Abstract

Design considerations for a heterodyne spatial tracking system utilizing pupil plane processing techniques and its advantages over traditional focal plane processing are described. Noise performance bounds, optimal and suboptimal local oscillator distributions, pull-in performance, and applications other than spatial tracking are discussed. Experimental verification of a one-axis closed-loop tracking system is presented.

© 1989 Optical Society of America

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References

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  1. E. A. Swanson, V. W. S. Chan, “Heterodyne Spatial Tracking System for Optical Space Communication,” IEEE Trans. Commun. COM-34, 118–126 (1986).
    [CrossRef]
  2. L. J. Sullian, “Infrared Coherent Radar,” in Proc. Soc. Photo. Opt. Instrum. Engr. 227, 148–161 (1980); DTIC AD-A102689.
  3. R. Teoste, W. J. Scouler, D. L. Spears, “Coherent Mono-pulse Tracking with a 10.6 μm Radar,” in Proceedings IEEE OSA Conf. Laser Engr. Appl., Washington, DC, June2, 1977.
  4. R. H. Kingston, “Coherent Optical Radar,” Opt. News, 27–31 (Summer1977).
    [CrossRef]
  5. J. H. McElroy et al., “CO2 Laser Communication System for Near-Earth Space Applications,” Proc. IEEE 65, No. 2, February1977, 221–251 (1977).
    [CrossRef]
  6. T. S. Wei, R. M. Gagliardi, “Direct Detection vs Heterodyne in Optical Beam Tracking,” in Proc. Soc. Photo. Opt. Instrum. Engr. 739, 189–196 (1987).
  7. J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1968).
  8. E. A. Swanson, J. K. Roberge, “Design Considerations and Experimental Results for Direct Detection Spatial Tracking Systems,” Opt. Eng. 18, 659–666 (1989).
  9. M. I. Skolnick, Radar Handbook (McGraw Hill, New York, 1970), Chapt. 21.
  10. D. K. Barton, Radar System Analysis (Artech, Dedhum, MA, 1979), Chap. 9.
  11. R. S. Bondurant et al., “Opto-Mechanical Subsystem for Space-Based Coherent Optical Communication,” in Proc. Soc. Photo. Opt. Instrum. Eng. 996, 92–100 (1988).
  12. W. L. Stutzman, G. A. Thiele, Antenna Theory and Design (Wiley, New York, 1981).
  13. C. L. Hayes, R. A. Brandewie, W. C. Davis, G. E. Meyers, “Experimental Test of an Infrared Phase Conjugation Adaptive Array,” J. Opt. Soc. Am. 67, 269–277 (1977).
    [CrossRef]
  14. K. A. Winick, P. Kumar, “Spatial Mode Matching Efficiencies for Heterodyned GaAlAs Semiconductor Lasers,” IEEE J. Lightwave Tech. LT-6, 513–520 (1988).
    [CrossRef]
  15. S. B. Alexander, “Design of Wide-Band Optical Heterodyne Balanced Mixer Receiver,” IEEE J. Lightwave Tech. LT-5, 523–537 (1987).
    [CrossRef]

1989 (1)

E. A. Swanson, J. K. Roberge, “Design Considerations and Experimental Results for Direct Detection Spatial Tracking Systems,” Opt. Eng. 18, 659–666 (1989).

1988 (2)

R. S. Bondurant et al., “Opto-Mechanical Subsystem for Space-Based Coherent Optical Communication,” in Proc. Soc. Photo. Opt. Instrum. Eng. 996, 92–100 (1988).

K. A. Winick, P. Kumar, “Spatial Mode Matching Efficiencies for Heterodyned GaAlAs Semiconductor Lasers,” IEEE J. Lightwave Tech. LT-6, 513–520 (1988).
[CrossRef]

1987 (2)

S. B. Alexander, “Design of Wide-Band Optical Heterodyne Balanced Mixer Receiver,” IEEE J. Lightwave Tech. LT-5, 523–537 (1987).
[CrossRef]

T. S. Wei, R. M. Gagliardi, “Direct Detection vs Heterodyne in Optical Beam Tracking,” in Proc. Soc. Photo. Opt. Instrum. Engr. 739, 189–196 (1987).

1986 (1)

E. A. Swanson, V. W. S. Chan, “Heterodyne Spatial Tracking System for Optical Space Communication,” IEEE Trans. Commun. COM-34, 118–126 (1986).
[CrossRef]

1980 (1)

L. J. Sullian, “Infrared Coherent Radar,” in Proc. Soc. Photo. Opt. Instrum. Engr. 227, 148–161 (1980); DTIC AD-A102689.

1977 (3)

R. H. Kingston, “Coherent Optical Radar,” Opt. News, 27–31 (Summer1977).
[CrossRef]

J. H. McElroy et al., “CO2 Laser Communication System for Near-Earth Space Applications,” Proc. IEEE 65, No. 2, February1977, 221–251 (1977).
[CrossRef]

C. L. Hayes, R. A. Brandewie, W. C. Davis, G. E. Meyers, “Experimental Test of an Infrared Phase Conjugation Adaptive Array,” J. Opt. Soc. Am. 67, 269–277 (1977).
[CrossRef]

Alexander, S. B.

S. B. Alexander, “Design of Wide-Band Optical Heterodyne Balanced Mixer Receiver,” IEEE J. Lightwave Tech. LT-5, 523–537 (1987).
[CrossRef]

Barton, D. K.

D. K. Barton, Radar System Analysis (Artech, Dedhum, MA, 1979), Chap. 9.

Bondurant, R. S.

R. S. Bondurant et al., “Opto-Mechanical Subsystem for Space-Based Coherent Optical Communication,” in Proc. Soc. Photo. Opt. Instrum. Eng. 996, 92–100 (1988).

Brandewie, R. A.

Chan, V. W. S.

E. A. Swanson, V. W. S. Chan, “Heterodyne Spatial Tracking System for Optical Space Communication,” IEEE Trans. Commun. COM-34, 118–126 (1986).
[CrossRef]

Davis, W. C.

Gagliardi, R. M.

T. S. Wei, R. M. Gagliardi, “Direct Detection vs Heterodyne in Optical Beam Tracking,” in Proc. Soc. Photo. Opt. Instrum. Engr. 739, 189–196 (1987).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1968).

Hayes, C. L.

Kingston, R. H.

R. H. Kingston, “Coherent Optical Radar,” Opt. News, 27–31 (Summer1977).
[CrossRef]

Kumar, P.

K. A. Winick, P. Kumar, “Spatial Mode Matching Efficiencies for Heterodyned GaAlAs Semiconductor Lasers,” IEEE J. Lightwave Tech. LT-6, 513–520 (1988).
[CrossRef]

McElroy, J. H.

J. H. McElroy et al., “CO2 Laser Communication System for Near-Earth Space Applications,” Proc. IEEE 65, No. 2, February1977, 221–251 (1977).
[CrossRef]

Meyers, G. E.

Roberge, J. K.

E. A. Swanson, J. K. Roberge, “Design Considerations and Experimental Results for Direct Detection Spatial Tracking Systems,” Opt. Eng. 18, 659–666 (1989).

Scouler, W. J.

R. Teoste, W. J. Scouler, D. L. Spears, “Coherent Mono-pulse Tracking with a 10.6 μm Radar,” in Proceedings IEEE OSA Conf. Laser Engr. Appl., Washington, DC, June2, 1977.

Skolnick, M. I.

M. I. Skolnick, Radar Handbook (McGraw Hill, New York, 1970), Chapt. 21.

Spears, D. L.

R. Teoste, W. J. Scouler, D. L. Spears, “Coherent Mono-pulse Tracking with a 10.6 μm Radar,” in Proceedings IEEE OSA Conf. Laser Engr. Appl., Washington, DC, June2, 1977.

Stutzman, W. L.

W. L. Stutzman, G. A. Thiele, Antenna Theory and Design (Wiley, New York, 1981).

Sullian, L. J.

L. J. Sullian, “Infrared Coherent Radar,” in Proc. Soc. Photo. Opt. Instrum. Engr. 227, 148–161 (1980); DTIC AD-A102689.

Swanson, E. A.

E. A. Swanson, J. K. Roberge, “Design Considerations and Experimental Results for Direct Detection Spatial Tracking Systems,” Opt. Eng. 18, 659–666 (1989).

E. A. Swanson, V. W. S. Chan, “Heterodyne Spatial Tracking System for Optical Space Communication,” IEEE Trans. Commun. COM-34, 118–126 (1986).
[CrossRef]

Teoste, R.

R. Teoste, W. J. Scouler, D. L. Spears, “Coherent Mono-pulse Tracking with a 10.6 μm Radar,” in Proceedings IEEE OSA Conf. Laser Engr. Appl., Washington, DC, June2, 1977.

Thiele, G. A.

W. L. Stutzman, G. A. Thiele, Antenna Theory and Design (Wiley, New York, 1981).

Wei, T. S.

T. S. Wei, R. M. Gagliardi, “Direct Detection vs Heterodyne in Optical Beam Tracking,” in Proc. Soc. Photo. Opt. Instrum. Engr. 739, 189–196 (1987).

Winick, K. A.

K. A. Winick, P. Kumar, “Spatial Mode Matching Efficiencies for Heterodyned GaAlAs Semiconductor Lasers,” IEEE J. Lightwave Tech. LT-6, 513–520 (1988).
[CrossRef]

IEEE J. Lightwave Tech. (2)

K. A. Winick, P. Kumar, “Spatial Mode Matching Efficiencies for Heterodyned GaAlAs Semiconductor Lasers,” IEEE J. Lightwave Tech. LT-6, 513–520 (1988).
[CrossRef]

S. B. Alexander, “Design of Wide-Band Optical Heterodyne Balanced Mixer Receiver,” IEEE J. Lightwave Tech. LT-5, 523–537 (1987).
[CrossRef]

IEEE Trans. Commun. (1)

E. A. Swanson, V. W. S. Chan, “Heterodyne Spatial Tracking System for Optical Space Communication,” IEEE Trans. Commun. COM-34, 118–126 (1986).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

E. A. Swanson, J. K. Roberge, “Design Considerations and Experimental Results for Direct Detection Spatial Tracking Systems,” Opt. Eng. 18, 659–666 (1989).

Opt. News (1)

R. H. Kingston, “Coherent Optical Radar,” Opt. News, 27–31 (Summer1977).
[CrossRef]

Proc. IEEE (1)

J. H. McElroy et al., “CO2 Laser Communication System for Near-Earth Space Applications,” Proc. IEEE 65, No. 2, February1977, 221–251 (1977).
[CrossRef]

Proc. Soc. Photo. Opt. Instrum. Eng. (1)

R. S. Bondurant et al., “Opto-Mechanical Subsystem for Space-Based Coherent Optical Communication,” in Proc. Soc. Photo. Opt. Instrum. Eng. 996, 92–100 (1988).

Proc. Soc. Photo. Opt. Instrum. Engr. (2)

T. S. Wei, R. M. Gagliardi, “Direct Detection vs Heterodyne in Optical Beam Tracking,” in Proc. Soc. Photo. Opt. Instrum. Engr. 739, 189–196 (1987).

L. J. Sullian, “Infrared Coherent Radar,” in Proc. Soc. Photo. Opt. Instrum. Engr. 227, 148–161 (1980); DTIC AD-A102689.

Other (5)

R. Teoste, W. J. Scouler, D. L. Spears, “Coherent Mono-pulse Tracking with a 10.6 μm Radar,” in Proceedings IEEE OSA Conf. Laser Engr. Appl., Washington, DC, June2, 1977.

M. I. Skolnick, Radar Handbook (McGraw Hill, New York, 1970), Chapt. 21.

D. K. Barton, Radar System Analysis (Artech, Dedhum, MA, 1979), Chap. 9.

J. W. Goodman, Introduction to Fourier Optics (McGraw Hill, New York, 1968).

W. L. Stutzman, G. A. Thiele, Antenna Theory and Design (Wiley, New York, 1981).

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Figures (15)

Fig. 1
Fig. 1

Focal plane processing.

Fig. 2
Fig. 2

Pupil plane processing (phase processing).

Fig. 3
Fig. 3

Pupil plane processing (amplitude processing).

Fig. 4
Fig. 4

Dead zone consideration.

Fig. 5
Fig. 5

Pupil plane tracking sensor.

Fig. 6
Fig. 6

Comparison of pupil plane and focal plane sum and difference channel mode-matching efficiencies and LO power loss.

Fig. 7
Fig. 7

Comparison of matched Gaussian focal plane and pupil plane discriminators.

Fig. 8
Fig. 8

Comparison of focal plane and pupil plane discriminators (d/ωl = 0.0).

Fig. 9
Fig. 9

Comparison of focal plane and pupil plane discriminators (d/ωl = 2.0).

Fig. 10
Fig. 10

Comparison of focal plane and pupil plane discriminators (d/ωl = 4.0).

Fig. 11
Fig. 11

Optical layout (1-axis).

Fig. 12
Fig. 12

Correlation processing.

Fig. 13
Fig. 13

Pupil plane discriminant.

Fig. 14
Fig. 14

NEA vs optical signal power.

Fig. 15
Fig. 15

Measured closed-loop and rejection transfer functions.

Equations (42)

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S = P s S ( x , y ) exp [ j k ( x θ x + y θ y ) j ω t ] ,
L = L ( x , y ) exp [ j ( ω + Δ ω ) t ] ,
1 = | S ( x , y ) | 2 dxdy
Sum = 2 P s m ( θ x , θ y ) cos ( Δ ω t ) + w Sum ( t ) ,
A z = 2 P s K A z ( θ x , θ y ) θ x sin ( Δ ω t ) + w A z ( t ) ,
m ( θ x , θ y ) = 2 0 0 S ( x , y ) L ( x , y ) cos ( k x θ x ) cos ( k y θ y ) dxdy 0 0 | L ( x , y ) | 2 dxdy ,
K A z ( θ x , θ y ) = 2 0 0 S ( x , y ) L ( x , y ) k x sinc ( k x θ x / π ) cos ( k y θ y ) dxdy 0 0 | L ( x , y ) | 2 dxdy ,
A z + = 2 P s m ( θ x , θ y ) 2 + ( K A z ( θ x , θ y ) θ x ) 2 2 × cos ( Δ ω t tan 1 [ K A z ( θ x , θ y ) θ x m ( θ x , θ y ) ] ) + w A z + ( t )
NESD = NEA 2 NEB ,
NESD = [ η P s h ν K A z ( 0 ) 2 ] 1 ,
NESD = [ η P s h ν 4 ( 0 0 S ( x , y ) L ( x , y ) kxdxdy ) 2 0 0 | L ( x , y ) | 2 dxdy ] 1 .
L ( x , y ) opt = x S ( x , y ) ,
NESD opt = [ η P s h ν | k x S ( x , y ) | 2 dxdy ] 1 .
l ( x , y ) = s ( x , y ) x ,
NESD opt = [ η P s h ν | S ( x , y ) x | 2 dxdy ] 1 ,
S ( x , y ) = 4 π d 2 circ ( 2 x 2 + y 2 d ) , ( plane wave )
S ( x , y ) = 2 π ω s 2 exp [ x 2 + y 2 ω s 2 ] , ( Gaussian )
S ( x , y ) = 1 4 π π d λ f 2 J 1 ( π d λ f x 2 + y 2 ) π d λ f x 2 + y 2 , ( Airy disk )
S ( x , y ) = 2 π ( 2 f k ω s ) 2 exp [ x 2 + y 2 ( 2 f k ω s ) 2 ] , ( Gaussian )
NESD [ η P s h ν π 2 4 1 ( λ d ) 2 ] 1 , ( plane wave or Airy disk )
NESD [ η P s h ν π 2 1 ( λ ω s ) 2 ] 1 . ( Gaussian )
NESD = [ η P s h ν 16 9 1 ( λ d ) 2 ] 1 . ( matched plane wave in pupil plane )
NESD = [ η P s h ν 64 9 π 2 1 ( λ d ) 2 ] 1 . ( matched Airy−disk in focal plane )
| m ( 0 ) | 2 = 8 ( 1 exp [ 1 4 ( d ω l ) 2 ] ( d ω l ) { 1 exp [ 1 2 ( d ω l ) 2 ] } 1 / 2 ) 2 ,
NESD = [ η P s h ν 1 ( λ d ) 2 32 { π erf [ 1 2 ( d ω l ) ] ( d ω l ) exp [ 1 4 ( d ω l ) 2 ] ( d ω l ) 2 { 1 exp ( 1 2 ( d ω l ) 2 ) } 1 / 2 } 2 ] 1 , ( pupil plane )
NESD = [ η P s h ν 1 ( λ d ) 2 8 { ( d ω l ) 0 1 d t t exp ( 1 4 ( t d ω l ) 2 ) 0 d r J 2 ( r ) J 0 ( t r ) [ 1 exp ( 1 2 ( d ω l ) 2 ) ] 1 / 2 } 2 ] 1 , ( focal plane )
LO power loss = 1 exp ( 1 2 ( d ω l ) 2 ) .
NESD ~ [ ( 0 0 s ( x , y ) x l ( x , y ) dxdy ) 2 0 0 | l ( x , y ) | 2 dxdy ( 0 0 S ( x , y ) l ( x , y ) dxdy ) 2 0 0 | l ( x , y ) | 2 dxdy ] 1 , ( focal plane )
NESD ~ [ ( 0 0 S ( x , y ) L ( x , y ) kxdxdy ) 2 0 0 | L ( x , y ) | 2 dxdy ( 0 0 S ( x , y ) L ( x , y ) dxdy ) 2 0 0 | L ( x , y ) | 2 dxdy ] 1 , ( pupil plane )
Sum = 2 P s exp [ ( k θ x 2 + θ y 2 ω s 8 ) 2 ] cos ( Δ ω t )
A z = 2 P s exp [ ( k θ x 2 + θ y 2 ω s 8 ) 2 ] 2 π 0 k θ x ω s 8 d τ exp ( τ 2 ) sin ( Δ ω t ) ( pupil plane )
A z = 2 P s exp [ ( k θ x 2 + θ y 2 ω s 8 ) 2 ] 2 π 0 k θ x ω s 8 d τ exp ( τ 2 ) cos ( Δ ω t ) ( focal plane )
Sum = 2 P s 4 π c 0 1 d y exp [ 1 4 ( d y ω l ) 2 ] cos ( kdy θ y 2 ) × 0 1 y 2 d x exp [ 1 4 ( d x ω l ) 2 ] cos ( kdx θ x 2 ) cos ( Δ ω t )
A z = 2 P s 4 π c 0 1 d y exp [ 1 4 ( d y ω l ) 2 ] cos ( kdy θ y 2 ) × 0 1 y 2 d x exp [ 1 4 ( d x ω l ) 2 ] sin ( kdx θ x 2 ) sin ( Δ ω t ) ( pupil plane )
A z = 2 P s 1 π c 0 d y 0 d x sgn ( x ) J 1 { x π θ x ( λ d ) } 2 + { y π θ y ( λ d ) } 2 ( x π θ x ( λ d ) ) 2 + ( y π θ y ( λ d ) ) 2 L ( x 2 + y 2 ) cos ( Δ ω t ) focal plane
L ( r ) = 0 1 d t t exp [ 1 4 ( t d ω l ) 2 ] J 0 ( t r )
c = 1 2 ( d ω l ) [ 1 exp ( 1 2 ( d ω l ) 2 ) ] 1 / 2
θ max N λ d
N d r o
NEA ideal = 1 K A z ( 0 ) NEB η γ P s h ν
NEA ideal = 1 K A z ( 0 ) NEB η γ P t r h ν { 1 + W η γ P c h ν } 1 / 2 ,
NEA experiment = 2 K A z ( 0 ) NEB η γ P t r 3 h ν { 1 + W η γ P c 2 h ν } 1 / 2 .

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