Abstract

A fast scanning method for one-dimensional surface profile measurement is proposed. The profile is measured by integration of a slope distribution of the surface obtained from angular deflection of a scanning laser beam. A scanning optical system that consists principally of a spherical concave mirror and a rotating scanner mirror has reasonably low cost and is insensitive to mechanical vibration because of its high-speed scanning, of the order of milliseconds. A surface profile of a polygonal mirror along a 5-mm width was measured with the scanning method and with an interferometer. The root-mean-square difference between the two measured results is 0.98 nm.

© 2004 Optical Society of America

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References

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  1. F. M. Smolka, T. P. Caudell, “Surface profile measurement and angular deflection monitoring using a scanning laser beam: a noncontact method,” Appl. Opt. 17, 3284–3289 (1978).
    [CrossRef] [PubMed]
  2. P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
    [CrossRef]
  3. I. Weingärtner, M. Schulz, C. Elster, “Novel scanning technique for ultraprecise measurement of topography,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 306–317 (1999).
    [CrossRef]
  4. J. D. Evans, “Method for approximating the radius of curvature of small concave spherical mirrors using a He-Ne laser,” Appl. Opt. 10, 995–996 (1971).
  5. M. V. Klein, Optics (Wiley, New York, 1970).

1978

1971

Caudell, T. P.

Church, E. L.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
[CrossRef]

Elster, C.

I. Weingärtner, M. Schulz, C. Elster, “Novel scanning technique for ultraprecise measurement of topography,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 306–317 (1999).
[CrossRef]

Evans, J. D.

Feng, S. K.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
[CrossRef]

Klein, M. V.

M. V. Klein, Optics (Wiley, New York, 1970).

Liu, W.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
[CrossRef]

Qian, S.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
[CrossRef]

Schulz, M.

I. Weingärtner, M. Schulz, C. Elster, “Novel scanning technique for ultraprecise measurement of topography,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 306–317 (1999).
[CrossRef]

Smolka, F. M.

Takacs, P. Z.

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
[CrossRef]

Weingärtner, I.

I. Weingärtner, M. Schulz, C. Elster, “Novel scanning technique for ultraprecise measurement of topography,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 306–317 (1999).
[CrossRef]

Appl. Opt.

Other

P. Z. Takacs, S. K. Feng, E. L. Church, S. Qian, W. Liu, “Long trace profile measurements on cylindrical aspheres,” in Advances in Fabrication and Metrology for Optics and Large Optics, J. B. Arnold, R. E. Parks, eds., Proc. SPIE966, 354–364 (1988).
[CrossRef]

I. Weingärtner, M. Schulz, C. Elster, “Novel scanning technique for ultraprecise measurement of topography,” in Optical Manufacturing and Testing III, H. P. Stahl, ed., Proc. SPIE3782, 306–317 (1999).
[CrossRef]

M. V. Klein, Optics (Wiley, New York, 1970).

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Figures (11)

Fig. 1
Fig. 1

Basic schematic for measurement of a one-dimensional surface profile by detection of angular deflection.

Fig. 2
Fig. 2

Optical system for scanning a beam by use of lens LN and scanner mirror SM.

Fig. 3
Fig. 3

Optical system for scanning a beam by use of spherical concave mirror CM and scanner mirror SM, where R is the radius of curvature of the concave mirror.

Fig. 4
Fig. 4

Introduction of plane mirror and sample surface S into Fig. 3. The PM and the S are put into incident path SM-CM and reflected path CM-SM, respectively.

Fig. 5
Fig. 5

Separation of sample surface S and plane mirror PM in Fig. 4. S is detached from the PM by ΔL, with the distance between CM and S maintained at R/2.

Fig. 6
Fig. 6

Optical system modified from Fig. 5. CM is given a displacement and a rotation. PM and S are given different rotations. Beam paths PM-CM and CM-S are inclined toward the y direction.

Fig. 7
Fig. 7

Displacement of the beam spot on detecting plane DP by the aberration of spherical concave mirror CM when sample surface S is flat. The center of curvature of CM is at origin O of a Cartesian-coordinate system. Rotation axis A of scanner mirror SM and DP is placed at conjugate points of CM.

Fig. 8
Fig. 8

Deflection of the beam spot on detecting plane DP. Sample surface S is inserted into beam path CM-DP. The traveling direction of the reflected beam is changed at point P owing to the slope θ of surface S.

Fig. 9
Fig. 9

Effect of positioning error of sample surface S. The position of S is shifted by δ l .

Fig. 10
Fig. 10

Profile F ST obtained from measurement of the standard plane with λ/20. Profile F ST shows the influence of the surface distortion of optical components used in the setup.

Fig. 11
Fig. 11

Measured surface profiles of a polygonal mirror.

Equations (15)

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dfxdx=tan θxθx.
12l  Δxdx= θxdx=fx.
L0r-L0i=2ΔL.
1L0i+1L0r=2R,
zD=-d/1-2d<0
xabr=-d2φ3,
β=1-2dφ.
2ΔL=-zD+d2d.
xθ=l tan β-l tan2θ+β+xabr,
xθ=-2lθ-2lθφ2+xabr,
φ2Rγ<w.
xθ=l-δltan β-l-δltan2θ+β+xabr.
xobs=-2l+δlθ-2l+δlθφ2-d2φ3-2δlφ,
xφl1-2d+lφ2,
ifi-αfCi2,

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