Abstract

The literature describes tracking devices that allow a single detector coupled to a spinning FM reticle to determine target location. The spinning FM reticles presented were limited to single parameter reticles of frequency vs angle, frequency vs radius, or phase. This study presents these parameters with their capabilities and limitations and shows that multiple parameters can be integrated into a single reticle. Also, a general equation is developed that describes any FM reticle of the spinning type.

© 1991 Optical Society of America

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References

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  1. Editors of Photonics Spectra Magazine, The Photonics Dictionary (Laurin Publishing Company, Pittsfield, MA, 1988), p. D-104.
  2. R. O. Carpenter, “Comparison of AM and FM Reticle Systems,” Appl. Opt. 2, 229–236 (1963).
    [CrossRef]
  3. R. D. Hudson, “Optical Modulation,” Infrared System Engineering (Wiley, New York, 1968), p. 235.
  4. M. Meads, G. Boreman, R. Driggers, C. Halford, “Effect of Phasing Sector Angular Extent in FM Reticles,” Opt. Eng., submitted.
  5. Z. W. Chao, J. L. Chu, “General Analysis of Frequency-Modulation Reticles,” Opt. Eng. 27, 440–442 (1988).
    [CrossRef]
  6. L. M. Biberman, Reticles in Electro-Optical Devices (Pergamon, New York, 1966).
  7. D. J. Lovell, “Electro-Optical Position Indicator System,” U.S. Patent2,997,699 (22Aug.1961).

1988 (1)

Z. W. Chao, J. L. Chu, “General Analysis of Frequency-Modulation Reticles,” Opt. Eng. 27, 440–442 (1988).
[CrossRef]

1963 (1)

Biberman, L. M.

L. M. Biberman, Reticles in Electro-Optical Devices (Pergamon, New York, 1966).

Boreman, G.

M. Meads, G. Boreman, R. Driggers, C. Halford, “Effect of Phasing Sector Angular Extent in FM Reticles,” Opt. Eng., submitted.

Carpenter, R. O.

Chao, Z. W.

Z. W. Chao, J. L. Chu, “General Analysis of Frequency-Modulation Reticles,” Opt. Eng. 27, 440–442 (1988).
[CrossRef]

Chu, J. L.

Z. W. Chao, J. L. Chu, “General Analysis of Frequency-Modulation Reticles,” Opt. Eng. 27, 440–442 (1988).
[CrossRef]

Driggers, R.

M. Meads, G. Boreman, R. Driggers, C. Halford, “Effect of Phasing Sector Angular Extent in FM Reticles,” Opt. Eng., submitted.

Halford, C.

M. Meads, G. Boreman, R. Driggers, C. Halford, “Effect of Phasing Sector Angular Extent in FM Reticles,” Opt. Eng., submitted.

Hudson, R. D.

R. D. Hudson, “Optical Modulation,” Infrared System Engineering (Wiley, New York, 1968), p. 235.

Lovell, D. J.

D. J. Lovell, “Electro-Optical Position Indicator System,” U.S. Patent2,997,699 (22Aug.1961).

Meads, M.

M. Meads, G. Boreman, R. Driggers, C. Halford, “Effect of Phasing Sector Angular Extent in FM Reticles,” Opt. Eng., submitted.

Appl. Opt. (1)

Opt. Eng. (1)

Z. W. Chao, J. L. Chu, “General Analysis of Frequency-Modulation Reticles,” Opt. Eng. 27, 440–442 (1988).
[CrossRef]

Other (5)

L. M. Biberman, Reticles in Electro-Optical Devices (Pergamon, New York, 1966).

D. J. Lovell, “Electro-Optical Position Indicator System,” U.S. Patent2,997,699 (22Aug.1961).

Editors of Photonics Spectra Magazine, The Photonics Dictionary (Laurin Publishing Company, Pittsfield, MA, 1988), p. D-104.

R. D. Hudson, “Optical Modulation,” Infrared System Engineering (Wiley, New York, 1968), p. 235.

M. Meads, G. Boreman, R. Driggers, C. Halford, “Effect of Phasing Sector Angular Extent in FM Reticles,” Opt. Eng., submitted.

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Figures (11)

Fig. 1
Fig. 1

Rising sun reticle.

Fig. 2
Fig. 2

Angular cosine modulated reticle.

Fig. 3
Fig. 3

Frequency vs angle functions with reticles.

Fig. 4
Fig. 4

Lovell reticle with radial dependence.

Fig. 5
Fig. 5

Reticle with a Gaussian m(r).

Fig. 6
Fig. 6

Frequency vs radius reticles.

Fig. 7
Fig. 7

Linear and squared phase reticles.

Fig. 8
Fig. 8

Various phase reticles.

Fig. 9
Fig. 9

Reticle descriptions using FM parameters.

Fig. 10
Fig. 10

Marriage with two nonconstant parameters.

Fig. 11
Fig. 11

Marriage with three nonconstant parameters.

Equations (21)

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T ( r , θ ) = 1 2 + 1 2 sgn ( cos m θ ) ,
I ( t ) = 0 R π π T ( r , θ ) δ [ r r 0 , θ ( ω t θ 0 ) ] r d θ d r
= 0 R π π [ 1 2 + 1 2 cos ( m θ ) ] δ [ r r 0 , θ ( ω t θ 0 ) ] r d θ d r ,
I ( t ) = A [ 1 2 + 1 2 cos m ( ω t θ 0 ) ] ,
T ( r , θ ) = 1 2 + 1 2 cos m ( θ + α cos θ ) .
I ( t ) = 1 2 + 1 2 cos m [ ( ω t θ 0 ) + α cos ( ω t θ 0 ) ] .
T ( θ ) = 1 2 + 1 2 cos g ( θ ) ,
f ( θ ) = d g ( θ ) d θ = d d θ [ m ( θ + α cos θ ) ] = m ( 1 α sin θ ) .
f ( ω t ) = d d t { m [ ω t θ 0 ) + α cos ( ω t θ 0 ) ] }
= m ω [ 1 α sin ( ω t θ 0 ) ]
f ( θ ) = d g ( θ ) d θ .
T ( r , θ ) = 1 2 + 1 2 cos [ θ m ( r ) ] = 1 2 + 1 2 cos [ θ ( 18 r R ) ] .
m ( r ) = 18 exp { 2 [ ( r R 2 ) R ] 2 } .
freq ( r , θ ) = m ( r ) f ( θ ) ,
f ( θ ) = d g ( θ ) d θ ,
T ( r , θ ) = 1 2 + 1 2 cos [ m ( r ) g ( θ ) ] .
T ( r , θ ) = 1 2 + 1 2 cos { 10 [ θ + ρ ( r ) ] } ,
ρ ( r ) = π 12 r R
ρ ( r ) = π 12 ( r R ) 2 .
T ( r , θ ) = 1 2 + 1 2 cos [ m ( r ) 0 θ + ρ ( r ) f ( α ) d α ] ,
T ( r , θ ) = 1 2 + 1 2 cos { 40 r R [ θ + 0 . 4 sin ( θ ) } .

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