Abstract

An experimental study was conducted to determine the effects of nonoptimum noise conditions upon the SNR of optical spatial filters. The experiments were performed utilizing matched and inverse filters that are generally recognized as the best types of filters for pattern recognition. Their signal-to-noise ratios were compared as a function of varying background noise. The results indicate that (1) the SNR is a decreasing function of increasing background noise size, and (2) the performance difference between the inverse and matched filters increases as the noise size decreases.

© 1971 Optical Society of America

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References

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  1. “Optical Spatial Filtering Techniques,” First Quarterly Report, 1 July–30 September 1961, Contract AF33(616)-8433 (Institute of Science and Technology, The University of Michigan, Ann Arbor).
  2. “Complex Spatial Filtering,” Final Report, June1965, Contract AF30(602)-3354 (Technical Operations Research).

Other (2)

“Optical Spatial Filtering Techniques,” First Quarterly Report, 1 July–30 September 1961, Contract AF33(616)-8433 (Institute of Science and Technology, The University of Michigan, Ann Arbor).

“Complex Spatial Filtering,” Final Report, June1965, Contract AF30(602)-3354 (Technical Operations Research).

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Figures (4)

Fig. 1
Fig. 1

Optical pattern recognition system.

Fig. 2
Fig. 2

Different types of background noise: (a) binary high frequency noise, (b) binary high-middle frequency noise, (c) binary high-middle-low frequency noise, (d) binary geometric shapes, (e) continuous tone high frequency noise, (f) continuous tone low frequency noise, (g) omnidirectional noise.

Fig. 3
Fig. 3

SNR as a function of background noise.

Fig. 4
Fig. 4

Detection output for geometric background [Fig. 4(d)] utilizing (a) inverse filter and (b) matched filter.

Tables (1)

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Table I Normalized Signal-to-Noise Ratios

Equations (7)

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S ( x ) = - + S ( μ ) H ( μ ) exp ( 2 π i μ x ) d μ ,
H ( μ ) = k / N ( μ ) · S * ( μ ) ,
S ( x ) = k N - + S * ( μ ) S ( μ ) exp ( 2 π i μ x ) d μ ,
H ( μ ) = 1 / S ( μ ) .
S ( x ) - + S ( μ ) S ( μ ) exp ( 2 π i μ x ) d μ .
H ( μ ) = K S * ( μ )
I s / I n = 10 ( Δ D / γ ) ,

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