ e - ξ b = | v T r F D - F | .
d 0 = λ D F ( D - F ) L ,
M = ( T r / T c ) T W ,
U = min ( T s , T r ) T r = T r T r = 1 ,
R t = U R s = v s d 0 = T T c W .
L s = ξ e - ξ b = | v T r F D - F | .
d 0 = λ D F ( D - F ) L c ,
M = T r W ,
U = min ( T s , T r ) T r = T r T r = 1 ,
R t = U R s = v s d 0 = W .

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