Abstract

Earlier workers have noticed that high-pass filtering produces a sharp dark line in precisely the location of the geometrical image of an edge. They proposed using this fact as an aid in measuring linewidth in microscopy but found that the other edge of the line caused significant error. In this paper, I examine that error as a function of normalized linewidth and normalized spatial-filter width and find that it may be limited to ±5% or so, provided that the spatial filter subtends between 0.25 and 0.3× the numerical aperture of the objective and that the linewidth exceeds about twice the resolution limit.

© 1983 Optical Society of America

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References

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  1. K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).
  2. R. E. Swing, “The theoretical basis of a new method for the accurate measurement of small line-widths,” in Proc. SPIE, Vol. 80, Developments in Semiconductor Microlithography, pp. 65–77 (1976).
    [CrossRef]
  3. P. J. S. Hutzler, “Spatial frequency filtering and its application to microscopy,” Appl. Opt. 16, 2264–2272 (1977).
    [CrossRef] [PubMed]
  4. M. Young, Optics and Lasers, An Engineering Physics Approach (Springer, New York, 1977), Chap. 6.
  5. M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions, Nat. Bur. Stds. (U.S.), Appl. Math. Series, Vol. 55, 1964 (reprinted by Dover, New York, 1965), Sect. 5.2, eqs. 1, 14, 36, 37.

1977 (1)

1976 (1)

R. E. Swing, “The theoretical basis of a new method for the accurate measurement of small line-widths,” in Proc. SPIE, Vol. 80, Developments in Semiconductor Microlithography, pp. 65–77 (1976).
[CrossRef]

1968 (1)

K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).

Birch, K. G.

K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).

Hutzler, P. J. S.

Swing, R. E.

R. E. Swing, “The theoretical basis of a new method for the accurate measurement of small line-widths,” in Proc. SPIE, Vol. 80, Developments in Semiconductor Microlithography, pp. 65–77 (1976).
[CrossRef]

Young, M.

M. Young, Optics and Lasers, An Engineering Physics Approach (Springer, New York, 1977), Chap. 6.

Appl. Opt. (1)

Developments in Semiconductor Microlithography (1)

R. E. Swing, “The theoretical basis of a new method for the accurate measurement of small line-widths,” in Proc. SPIE, Vol. 80, Developments in Semiconductor Microlithography, pp. 65–77 (1976).
[CrossRef]

Opt. Acta (1)

K. G. Birch, “A spatial frequency filter to remove zero frequency,” Opt. Acta 15, 113–127 (1968).

Other (2)

M. Young, Optics and Lasers, An Engineering Physics Approach (Springer, New York, 1977), Chap. 6.

M. Abramowitz, I. A. Stegun, Eds. Handbook of Mathematical Functions, Nat. Bur. Stds. (U.S.), Appl. Math. Series, Vol. 55, 1964 (reprinted by Dover, New York, 1965), Sect. 5.2, eqs. 1, 14, 36, 37.

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Figures (4)

Fig. 1
Fig. 1

Filtered images of a single edge normalized to incident intensity: (left) w = 0.2; (right) w = 0.4. Positions of secondary zeros have shifted, and secondary maxima have increased in intensity.

Fig. 2
Fig. 2

Images of slit whose width is two resolution limits. Upper left–no filtering. Upper right–w = 0.2; apparent linewidth is 2.16, not 2. Lower left–w = 0.4; apparent linewidth is 1.68. Lower right–w = 0.6; apparent linewidth is 1.36, and third and fourth maxima are now significant.

Fig. 3
Fig. 3

Percent error as a function of normalized spatial-filter width for five different linewidths: — — —, linewidth equals 2 resolution limits; – – – – –, 3; - - - - -, 4; —, 5; and …, 10.

Fig. 4
Fig. 4

Approximate envelopes of a complete set of curves like those in Fig. 3: —, all linewidths of ≥2 resolution limits; - - - - - - -, ≥3 resolution limits.

Equations (4)

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π E ( x ) = S i ( π x ) - S i ( π x / w ) ,
S i ( z ) = 0 z ( sin t / t ) d t .
π 2 I ( x ) = [ E ( x ) + E ( x + S ) ] 2 ,
e = ( S - S ) / S ;

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