Abstract

Defects in rectangular x-y axis decomposable periodic patterns are found to be detected by an omnidirectional (r-θ axis decomposable) spatial filter optical system, where use is made of the spectral difference between periodic patterns and defects. A novel omnidirectional spatial filter, which has bandpass characteristics, is designed to block all the repetitive periodic regular pattern spectra and pass the defect information carrying spectra. According to a computer simulation, the minimum detectable defect size using this optical system is about one-twentieth that of the periodic pattern pitch. This novel optical system is characterized by its ability to detect defects at any location and rotation (shift and rotation immunity of the optical system) and also to be insensitive to object magnification by the frequency domain operation characteristics. This filter application is not limited to 2-D rectangular periodic-pattern-defects detection, but defects in 1-D or skew periodic patterns are also detected by the same filter.

© 1980 Optical Society of America

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References

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  1. L. S. Watkins, Proc. IEEE 57, 1634 (1969).
    [CrossRef]
  2. H. Dammann, M. Kock, Opt. Commun. 3, 251(1971).
    [CrossRef]
  3. N. M. Axelrod, Proc. IEEE 60, 447 (1972).
    [CrossRef]
  4. A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
    [CrossRef]

1973 (1)

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

1972 (1)

N. M. Axelrod, Proc. IEEE 60, 447 (1972).
[CrossRef]

1971 (1)

H. Dammann, M. Kock, Opt. Commun. 3, 251(1971).
[CrossRef]

1969 (1)

L. S. Watkins, Proc. IEEE 57, 1634 (1969).
[CrossRef]

Axelrod, N. M.

N. M. Axelrod, Proc. IEEE 60, 447 (1972).
[CrossRef]

Dammann, H.

H. Dammann, M. Kock, Opt. Commun. 3, 251(1971).
[CrossRef]

Flamholz, A. L.

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

Frost, H. A.

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

Kock, M.

H. Dammann, M. Kock, Opt. Commun. 3, 251(1971).
[CrossRef]

Watkins, L. S.

L. S. Watkins, Proc. IEEE 57, 1634 (1969).
[CrossRef]

IBM J. Res. Dev. (1)

A. L. Flamholz, H. A. Frost, IBM J. Res. Dev. 17, 509 (1973).
[CrossRef]

Opt. Commun. (1)

H. Dammann, M. Kock, Opt. Commun. 3, 251(1971).
[CrossRef]

Proc. IEEE (2)

N. M. Axelrod, Proc. IEEE 60, 447 (1972).
[CrossRef]

L. S. Watkins, Proc. IEEE 57, 1634 (1969).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Novel coherent light-defect optical detection system. The object placed at the front focal plane of the first lens and illuminated by a coherent light makes its Fourier pattern at the back focal plane of the lens. An annular filter at the focal plane blocks all the image information and permits only defect information to pass. The defect pattern is mapped at the back focal plane of the second Fourier transform lens.

Fig. 2
Fig. 2

Omnidirectional filter design principle. A pitch p regular 1-D periodic pattern has a periodic Fourier pattern (a) of pitch λf/p, where p is the object pattern pitch, f is the lens focal length, and λ is the coherent light wavelength. When an object has 2-D patterns, the Fourier image is also expressed as the product of the above formula. This pattern will be changed to a circular pattern after subsequent incremental rotations. The simplest annular bandpass filter, whose passband is the area between the zeroth- and first-order diffracted light positions of the periodic object, passes almost all the defect information and blocks all the regular pattern information to detect defects efficiently, because the defect spectral profile is Gaussian, centered at dc. (b) Number of spots per centimeter in a linear array.

Fig. 3
Fig. 3

Fourier pattern for a rectangular periodic pattern. (a) A rectangular periodic pattern (a grid) has a periodic Fourier pattern as depicted in Eq. (1). (b) When the pattern in real space is rotated, the corresponding Fourier pattern rotates by the same amount, whose traces give rise to coaxial rings.

Fig. 4
Fig. 4

Annular filter experimental results. Various kinds of defects in periodic patterns [(a-1), (a-2)] can be detected by the optical system with this novel filter optical system that uses a single passband filter (Fig. 1) to give the results shown in (b-1), (b-2), where N is about 50.

Fig. 5
Fig. 5

Filter rotation immunity property. The sample rectangular object with defects, whose filtered pattern is shown in (a), is rotated six times (60° each time). The multiply exposed filtered image (b) is obtained where defects in any direction give an equal intensity level.

Fig. 6
Fig. 6

Rotationally symmetric bandpass filter computer simulation. The outputs from an annular bandpass filter, whose passband is between r1 and r0, are simulated by a computer where rectangular defect areas are varied in scale.

Fig. 7
Fig. 7

Annular filter PSF. The computer simulation is made to obtain the annular filter response function, the PSF. Both analytical solutions given by Eq. (4), where n is assumed to be 1, and corresponding approximated solution [Eq. (5)] are plotted.

Fig. 8
Fig. 8

Modified annular filter optical system for automatic inspection. When the optical inspection system (Fig. 1) is modified, where the object is imaged on the output plane and the spatial filter is inserted at the Fourier plane between the imaging lens and the output plane, the 2-D detector can be replaced by a point detector like a photomultiplier, i.e., even defects in large area objects can be detected by a point detector with high SNR.

Fig. 9
Fig. 9

Defect scanning signal from a point detector. A 2-D periodic pattern with defects is rotated in the optics shown in Fig. 8. Data from a point detector (a photomultiplier) show low shading noise and high contrast, as displayed on a CRT. This photograph shows a single scanning line.

Equations (7)

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( m λ f / p x ) × ( n λ f / p y ) ,
d m , n = λ f [ ( m p x ) 2 + ( n p y ) 2 ] 1 / 2 .
d m , n = λ f p ( m 2 + n 2 ) 1 / 2 .
i = 1 2 n + 1 r i + 1 J 1 ( 2 π r i + 1 ξ ρ ) r i J 1 ( 2 r i ξ ρ ) ξ ρ ,
r 2 J 1 ( 2 π r 2 ξ ρ ) ξ ρ .
i = 3 2 n + 1 2 π ( r i + 1 r i ) r i J 0 ( 2 π r 1 ξ ρ ) ,
r 2 J 1 ( 2 π r 2 ξ ρ ) / ξ ρ + i = 3 2 n + 1 2 π ( r i + 1 r i ) r i J 0 ( 2 π r i ξ ρ ) ,

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