Abstract

A chopper-modulated infrared detection system is investigated, and an error expression is found under the condition of minimizing the mean-square error of the approximating output function. The filtering problem for a periodic input filter and nonstationary input is solved. The error expression is evaluated and computer simulations are performed. Computer optimization of the chopper pattern is also presented. In particular, standard chopper blades are shown to be not always the best.

© 1969 Optical Society of America

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References

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  1. G. L. Turin, IRE Trans. Information Theory 3, 5 (1957).
    [Crossref]
  2. A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw–Hill Book Co., New York, 1965).
  3. S. W. Golomb, Digital Communications with Space Applications (Prentice–Hall, Englewood Cliffs, N. J., 1964).
  4. W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw–Hill Book Co., Inc., New York, 1958).
  5. D. J. Wilde, Optimum Seeking Methods (Prentice–Hall, Englewood Cliffs, N. J., 1964).
  6. T. Manwell, Error Analysis for a Chopper-Modulated Infrared Detection System (, 1967).

1957 (1)

G. L. Turin, IRE Trans. Information Theory 3, 5 (1957).
[Crossref]

Davenport, W. B.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw–Hill Book Co., Inc., New York, 1958).

Golomb, S. W.

S. W. Golomb, Digital Communications with Space Applications (Prentice–Hall, Englewood Cliffs, N. J., 1964).

Manwell, T.

T. Manwell, Error Analysis for a Chopper-Modulated Infrared Detection System (, 1967).

Papoulis, A.

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw–Hill Book Co., New York, 1965).

Root, W. L.

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw–Hill Book Co., Inc., New York, 1958).

Turin, G. L.

G. L. Turin, IRE Trans. Information Theory 3, 5 (1957).
[Crossref]

Wilde, D. J.

D. J. Wilde, Optimum Seeking Methods (Prentice–Hall, Englewood Cliffs, N. J., 1964).

IRE Trans. Information Theory (1)

G. L. Turin, IRE Trans. Information Theory 3, 5 (1957).
[Crossref]

Other (5)

A. Papoulis, Probability, Random Variables and Stochastic Processes (McGraw–Hill Book Co., New York, 1965).

S. W. Golomb, Digital Communications with Space Applications (Prentice–Hall, Englewood Cliffs, N. J., 1964).

W. B. Davenport and W. L. Root, An Introduction to the Theory of Random Signals and Noise (McGraw–Hill Book Co., Inc., New York, 1958).

D. J. Wilde, Optimum Seeking Methods (Prentice–Hall, Englewood Cliffs, N. J., 1964).

T. Manwell, Error Analysis for a Chopper-Modulated Infrared Detection System (, 1967).

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Figures (6)

Fig. 1
Fig. 1

Optical system.

Fig. 2
Fig. 2

Schematic diagram.

Fig. 3
Fig. 3

Chopper-blade patterns for traditional and for pseudo-random choppers.

Fig. 4
Fig. 4

Post-filter functions for traditional and for pseudo-random choppers.

Fig. 5
Fig. 5

Input–output pairs.

Fig. 6
Fig. 6

A complete processing sequence.

Equations (24)

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= E A d a [ x ( a ) - y ( a ) ] 2 ,
w ( t ) = A x ( a ) h ( v t - a ) d a ,
y ( a ) = 0 N T [ w ( t ) + n ( t ) ] g ( a v - t ) d t .
E A d a [ x ( a ) - y ( a ) ] 2 = x - y , x - y .
= x - y o p , x - y o p
x - y o p , y = 0 ,
= x , x - x , y o p .
[ S ] j , k = A d a A d a E [ x ( a ) x ( a ) ] × exp { i r ( k a - j a ) } × sin ( j - k ) α / r / ( j - k ) α / r
[ H S ] j , k = N T h - j h k S j , k + σ 2 δ j , k
[ S H ] j , k = S j , k + [ σ 2 / ( N T h - j h k ) ] δ j , k
( s ) k = ( 2 α ) - 1 S k , k
( h s ) k = h - k S k , k
( g o p ) k = g o p k
( 1 / 2 π r ) k = 1 2 π r .
( x , y ) = k x k y - k .
( g o p ) = [ H S ] - 1 ( h s ) .
g o p ( t ) = k exp { i k l 2 π T } [ ( H S ) - 1 ( h s ) ] k ,
( ( 2 π r ) - 1 , s )
= ( ( 2 π r ) - 1 , s ) - ( ( S H ) - 1 s , s ) ,
x ( a ) = k = 1 K I k f ( a - a k ) ,
S j , k = f j f - k ( M E ( I 2 ) sin ( j - k ) α / r ( j - k ) α / r + M 2 E 2 ( I ) sin j α / r j α / r sin k α / r k α / r ) × ( sin ( j - k ) α / r ( j - k ) α / r ) .
S k , k = 2 α ( M E ( I 2 ) f k f - k + M 2 E 2 ( I ) f 0 f 0 δ k , 0 ) ,
¯ = k = 1 10 ˆ k 10
σ ¯ = ( k = 1 10 ( ˆ k - ¯ ) 2 10 ) 1 2