Abstract

The effect of film nonlinearity in recording a spatial matched filter for optical signal detection is to record a distorted signal rather than the original target signal. This distorted signal could cause a large false alarm rate if it is severely distorted. We propose a method that requires an additional mask immediately before the holographic matched filter to convert the original signal to the distorted signal before processing the signal through the nonlinear matched filter. This process will, in theory, eliminate all the false alarm signal caused by film nonlinearity. The transmittance function of the mask is calculated for a given target signal and given matched filter recording parameters. For a particular choice of recording parameter, the mask can be fabricated by directly exposing the Fourier spectrum of the target signal. A computer simulation using a square function as target signal proves the validity of this technique.

© 1977 Optical Society of America

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References

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    [CrossRef]
  2. A. A. Friesem, J. Zelenka, Appl. Opt. 6, 1755 (1967).
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

1973 (1)

1970 (1)

1968 (3)

1967 (1)

1965 (1)

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

1964 (1)

A. Vander Lugt, IRE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Binns, R. A.

Considine, P.

R. Gonsalves, R. Dumais, P. Considine, in SPIE Seminar Proceedings (1974), Vol. 45.

Cooley, J. W.

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

Dickinson, A.

Dumais, R.

R. Gonsalves, R. Dumais, P. Considine, in SPIE Seminar Proceedings (1974), Vol. 45.

Friesem, A. A.

Gonsalves, R.

R. Gonsalves, R. Dumais, P. Considine, in SPIE Seminar Proceedings (1974), Vol. 45.

Goodman, J. W.

Kozma, A.

A. Kozma, Opt. Acta 15, 527 (1968).
[CrossRef]

Raso, D. J.

Rotz, F. B.

Strubin, H. B.

Tukey, J. W.

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

Vander Lugt, A.

A. Vander Lugt, F. B. Rotz, Appl. Opt. 9, 215 (1970).
[CrossRef]

A. Vander Lugt, IRE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Watrasiewicz, B. M.

Zelenka, J.

Appl. Opt. (3)

IRE Trans. Inf. Theory (1)

A. Vander Lugt, IRE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

J. Opt. Soc. Am. (2)

Math. Comput. (1)

J. W. Cooley, J. W. Tukey, Math. Comput. 19, 297 (1965).
[CrossRef]

Opt. Acta (1)

A. Kozma, Opt. Acta 15, 527 (1968).
[CrossRef]

Other (1)

R. Gonsalves, R. Dumais, P. Considine, in SPIE Seminar Proceedings (1974), Vol. 45.

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Figures (10)

Fig. 1
Fig. 1

Transfer curves of amplitude ratio Ta = |G|/|F| vs target spectrum amplitude |F| for a nonlinearly recorded matched filter.

Fig. 2
Fig. 2

Transfer curves of Ta = |G|/|F| vs target spectrum intensity |F|2 and TaE characteristic curve for the 649-F plate.

Fig. 3
Fig. 3

Output signal for a nonlinearly recorded matched filter: (A) reconstructed signal for the low pass matched filter; (B) reconstructed signal for the high pass matched filter; (C) output correlation function for the low pass matched filter; (D) output correlation function for the high pass matched filter.

Fig. 4
Fig. 4

Output correlation functions for a set of input signals for the high pass matched filter: solid line, for D = 29; dashed line, for D less than 29; dotted line, for D larger than 29.

Fig. 5
Fig. 5

Same as Fig. 4 for low pass matched filter.

Fig. 6
Fig. 6

On-axis peak correlation as a function of input signal size D = 3 to D = 61: curve 1, for low pass filter; curve 2, for high pass filter.

Fig. 7
Fig. 7

Output correlation functions for the high pass matched filter using a direct compensation technique for the same set of input signals as in Fig. 4.

Fig. 8
Fig. 8

Impulse response of a nonlinearly recorded square target function (29 × 29).

Fig. 9
Fig. 9

Cross-correlation function of a square letter O with target square function (29 × 29).

Fig. 10
Fig. 10

Cross-correlation function of a small square function (9 × 9) with target square function (29 × 29).

Equations (9)

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C = | B ( p , q ) S F * d p d q . | 2 B ( p , q ) S 2 d p d q B ( p , q ) F 2 d p d q 1 ,
B ( p , q ) S 2 d p d q
B ( p , q ) F 2 d p d q
C n = | B ( p , q ) S G * d p d q | 2 B ( p , q ) S 2 d p d q B ( p , q ) G 2 d p d q 1.
K = C n C n ( F ) = K 0 | B ( p , q ) S G * d p d q | 2 B ( p , q ) S 2 d p d q ,
K 0 = B ( p , q ) F 2 d p d q | B ( p , q ) F G * d p d q | 2
S t = S T a = ( G / F ) S .
C n = | B ( p , q ) S t G * d p d q | 2 B ( p , q ) S t 2 d p d q             B ( p , q ) G 2 d p d q 1 ,
S t 2 d p d q ,

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