Abstract

A mathematical method to identity aspheric surfaces of revolution is described. A spherical mechanical probe contacts the surface to be measured in the profilometric apparatus used. The method corrects for tilt, decentering, and the use of a non-point contact probe.

© 1998 Optical Society of America

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References

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  1. R. Palum, “Surface Profile Error Measurement for Small Rotationally Symmetric Surfaces,” Proc. SPIE966, (SPIE Press, Bellingham, Wash., 1988), pp. 138–149.
  2. D. P. Hamblen, M. R. Jones, “Lens curvature measurements by shadow projection profilometry,” Eng. Lab. Notes in Opt. & Phot. News 6(2), (1995).

1995 (1)

D. P. Hamblen, M. R. Jones, “Lens curvature measurements by shadow projection profilometry,” Eng. Lab. Notes in Opt. & Phot. News 6(2), (1995).

Hamblen, D. P.

D. P. Hamblen, M. R. Jones, “Lens curvature measurements by shadow projection profilometry,” Eng. Lab. Notes in Opt. & Phot. News 6(2), (1995).

Jones, M. R.

D. P. Hamblen, M. R. Jones, “Lens curvature measurements by shadow projection profilometry,” Eng. Lab. Notes in Opt. & Phot. News 6(2), (1995).

Palum, R.

R. Palum, “Surface Profile Error Measurement for Small Rotationally Symmetric Surfaces,” Proc. SPIE966, (SPIE Press, Bellingham, Wash., 1988), pp. 138–149.

Eng. Lab. Notes in Opt. & Phot. News (1)

D. P. Hamblen, M. R. Jones, “Lens curvature measurements by shadow projection profilometry,” Eng. Lab. Notes in Opt. & Phot. News 6(2), (1995).

Other (1)

R. Palum, “Surface Profile Error Measurement for Small Rotationally Symmetric Surfaces,” Proc. SPIE966, (SPIE Press, Bellingham, Wash., 1988), pp. 138–149.

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Figures (3)

Figure 1
Figure 1

The profile metric apparatus that was used.

Figure 2
Figure 2

Schematic of the measuring method with a non-point probe.

Figure 3
Figure 3

Difference in microns between the fitted conicoid and the data taken with Augen’s profilometer.

Equations (5)

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x i = x m + R s sin θ , z i = z m + R s   ( 1 cos θ ) ,   and tan θ = d z m ( x m ) / d x m ,
1 c = 1 2 Σ z i 3 Σ x i 2 z i 2 Σ x i 2 z i Σ z i 4 ( Σ z i 3 ) 2 Σ z i 2 Σ z i 4 ε = Σ z i 2 Σ x i 2 z i 2 Σ x i 2 z i Σ z i 3 ( Σ z i 3 ) 2 Σ z i 2 Σ z i 4
X 2 + B X Z + C Z 2 + D X + E Z   +   F = 0 ,
B = ( 2 m / φ ) ,   C = β / φ , D = 2 / φ ( m z 0 x 0 + R sin θ ) , E = 2 / φ ( β z 0 + m x 0 R cos θ ) ,   and F = 1 / φ ( φ x 0 2 2 m x 0 z 0 + β z 0 2 ) 2 R / φ ( x 0 sin θ z 0 cos θ ) ,
( x y ) = ( cos θ   sin θ sin θ cos θ ) ( X x 0 Z z 0 ) .

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