Abstract

The use of a self-developed body-centered reference for precision pulsed laser hot spot tracking is examined through a numerical computer simulation based on a solution of the heat equation with time varying input flux. Tracking resolution and sensitivity in two commonly used infrared sensor bands are compared. To cope with inherent instability, a simple compensation scheme is suggested with a demonstrated improvement in boresight error drift. Optimum performance is obtainable by judicious selection of sensor wavelength bands and sampling times relative to laser pulse time.

© 1983 Optical Society of America

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References

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  1. P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 864.
  2. H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 112.

Carslaw, H. S.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 112.

Feshback, H.

P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 864.

Jaeger, J. C.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 112.

Morse, P. M.

P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 864.

Other

P. M. Morse, H. Feshback, Methods of Theoretical Physics (McGraw-Hill, New York, 1953), Vol. 1, p. 864.

H. S. Carslaw, J. C. Jaeger, Conduction of Heat in Solids (Oxford U.P., London, 1959), p. 112.

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Figures (17)

Fig. 1
Fig. 1

Heat equation boundary conditions geometry.

Fig. 2
Fig. 2

Hot spot separate aperture tracking geometry.

Fig. 3
Fig. 3

Target aimpoint temperature vs time for Table I input parameters.

Fig. 4
Fig. 4

Incident sensor spectral radiance at λ = 10.6 μm vs time for Table I input parameters.

Fig. 5
Fig. 5

Incident sensor spectral radiance at λ = 3.8 μm vs time for Table I input parameters.

Fig. 6
Fig. 6

Control system configuration: n(t) = noise input and σbs is boresight error.

Fig. 7
Fig. 7

Laser aimpoint position in target coordinates vs time.

Fig. 8
Fig. 8

The 10.6-μm sensor centroid position vs time as sampled just prior to laser pulse.

Fig. 9
Fig. 9

The 10.6-μm sensor centroid position vs time as sampled at laser pulse peak.

Fig. 10
Fig. 10

The 3.8-μm sensor centroid position vs time as sampled just prior to laser pulse.

Fig. 11
Fig. 11

Target aimpoint temperature vs time as sampled just prior to laser pulse for selected angular jitter values at 2-km range.

Fig. 12
Fig. 12

Target aimpoint position error and corresponding sensor radiance centroid position vs time for a boresight error of 6.75 μrad at 2.0-km range.

Fig. 13
Fig. 13

Target aimpoint position error vs time for several pulse compensation numbers.

Fig. 14
Fig. 14

Target aimpoint position error vs time with angular peak jitter of 1.25 μrad at 2.0 km. Static boresight error of 6.75 μrad at 2 km.

Fig. 15
Fig. 15

Target aimpoint position error vs time with angular peak jitter of 2.5 μrad at 2.0 km. Static boresight error of 6.75 μrad at 2 km.

Fig. 16
Fig. 16

Target aimpoint position error vs time with angular peak jitter of 5.0 μrad at 2.0 km. Static boresight error of 6.75 μrad at 2 km.

Fig. 17
Fig. 17

Comparative target aimpoint position error vs time for selected peak angular jitter values with 1 pulse compensation.

Tables (1)

Tables Icon

Table I Base Line Parameters

Equations (18)

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2 T ( r ¯ , t ) α 2 T t ( r ¯ , t ) = 0 ,
r ¯ =
K T z ( d , t ) = h [ T ( d , t ) T 0 ] Q ( d , t ) ,
K T z ( 0 , t ) = 0 ,
T ( r ¯ , 0 ) = T 0 ( K ) .
T ( r ¯ , t ) = 0 t + d t 0 V 0 d V 0 ρ ( r ¯ , t ) G + 1 4 π 0 t + d t 0 s d s ( G grad T T grad G ) + α 2 4 π × v 0 d V 0 [ T ( r ¯ , t ) G ] t 0 = 0 ,
G ( r ¯ , t r ¯ 0 , t 0 ) = n C n ( t , t 0 ) T n ( r ¯ ) T n * ( r ¯ 0 ) .
2 G α 2 G t = 4 π δ ( r ¯ r ¯ 0 ) δ ( t t 0 ) ,
C n ( t t 0 ) = 4 π α 2 exp [ λ n 2 ( t t 0 ) α 2 ] u ( t t 0 ) ,
Q ( x 0 , y 0 , t 0 ) = Q 0 N = 0 exp ( 2 σ 2 { [ x 0 f ( N ) ] 2 + [ y 0 g ( N ) ] 2 } ) × [ u ( t 0 N T ) u ( t 0 N T τ ) ] ,
T n ( x , y , z ) = A n 2 π cos ( β n z ) exp ( iax ) d a exp ( iby ) d b ,
tan ( β n d ) = h k β n ,
A n 2 = 2 β n sin ( β n d ) cos ( β n d ) + β n d
G ( r ¯ , t r ¯ 0 , t 0 ) = 4 π α 2 u ( t t 0 ) n = 0 exp [ λ n 2 α 2 ( t t 0 ) ] × A n 2 cos ( β n z ) cos ( β n z 0 ) 1 4 π 2 × exp [ i a ( x x 0 ) ] d a × exp [ i b ( y y 0 ) ] d b .
T ( x , y , d , t ) = T 0 + Q 0 α 2 K N = 0 n = 0 A n 2 cos 2 ( β n d ) × 0 t + d t 0 u ( t t 0 ) exp [ β n 2 α 2 ( t t 0 ) ] × [ u ( t 0 N T ) u ( t 0 N T τ ) ] × [ exp ( 2 α 2 { [ x f ( N ) ] 2 + [ y g ( N ) ] 2 σ 2 α 2 + 8 ( t t 0 ) } ) ] .
T ( x , y , d , t ) = Q 0 K N = 0 n = 0 A n 2 β n 2 cos 2 ( β n d ) × exp ( 2 σ 2 { [ x f ( N ) ] 2 + [ y g ( N ) ] 2 } ) × ( { 1 exp [ β n 2 α 2 ( t N T ) ] } u ( t N T ) { 1 exp [ β n 2 α 2 ( t N T τ ) ] } u ( t N T τ ) + T 0 .
R ¯ = dRRW λ ( R ) dRW λ ( R ) ,
W λ ( r ) = ( λ ) C 1 λ 5 { 1 exp [ C 2 λ T ( r ) ) 1 } ,

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