Abstract

In conventional real-time electrooptical signal processors, the variation of the output intensity with time is directly detected with a photodetector. As a result of this, any information carried in the phase of the light is lost. However, if the light is detected coherently, i.e., it is heterodyned with another coherent local oscillator light source on the detector surface, the phase associated with the amplitude of the light may be preserved. This paper presents the results of a theoretical and experimental study of the properties of real-time electrooptical spectrum analyzers with coherent detection. Basic equations of operation are presented and discussed, and confirmed by experiment, and it is concluded that the construction of such devices is feasible.

© 1967 Optical Society of America

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References

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  1. L. B. Lambert, Inst. Radio Engrs. Intern. Conv. Record 10, 69 (1962).
  2. M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
    [CrossRef]
  3. J. S. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
    [CrossRef]
  4. E. Abbe, Arch. Mikroskop. Anat. 9, 413 (1873).
    [CrossRef]
  5. M. Born, E. Wolf, Principles of Optics, (Pergamon Press, New York, 1964), 2nd ed. pp. 419–424.
  6. J. E. Rhodes, Am. J. Phys. 21, 337 (1952).
    [CrossRef]
  7. L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).
  8. M. Arm, L. Lambert, B. Silverberg, Inst. Radio Engrs. Intern. Conv. Record 10, 79 (1962).
  9. A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).
  10. E. Leith, J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).
    [CrossRef]
  11. M. King, “Heterodyne-Type Electro-Optical Signal Processors,” Tech. Rept. T-2/321 (Electronics Research Laboratories, Columbia University, New York, 1966), unclassified.

1964 (3)

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[CrossRef]

J. S. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

1963 (1)

1962 (2)

M. Arm, L. Lambert, B. Silverberg, Inst. Radio Engrs. Intern. Conv. Record 10, 79 (1962).

L. B. Lambert, Inst. Radio Engrs. Intern. Conv. Record 10, 69 (1962).

1960 (1)

L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

1952 (1)

J. E. Rhodes, Am. J. Phys. 21, 337 (1952).
[CrossRef]

1873 (1)

E. Abbe, Arch. Mikroskop. Anat. 9, 413 (1873).
[CrossRef]

Abbe, E.

E. Abbe, Arch. Mikroskop. Anat. 9, 413 (1873).
[CrossRef]

Arm, M.

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[CrossRef]

M. Arm, L. Lambert, B. Silverberg, Inst. Radio Engrs. Intern. Conv. Record 10, 79 (1962).

Born, M.

M. Born, E. Wolf, Principles of Optics, (Pergamon Press, New York, 1964), 2nd ed. pp. 419–424.

Cutrona, L. J.

L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Gerig, J. S.

J. S. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

King, M.

M. King, “Heterodyne-Type Electro-Optical Signal Processors,” Tech. Rept. T-2/321 (Electronics Research Laboratories, Columbia University, New York, 1966), unclassified.

Lambert, L.

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[CrossRef]

M. Arm, L. Lambert, B. Silverberg, Inst. Radio Engrs. Intern. Conv. Record 10, 79 (1962).

Lambert, L. B.

L. B. Lambert, Inst. Radio Engrs. Intern. Conv. Record 10, 69 (1962).

Leith, E.

E. Leith, J. Upatnieks, J. Opt. Soc. Am. 53, 1377 (1963).
[CrossRef]

L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Montague, H.

J. S. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

Palermo, C.

L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Porcello, L.

L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

Rhodes, J. E.

J. E. Rhodes, Am. J. Phys. 21, 337 (1952).
[CrossRef]

Silverberg, B.

M. Arm, L. Lambert, B. Silverberg, Inst. Radio Engrs. Intern. Conv. Record 10, 79 (1962).

Upatnieks, J.

Vander Lugt, A.

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

Weissman, I.

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, (Pergamon Press, New York, 1964), 2nd ed. pp. 419–424.

Am. J. Phys. (1)

J. E. Rhodes, Am. J. Phys. 21, 337 (1952).
[CrossRef]

Arch. Mikroskop. Anat. (1)

E. Abbe, Arch. Mikroskop. Anat. 9, 413 (1873).
[CrossRef]

IEEE Trans. (1)

A. Vander Lugt, IEEE Trans. IT-10, 139 (1964).

Inst. Radio Engrs. Intern. Conv. Record (2)

L. B. Lambert, Inst. Radio Engrs. Intern. Conv. Record 10, 69 (1962).

M. Arm, L. Lambert, B. Silverberg, Inst. Radio Engrs. Intern. Conv. Record 10, 79 (1962).

Inst. Radio Engrs. Trans. (1)

L. J. Cutrona, E. Leith, C. Palermo, L. Porcello, Inst. Radio Engrs. Trans. IT-6, 386 (1960).

J. Opt. Soc. Am. (1)

Proc. IEEE (2)

M. Arm, L. Lambert, I. Weissman, Proc. IEEE 52, 842 (1964).
[CrossRef]

J. S. Gerig, H. Montague, Proc. IEEE 52, 1753 (1964).
[CrossRef]

Other (2)

M. Born, E. Wolf, Principles of Optics, (Pergamon Press, New York, 1964), 2nd ed. pp. 419–424.

M. King, “Heterodyne-Type Electro-Optical Signal Processors,” Tech. Rept. T-2/321 (Electronics Research Laboratories, Columbia University, New York, 1966), unclassified.

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Figures (10)

Fig. 1
Fig. 1

Ideal circular thin lens.

Fig. 2
Fig. 2

Acoustic light modulator.

Fig. 3
Fig. 3

Electrooptical spectrum analyzer with coherent detection.

Fig. 4
Fig. 4

Electrooptical correlator with coherent detection.

Fig. 5
Fig. 5

Experimental electrooptical spectrum analyzer.

Fig. 6
Fig. 6

Mechanics of light scattering. (a) acoustic light modulator, (b) grating.

Fig. 7
Fig. 7

Intensity pattern of perfect grating.

Fig. 8
Fig. 8

Linear dependence of heterodyne signal amplitude on input signal.

Fig. 9
Fig. 9

Relative phase of input and output signals. (a) Input phase varied from 0–2π rad. (b) Test of phase meter stability.

Fig. 10
Fig. 10

Quadratic dependence of intrinsic output on input.

Equations (13)

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- E s exp [ j 2 π ν ( t - 2 F c ) ] j λ F - P / 2 P / 2 - P / 2 P / 2 A ( x , y ) × exp [ j ϕ ( x , y ) ] exp [ - j 2 π λ F ( x x + y y ) ] d y d x .
ψ ( x , t ) = ψ v ( t - x / s ) ,
E s exp [ j 2 π ν t ] exp [ - j ψ ( x , t ) ] .
E s exp [ j 2 π ν t ] [ 1 - j ψ ( x , t ) ] .
- ( P / λ F ) E s exp [ j 2 π ν ( t - 2 F / c ) ] ψ exp [ - j ( 2 π / λ F ) x s t ] A × A ( x / λ F , t ) exp [ j ϕ ( x / λ F , t ) ] .
I ( x / λ F , t ) = I L O + ( P ψ / λ F ) 2 A 2 ( x / λ F , t ) I s + ( 2 P ψ / λ F ) ( I L O I s ) ½ A ( x / λ F , t ) cos [ 2 π ( x s / λ F ) t - ϕ ( x / λ F , t ) + θ ] .
I ( x / ( λ F , t ) = ( P ψ / λ F ) 2 A 2 ( x / λ F , t ) I s .
I L O + I s ( K ψ / 2 ) 2 Env 2 { C ( t ) } + ( I L O I s ) ½ K ψ C ( t ) ,
I ( x / λ F , t ) = I L O + I s ( K Ψ / 2 ) 2 f 2 ( t ) + ( I L O I s ) ½ K Ψ f ( t ) cos [ ω 0 t + g ( t ) ] ,
K = { 2 P / λ F for the spectrum analyzer a 1 P / λ F for the correlator ,
Phase error = ( 1 - d / F ) ( r 2 / 2 F ) ,
I L O + ( P P ψ / λ F ) 2 I s + ( 2 P P ψ / λ F ) ( I L O I s ) ½ × cos [ 4 π × 10 7 t - ϕ + θ ] ,
( P P ψ / λ F ) 2 I s ,

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