Abstract

A new class of target for object identification and mask alignment is described. It has some fractal properties and is designed to be viewed by an optical correlator.

© 1995 Optical Society of America

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References

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  1. R. D. Juday, “Three-dimensional moiré pattern alignment,” U.S. patent5,052,807 (October1, 1991).
  2. Y.-C. Park, S.-W. Kim, Appl. Opt. 33, 5171 (1994).
    [CrossRef] [PubMed]

1994

Juday, R. D.

R. D. Juday, “Three-dimensional moiré pattern alignment,” U.S. patent5,052,807 (October1, 1991).

Kim, S.-W.

Park, Y.-C.

Appl. Opt.

Other

R. D. Juday, “Three-dimensional moiré pattern alignment,” U.S. patent5,052,807 (October1, 1991).

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Figures (7)

Fig. 1
Fig. 1

Dimensions and coordinates in the Cartesian image.

Fig. 2
Fig. 2

Dimensions and coordinates in the log-polar image.

Fig. 3
Fig. 3

Wrapping the Cartesian image into the log-polar image.

Fig. 4
Fig. 4

Dapple made from a low-resolution Cartesian image (64 × 64), so that the Cartesian pixels are visible in the log-polar image. Note that the bricks are essentially square because the mapping is conformal.

Fig. 5
Fig. 5

Dapple made with a high-resolution (512 × 512) Cartesian image, σx = σy = 32, so there is the same resolution radially as azimuthally.

Fig. 6
Fig. 6

Same as Fig. 5, but with σx = 8, σy = 32, so the pattern is relatively insensitive to magnification differences.

Fig. 7
Fig. 7

Same as Figs. 5 and 6, but with σx = 32, σy = 8, so the pattern is relatively insensitive to rotational differences.

Equations (4)

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ρ k 2 ( i , j ) = ( C x k + 1 - i ) 2 σ x 2 + ( C y k + 1 - j ) 2 σ y 2 ,
C x k { 0 , DIM 1 } ,             C y k { 0 , DIM2 } .
factor ( i , j ) = k = 1 4 exp [ - ρ k 2 ( i , j ) ] .
i = 1 + ln  r - ln  a ln ( DIM 3 / 2 ) ( DIM 1 - 1 ) , j = 1 + atan 2 ( y , x ) 2 π ( DIM2 - 1 ) ,

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