Abstract

An ultrahigh accuracy 3-D profilometer using a laser heterodyne interferometer has been developed. The profiles of aspheric lenses and their molds have been measured. It can measure not only the rectangular coordinates but also the polar coordinates of the surface profile. The measuring accuracy of each of the three axes is 0.01–0.05 μm if the inclination of the investigated surface is less than ±25°. The accuracy of the polar coordinate measurement is also better than 0.05 μm when the inclination of the aspheric surface is less than ±55°. The dynamic range of the X-Y-Z measurement is 40 × 40 × 20 (mm).

© 1987 Optical Society of America

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References

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  1. K. Yoshizumi, Y. Okino, “Precise Measuring System for Aspheric Surfaces,” Kogaku (Jpn. J. Opt.) 12, 450 (1983).
  2. K. Yoshizumi, Y. Okino, “Precise Measuring Method for Aspheric Surfaces Using a Laser Heterodyne Interferometer,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper FD1.
  3. D. Visser, T. G. Gijsbers, R. A. M. Jorna, “Molds and Measurements for Replicated Aspheric Lenses for Optical Recording,” Appl. Opt. 24, 1848 (1985).
    [CrossRef] [PubMed]
  4. Y. Fainman, E. Lenz, J. Shamir, “Optical Profilometer: a New Method for High Sensitivity and Wide Dynamic Range,” Appl. Opt. 21, 3200 (1982).
    [CrossRef] [PubMed]
  5. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8.
  6. H. Takasaki, N. Umeda, M. Tsukiji, “Stabilized Transverse Zeeman Laser as a New Light Source for Optical Measurement,” Appl. Opt. 19, 435 (1980).
    [CrossRef] [PubMed]

1985 (1)

1983 (1)

K. Yoshizumi, Y. Okino, “Precise Measuring System for Aspheric Surfaces,” Kogaku (Jpn. J. Opt.) 12, 450 (1983).

1982 (1)

1980 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8.

Fainman, Y.

Gijsbers, T. G.

Jorna, R. A. M.

Lenz, E.

Okino, Y.

K. Yoshizumi, Y. Okino, “Precise Measuring System for Aspheric Surfaces,” Kogaku (Jpn. J. Opt.) 12, 450 (1983).

K. Yoshizumi, Y. Okino, “Precise Measuring Method for Aspheric Surfaces Using a Laser Heterodyne Interferometer,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper FD1.

Shamir, J.

Takasaki, H.

Tsukiji, M.

Umeda, N.

Visser, D.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8.

Yoshizumi, K.

K. Yoshizumi, Y. Okino, “Precise Measuring System for Aspheric Surfaces,” Kogaku (Jpn. J. Opt.) 12, 450 (1983).

K. Yoshizumi, Y. Okino, “Precise Measuring Method for Aspheric Surfaces Using a Laser Heterodyne Interferometer,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper FD1.

Appl. Opt. (3)

Kogaku (Jpn. J. Opt.) (1)

K. Yoshizumi, Y. Okino, “Precise Measuring System for Aspheric Surfaces,” Kogaku (Jpn. J. Opt.) 12, 450 (1983).

Other (2)

K. Yoshizumi, Y. Okino, “Precise Measuring Method for Aspheric Surfaces Using a Laser Heterodyne Interferometer,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1983), paper FD1.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980), Chap. 8.

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Figures (19)

Fig. 1
Fig. 1

Measurement of a flat mirror surface. Two measurements were made in the same path. Repeatability and linearity proved to be <0.01 μm.

Fig. 2
Fig. 2

Linearity of the X-Y stage movement while measuring the flat mirror shown in Fig. 1.

Fig. 3
Fig. 3

Schematic configuration of Z-axis measuring optics. Only the measured object and reference mirror are fixed on the table during the X-Y-Z measurement. The other elements move simultaneously. But in polar coordinate measuring, only the measured object rotates around the X axis.

Fig. 4
Fig. 4

Measuring geometry of X-Y-Z and polar dR-Q measurement.

Fig. 5
Fig. 5

Concept for the incline servo. Flat wavefronts H1 and H3 of parallel rays become spherical ones H2 and H4 after transmitting objective and servo lenses. The servo lens moves from the dotted to the solid line according to the inclination of the measured object. The numerical aperture (N.A.) of the objective lens is 0.6, so direction of the rim ray becomes 36°.

Fig. 6
Fig. 6

Schematic diagram of the profilometer.

Fig. 7
Fig. 7

Measurement of a precise 9.525-mm sphere whose shape differs by <0.02 μm from an ideal sphere. Measured ±2 mm from the top of the sphere twice in the Y-direction, a portion of the measured numerical data is shown. The X, Y, and Z values are the raw data. Zd is the difference from the ideal sphere R = 4.7625 mm. Inclined angles of the surface are ±25° at Y = ±2 mm. Measuring accuracy of these data was within ±0.05 μm.

Fig. 8
Fig. 8

A 3-D graph showing the measurement of a 9.525-mm sphere scanned in the X and Y directions, respectively.

Fig. 9
Fig. 9

Polar coordinate measurement of a 9.525-mm sphere. The measured range is ±40°. A portion of the measured numerical data is also shown.

Fig. 10
Fig. 10

Measurement of the molds of an aspheric lens for an optical disk player; N.A. = 0.5. Differences from the design spheres are plotted: (1) polar measurement of the mold of the first surface; (2) rectangular measurement of the mold of the second surface.

Fig. 11
Fig. 11

Measurement of the molds of the aspheric lens. Differences from the design data are plotted. The raw data, shown in Fig. 10, are dealt with by a computerized alignment program. (1) The first surface of the mold. Polar and rectangular, X-Z and Y-Z, measured data are plotted in the graph. (2) Rectangular measurement of the mold of the second surface.

Fig. 12
Fig. 12

Measurement of a glass lens which is formed by the molds mentioned in Fig. 11. Differences from the design data are plotted. These forms are inverted and resemble each other. (1) The first surface of the mold. Polar and rectangular, X-Z and Y-Z, measured data are plotted in the graph. (2) Rectangular measurement of the mold of the second surface.

Fig. 13
Fig. 13

Test of this lens using a Twyman-Green interferogram measured in transmission. The shape and dimension of the wavefront aberration correspond closely with the measured surface deviation from the design data of the first surfaces of the mold and the lens shown in Figs. 11(1) and 12(1).

Fig. 14
Fig. 14

Measurement of the improved first surface of the mold. Deviation from the design data is <0.05 μm.

Fig. 15
Fig. 15

Test of the improved lens using the interferogram measured in transmission.

Fig. 16
Fig. 16

Cat’s eye measurement of the 9.525 mm sphere measured from the position of the objective lens. The vertical axis shows Zd. The amount of Zd indicates the focus error of the profilometer. The measuring error of the direct measurement was ten times smaller than the focus error.

Fig. 17
Fig. 17

When the focus error is δ and the inclined angle of the surface is θ, the measuring error ΔZ becomes δ(1 − cosθ).

Fig. 18
Fig. 18

Comparison of the ASP cat’s eye measurement of a lathed brass surface and a measurement using a contact stylus gauge with a 1-μm point.

Fig. 19
Fig. 19

Photograph of the ASP.

Equations (4)

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I 1 ( ρ ) = I 0 exp [ - ( 2 π N A e ρ / λ 1 ) 2 ] ,
I 2 ( ρ ) = I 0 B e sinc 2 ( 2 π N A · ρ / λ 2 ) ,
Z d = Z + R ± ( R 2 - X 2 - Y 2 ) 1 / 2 .
Δ Z = δ ( 1 - cos θ ) ,

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