Abstract

A test pattern may be compared with a reference pattern by placing the two side by side in a coherent beam. If the compared patterns are sufficiently similar, regular parallel fringes will modulate the common Fraunhofer diffraction pattern of the compared samples. The regularity of the interference fringes is a measure of the similarity between the compared patterns. The sensitivity of the method is not disturbed by small absolute and relative displacements of test and reference signals. The effect of even small rotations is, however, severe. The effect of random noise is to reduce the contrast of the interference fringes.

© 1971 Optical Society of America

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References

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  1. A. Vander Lugt, IEEE Trans. Inform. Theory IT10, 139 (1964).
    [CrossRef]
  2. A. Vander Lugt, Appl. Opt. 6, 1221 (1967).
    [CrossRef]
  3. A. Vander Lugt, F. B. Rotz, Appl. Opt. 9, 215 (1970).
    [CrossRef]
  4. W. T. Cathey, J. G. Doidge, J. Opt. Soc. Am. 56, 1139 (1966).
    [CrossRef]
  5. J. Guild, Diffraction Gratings as Measuring Scales (Oxford U. P., London, 1960), Chaps. 3 and 4.
  6. V. Ascoli-Bartoli, A. De Angelis, M. Nardi, Appl. Opt. 8, 59 (1969).
    [CrossRef] [PubMed]
  7. L. Levi, Applied Optics (Wiley, New York, 1968), pp. 429–430.
  8. D. C. Burnham, Appl. Opt. 9, 2565 (1970).
    [CrossRef] [PubMed]

1970 (2)

1969 (1)

1967 (1)

1966 (1)

1964 (1)

A. Vander Lugt, IEEE Trans. Inform. Theory IT10, 139 (1964).
[CrossRef]

Appl. Opt. (4)

IEEE Trans. Inform. Theory (1)

A. Vander Lugt, IEEE Trans. Inform. Theory IT10, 139 (1964).
[CrossRef]

J. Opt. Soc. Am. (1)

Other (2)

J. Guild, Diffraction Gratings as Measuring Scales (Oxford U. P., London, 1960), Chaps. 3 and 4.

L. Levi, Applied Optics (Wiley, New York, 1968), pp. 429–430.

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Figures (8)

Fig. 1
Fig. 1

Optical system for pattern comparison.

Fig. 2
Fig. 2

(a) Fraunhofer diffraction pattern resulting from the comparison of identical letters c. (b) Fraunhofer diffraction pattern resulting from the comparison of c and z.

Fig. 3
Fig. 3

(a) Comparison of identical fingerprints. (The center of the diffraction pattern is in the lower left-hand corner in all illustrations of fingerprint comparisons.) (b) Comparison of different fingerprints.

Fig. 4
Fig. 4

Comparison of identical letters z. Direction of translation 45° to baseline.

Fig. 5
Fig. 5

Comparison of identical fingerprints with relative rotation of 0.05 rad.

Fig. 6
Fig. 6

Comparison of identical fingerprints with granular noise superimposed on one of the prints.

Fig. 7
Fig. 7

Comparison of partially similar patterns.

Fig. 8
Fig. 8

Comparison of identical fingerprints after averaging in the q direction with a cylindrical lens system.

Equations (13)

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S ( p , q ) = s ( x , y ) exp i ( p x + q y ) d x d y ,
ϕ = λ p / 2 π
ψ = λ q / 2 π .
s 2 ( x , y ) = s 1 ( x - d , y ) ,
S ( p , q ) = [ s 1 ( x , y ) + s 1 ( x - d , y ) ] exp i ( p x + q y ) d x d y = ( 1 + exp i p d ) S 1 ( p , q ) ,
S ( p , q ) S * ( p , q ) = 4 cos 2 ( p d / 2 ) · S 1 ( p , q ) S 1 * ( p , q ) .
p d = ( 2 n + 1 ) π
S 1 ( p cos θ + q sin θ , q cos θ - p sin θ ) .
S 1 ( p cos θ + q sin θ , q cos θ , - p sin θ ) S 1 ( p + q θ , q - p θ ) S 1 ( p , q ) + q θ [ S 1 / p ] - p θ [ S 1 / q ] .
p = 11 π / d .
ψ θ [ S 1 / ϕ ] - ϕ θ [ S 1 / ψ ] .
S ( p , q ) = [ s 1 ( x , y ) + s 1 ( x - d , y ) + m ( x , y ) ] · exp i ( p x + q y ) d x d y = ( 1 + exp i p d ) S 1 ( p , q ) + M ( p , q ) .
S ( p , q ) 2 = 4 cos 2 ( p d / 2 ) [ ( S 1 ( p , q ) 2 + Re S ( p , q ) M * ( p , q ) - Im S ( p , q ) M * ( p , q ) tan ( p d / 2 ) ] + M ( p , q ) 2 .

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