Abstract

This paper presents a nonmechanical method of measuring temporally coherent light which may be dominated by incoherent background radiation. To obtain detection in the presence of high levels of incoherent radiation, the detector must reject constant and fluctuating contributions due to incoherent light. Extreme sensitivity of the method derives from preferentially modulating the coherent light in such a way that the exact periodicity of the resulting detected signal component is known, permitting, in principle, processing gains which are almost arbitrarily large. Wavelength estimates are also obtained, even when the coherent source power is orders of magnitude less than the power of background radiation. The approach lends itself to rugged and easily constructed implementation. This paper then provides an in-depth noise analysis of the general approach. Numerical examples are also given. Results of a crude laboratory test are presented. Although limited by shortcomings of the components at hand, the experiment demonstrated easy measurement of coherent radiation >40 dB below the ambient incoherent light and discernible output at a signal-to-interference level of −53 dB.

© 1991 Optical Society of America

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References

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  1. J. Jannson, T. Jannson, E. Wolf, “Spatial Coherence Discrimination in Scattering,” Opt. Lett. 13, 1060–1062 (1988).
    [CrossRef] [PubMed]
  2. T. R. O’Meara, “Optical Notch Filter for Discriminating Against Coherent Radiation,” U.S. Patent4,874,223 (17Oct.1989).
  3. C. J. Duffy, D. Hickman, “A Temporal Coherence-Based Optical Sensor,” Sensors Actuators, 18, 17–31 (1989).
    [CrossRef]
  4. R. Crane, “Laser Detection by Coherence Discrimination,” Opt. Eng. 18, 212–217 (1979).
  5. E. T. Siebert, “Analyzer for Coherent Radiation,” U.S. Patent4,309,108 (5Jan.1982).
  6. R. Crane, “Imaging Coherent Radiometer,” U.S. Patent4,735,507 (5Apr.1988).
  7. R. J. Amodeo, W. K. Krohn, “Apparatus for Detecting Coherent Radiation and Unequal Path Interferometers,” U.S. Patent4,595,292 (17June1986).
  8. W. T. Krohn, M. J. McNally, R. Abreu, “Coherent Radiation Detecting Apparatus,” U.S. Patent4,600,307 (15July1986).
  9. I.-C. Chang, “Acoustic-Optic Coherent Modulator and Detection System,” U.S. Patent4,217,036 (12Aug.1980).
  10. H. E. Bates, “Optical Coherence Measuring Device,” U.S. Patent4,076,423, (28Feb.1978).
  11. M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, NJ1964), Chap. 1.
  12. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  13. M. Abramowitz, I. A. Stegun, Ed., Handbook of Mathematical Functions, National Bureau of Standards (1964), p. 361.
  14. R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 7, 8, 9, and 14.
  15. D. L. Snyder, Random Point Processes (Wiley, New York, 1975).

1989 (1)

C. J. Duffy, D. Hickman, “A Temporal Coherence-Based Optical Sensor,” Sensors Actuators, 18, 17–31 (1989).
[CrossRef]

1988 (1)

1979 (1)

R. Crane, “Laser Detection by Coherence Discrimination,” Opt. Eng. 18, 212–217 (1979).

Abreu, R.

W. T. Krohn, M. J. McNally, R. Abreu, “Coherent Radiation Detecting Apparatus,” U.S. Patent4,600,307 (15July1986).

Amodeo, R. J.

R. J. Amodeo, W. K. Krohn, “Apparatus for Detecting Coherent Radiation and Unequal Path Interferometers,” U.S. Patent4,595,292 (17June1986).

Bates, H. E.

H. E. Bates, “Optical Coherence Measuring Device,” U.S. Patent4,076,423, (28Feb.1978).

Beran, M. J.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, NJ1964), Chap. 1.

Boyd, R. W.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 7, 8, 9, and 14.

Chang, I.-C.

I.-C. Chang, “Acoustic-Optic Coherent Modulator and Detection System,” U.S. Patent4,217,036 (12Aug.1980).

Crane, R.

R. Crane, “Laser Detection by Coherence Discrimination,” Opt. Eng. 18, 212–217 (1979).

R. Crane, “Imaging Coherent Radiometer,” U.S. Patent4,735,507 (5Apr.1988).

Duffy, C. J.

C. J. Duffy, D. Hickman, “A Temporal Coherence-Based Optical Sensor,” Sensors Actuators, 18, 17–31 (1989).
[CrossRef]

Hickman, D.

C. J. Duffy, D. Hickman, “A Temporal Coherence-Based Optical Sensor,” Sensors Actuators, 18, 17–31 (1989).
[CrossRef]

Jannson, J.

Jannson, T.

Krohn, W. K.

R. J. Amodeo, W. K. Krohn, “Apparatus for Detecting Coherent Radiation and Unequal Path Interferometers,” U.S. Patent4,595,292 (17June1986).

Krohn, W. T.

W. T. Krohn, M. J. McNally, R. Abreu, “Coherent Radiation Detecting Apparatus,” U.S. Patent4,600,307 (15July1986).

McNally, M. J.

W. T. Krohn, M. J. McNally, R. Abreu, “Coherent Radiation Detecting Apparatus,” U.S. Patent4,600,307 (15July1986).

O’Meara, T. R.

T. R. O’Meara, “Optical Notch Filter for Discriminating Against Coherent Radiation,” U.S. Patent4,874,223 (17Oct.1989).

Parrent, G. B.

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, NJ1964), Chap. 1.

Siebert, E. T.

E. T. Siebert, “Analyzer for Coherent Radiation,” U.S. Patent4,309,108 (5Jan.1982).

Snyder, D. L.

D. L. Snyder, Random Point Processes (Wiley, New York, 1975).

Wolf, E.

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Opt. Eng. (1)

R. Crane, “Laser Detection by Coherence Discrimination,” Opt. Eng. 18, 212–217 (1979).

Opt. Lett. (1)

Sensors Actuators (1)

C. J. Duffy, D. Hickman, “A Temporal Coherence-Based Optical Sensor,” Sensors Actuators, 18, 17–31 (1989).
[CrossRef]

Other (12)

T. R. O’Meara, “Optical Notch Filter for Discriminating Against Coherent Radiation,” U.S. Patent4,874,223 (17Oct.1989).

E. T. Siebert, “Analyzer for Coherent Radiation,” U.S. Patent4,309,108 (5Jan.1982).

R. Crane, “Imaging Coherent Radiometer,” U.S. Patent4,735,507 (5Apr.1988).

R. J. Amodeo, W. K. Krohn, “Apparatus for Detecting Coherent Radiation and Unequal Path Interferometers,” U.S. Patent4,595,292 (17June1986).

W. T. Krohn, M. J. McNally, R. Abreu, “Coherent Radiation Detecting Apparatus,” U.S. Patent4,600,307 (15July1986).

I.-C. Chang, “Acoustic-Optic Coherent Modulator and Detection System,” U.S. Patent4,217,036 (12Aug.1980).

H. E. Bates, “Optical Coherence Measuring Device,” U.S. Patent4,076,423, (28Feb.1978).

M. J. Beran, G. B. Parrent, Theory of Partial Coherence (Prentice-Hall, Englewood Cliffs, NJ1964), Chap. 1.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

M. Abramowitz, I. A. Stegun, Ed., Handbook of Mathematical Functions, National Bureau of Standards (1964), p. 361.

R. W. Boyd, Radiometry and the Detection of Optical Radiation (Wiley, New York, 1983), Chap. 7, 8, 9, and 14.

D. L. Snyder, Random Point Processes (Wiley, New York, 1975).

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Figures (8)

Fig. 1
Fig. 1

General system.

Fig. 2
Fig. 2

Exploded view of the general polarization interferometer.

Fig. 3
Fig. 3

Block diagram of the processing electronics. Amplifiers, some filters, and other support electronics are not shown. Portions or all of this system may be implemented in digital hardware, with a subset implemented in software.

Fig. 4
Fig. 4

Exploded view of the interferometer using a nonbirefringent electrooptic modulator.

Fig. 5
Fig. 5

Exploded view of the interferometer using birefringent electrooptic modulators.

Fig. 6
Fig. 6

Model of the output generation for noise calculations.

Fig. 7
Fig. 7

Experimental arrangement. Processing circuitry is not shown.

Fig. 8
Fig. 8

Output for a chopped laser power of 300 nW and an incoherent light power of 3 mW. Upper and lower traces are the first and second harmonic, respectively. The laser light was introduced with a polarization at 45° to the polarizer. Gross sinusoidal variation on the two traces resulted from heating in the crystal, an effect exaggerated by the large value of a and by the heating deliberately introduced by the author to verify the predicted phase relationship of these two outputs. The on–off modulation evident under the sinusoids was caused by the chopping. The low pass filter had a bandwidth of 400 Hz. The upper trace has an SNR of ~27 dB, the lower has an SNR of ~29dB.

Equations (86)

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A y ( t ) A z * ( t + τ ) = 1 2 Γ ( τ ) .
B y ( t ) = A y ( t a y + b y s ( t ) c )
B z ( t ) = A z ( t a z + b z s ( t ) c ) ,
B y ( t ) B z * ( t + τ ) = 1 2 Γ ( a y a z + ( b y b z ) s ( t ) c + τ ) .
I ( t ) = 1 2 | B y ( t ) + B z ( t ) | 2 = 1 2 [ Γ ( 0 ) + Re Γ ( a y a z + ( b y b z ) s ( t ) c ) ] .
a = a y a z
b = b y b z .
I ( t ) = 1 2 [ Γ ( 0 ) + Re Γ ( a + b s ( t ) c ) ] .
| a | | b | V l .
I ( t ) = 1 2 Γ ( 0 ) ( incoherent light ) .
I ( t ) = 1 2 Γ ( 0 ) { 1 + cos [ 2 π a + b s ( t ) λ ] } ( coherent light ) ,
| a | + | b | V L .
| a | | b | V ,
L | a | l .
s ( t ) = V cos ( 2 π f t ) .
cos ( α + β ) = cos ( α ) cos ( β ) sin ( α ) sin ( β ) ,
cos ( z cos θ ) = J 0 ( z ) + 2 k = 1 ( 1 ) k J 2 k ( z ) cos ( 2 k θ )
sin ( z cos θ ) = 2 k = 1 ( 1 ) k J 2 k + 1 ( z ) cos [ ( 2 k + 1 ) θ ] ,
I ( t ) = 1 2 Γ ( 0 ) [ 1 + cos ( a λ ) J 0 ( V b λ ) + 2 cos ( a λ ) k = 1 ( 1 ) k J 2 k ( V b λ ) cos [ 2 π ( 2 k ) f t ] 2 sin ( a λ ) k = 0 ( 1 ) k J 2 k + 1 ( V b λ ) cos [ 2 π ( 2 k + 1 ) f t ] ] .
h 1 = Γ ( 0 ) | sin ( a λ ) J 1 ( V b λ ) | , h 2 = Γ ( 0 ) | cos ( a λ ) J 2 ( V b λ ) | , h 3 = Γ ( 0 ) | sin ( a λ ) J 3 ( V b λ ) | ,
h 4 = Γ ( 0 ) | cos ( a λ ) J 4 ( V b λ ) | ,
S = w 1 H 1 2 + w 2 H 2 2 = Γ 2 ( 0 ) F ( λ ) + ( noise terms ) ,
F ( λ ) = R 2 R 2 ( λ ) [ w 1 sin 2 ( a λ ) J 1 2 ( V b λ ) + w 2 cos 2 ( a λ ) J 2 2 ( V b λ ) ] ,
m i = min λ Λ { R R ( λ ) J i ( V b λ ) }
M i = min λ Λ { R R ( λ ) J i ( V b λ ) } ,
w i = 1 m i M i .
max { M 1 m 1 , M 2 m 2 } .
R 1 = H 3 2 H 1 2 = J 3 2 ( V b λ ) J 1 2 ( V b λ ) ,
R 2 = H 4 2 H 2 2 = J 4 2 ( V b λ ) J 2 2 ( V b λ ) .
a = s ( n o n e ) .
Δ n z ( t ) = r 41 n 3 2 E ( t ) ,
Δ n y ( t ) = r 41 n 3 2 E ( t ) .
L [ Δ n y ( t ) Δ n y ( t ) ] = L r 41 n 3 E ( t ) = L r 41 n 3 s ( t ) H ,
b = ( r 41 n 3 ) ( L H ) .
V ( L H ) = 4 . 9 × 10 4 V .
a = L 1 n o + L 2 n e ( L 1 n e + L 2 n o ) = ( L 1 L 2 ) ( n o n e ) .
Δ n y = 1 2 r 13 n 0 3 E
Δ n 2 = 1 2 r 33 n e 3 E ,
b s ( t ) = 1 2 L 1 + L 2 H ( r 33 n e 2 r 13 n o 2 ) s ( t ) ,
b = 1 2 L 1 + L 2 H ( r 33 n e 2 r 13 n o 2 ) .
V L 1 + L 2 H = 18 . 6 kV .
L 1 L 2 = 1 . 1 mm .
μ b = ( e R ) 2 B ( λ d + λ i + 2 k T e 2 R )
μ s = ( e R ) 2 ( λ c 2 4 + B λ c ) ( e R λ c 2 ) 2 ,
E { X } = ( e R ) 2 B ( λ d + λ i + λ c + 2 k T e 2 R ) + ( e R ) 2 λ c 2 4 .
var { X } = 2 ( e R ) 4 B 2 ( λ d + λ i + 2 k T e 2 R ) 2 = 2 μ b 2 .
λ i = I A R m e
λ c = P c R ( λ ) 2 e ,
R m = I ( λ ) I R ( λ ) d λ
μ s > ( 1 + 2 s ) μ b .
λ c > 2 ( 1 + 2 s ) B ( λ d + λ i + 2 k T e 2 R )
P c > 4 e R ( λ ) ( 1 + 2 s ) B ( λ d + I A R m e + 2 k T e 2 R ) .
P c > 4 R ( λ ) ( 1 + 2 s ) 2 k T B R ( 1 + λ d e 2 R 2 k T ) .
P c > ( 1 + 2 s ) 16 B I A e R ( λ ) ( R m R ( λ ) ) .
P 1 = 2 P o | cos 2 ( θ ) sin ( a λ ) J 1 ( V b λ ) |
P 2 = 2 P o | cos 2 ( θ ) cos ( a λ ) J 2 ( V b λ ) | ,
μ b = ( e R ) 2 B ( λ d + I A R m 4 e + 2 k T e 2 R ) ( w 1 + w 2 ) ,
μ s = P o 2 F ( λ ) cos 4 ( θ ) 4 .
var { S } = 2 μ b 2 w 1 2 + w 2 2 ( w 1 + w 2 ) 2 .
μ s > ( 1 + r s ) μ b ,
r = 2 ( w 1 2 + w 2 2 ) w 1 + w 2
[ P o ] no background = 8 ( 1 + r s ) R k T B ( w 1 + w 2 ) F ( λ ) ( 1 + e 2 R λ d 2 k T ) .
[ P o ] large background = ( 1 + r s ) e R 2 B I A R m ( w 1 + w 2 ) F ( λ ) .
μ s ( t ) = ( R R ( λ ) 4 ) 2 ( P c ( t o ) h F ( t t o ) d t o + P c ( t o ) [ 2 cos ( 2 π f t o ) + cos ( 4 π f t o ) ] h F ( t t o ) d t o ) 2 ,
h ( t , t o ) = h F ( t t o ) cos ( 2 π f t o ) .
h 2 ( t , t o ) d t o = B and h 4 ( t , t o ) d t o = 3 B 3 ,
λ ( t ) = λ d + λ i ( t ) + λ c [ 1 + cos ( 2 π f t ) ] ,
γ 2 ( τ ) d τ = T c ,
E { λ i ( t ) } = λ o ,
cov { λ i ( t ) , λ i ( t + τ ) } = λ o 2 γ 2 ( τ ) n .
E { P ( t ) | λ } = e R h ( t , t o ) λ ( t o ) d t o ,
E { P ( t ) P ( T ) 2 ¯ | λ } = ( e R ) 2 h 2 ( t , t o ) λ ( t o ) d t o ,
E { ( P ( t ) P ( T ) ¯ ) 4 | λ } = ( e R ) 4 h 4 ( t , t o ) λ ( t o ) d t o + 3 ( e R ) 4 ( h 2 ( t , t o ) λ ( t o ) d t o ) 2 .
E { P ( t ) } = 1 2 e R λ c
E { P 2 ( t ) } = ( e R ) 2 B ( λ o + λ d + λ c ) + E 2 { P ( t ) } .
E { P 4 ( t ) } = 2 ( e R ) 4 B 3 ( λ o + λ d ) + 3 ( e R ) 4 B 2 [ ( λ o + λ d ) 2 + 2 B T c λ o 2 n ] ,
2 B T c n 1 ,
E { P 4 ( t ) } = 2 ( e R ) 4 B 3 ( λ o + λ d ) + 3 ( e R ) 4 B 2 ( λ o + λ d ) 2 .
E { N ( t ) } = 0 ,
E { N 2 ( t ) } = 2 R k T B ,
E { N 4 ( t ) } = 3 ( 2 R k T B ) 2 .
X = [ P ( t ) + N ( t ) ] 2 | t = t o
E { X } = ( e R ) 2 B ( λ o + λ d + 2 k T e 2 R ) + ( e R ) 2 ( λ c 2 4 + B λ c ) .
var { X } = 2 ( e R ) 4 B 2 [ ( λ o + λ d + 2 k T e 2 R ) 2 + B ( λ o + λ d ) ] .
λ o + λ d B ,
var { X } = 2 ( e R ) 4 B 2 ( λ o + λ d + 2 k T e 2 R ) 2 .

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