Abstract

Tracing of a random profile with a mechanical profiler with a spherical tipped stylus has been investigated by means of computer simulation. It is shown that the fractional measuring errors of rms roughness depend on only the ratio of rms roughness σ to the stylus tip radius r and the ratio of rms roughness to the 1/e correlation length ρc. The ratios σ/r were in the range of 0.005–0.05 and the ratios σ/ρc were equal to 0.028 and 0.048.

© 1997 Optical Society of America

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References

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  1. K. A. O’Donnell, “Effects of finite stylus width in surface contact profilometry,” Appl. Opt. 32, 4922–4928 (1993).
    [CrossRef] [PubMed]
  2. V. Radhakrishnan, “Effect of stylus radius on the roughness values measured with tracing stylus instruments,” Wear 16, 325–335 (1970).
    [CrossRef]
  3. V. S. Luk’yanov, O. K. Komorovskii, “Error of determining surface roughness parameters by feeler probes,” Meas. Tech. (USSR) 19, 1707–1710 (1976).
  4. J. M. Bennett, J. H. Dancy, “Stylus profiling instrument for measuring statistical properties of smooth optical surfaces,” Appl. Opt. 20, 1785–1802 (1981).
    [CrossRef] [PubMed]
  5. V. S. Luk’yanov, Y. A. Rudzit, Parameters of Surface Roughness (in Russian) (Publishing House of Standards, Moscow, 1979).

1993 (1)

1981 (1)

1976 (1)

V. S. Luk’yanov, O. K. Komorovskii, “Error of determining surface roughness parameters by feeler probes,” Meas. Tech. (USSR) 19, 1707–1710 (1976).

1970 (1)

V. Radhakrishnan, “Effect of stylus radius on the roughness values measured with tracing stylus instruments,” Wear 16, 325–335 (1970).
[CrossRef]

Bennett, J. M.

Dancy, J. H.

Komorovskii, O. K.

V. S. Luk’yanov, O. K. Komorovskii, “Error of determining surface roughness parameters by feeler probes,” Meas. Tech. (USSR) 19, 1707–1710 (1976).

Luk’yanov, V. S.

V. S. Luk’yanov, O. K. Komorovskii, “Error of determining surface roughness parameters by feeler probes,” Meas. Tech. (USSR) 19, 1707–1710 (1976).

V. S. Luk’yanov, Y. A. Rudzit, Parameters of Surface Roughness (in Russian) (Publishing House of Standards, Moscow, 1979).

O’Donnell, K. A.

Radhakrishnan, V.

V. Radhakrishnan, “Effect of stylus radius on the roughness values measured with tracing stylus instruments,” Wear 16, 325–335 (1970).
[CrossRef]

Rudzit, Y. A.

V. S. Luk’yanov, Y. A. Rudzit, Parameters of Surface Roughness (in Russian) (Publishing House of Standards, Moscow, 1979).

Appl. Opt. (2)

Meas. Tech. (USSR) (1)

V. S. Luk’yanov, O. K. Komorovskii, “Error of determining surface roughness parameters by feeler probes,” Meas. Tech. (USSR) 19, 1707–1710 (1976).

Wear (1)

V. Radhakrishnan, “Effect of stylus radius on the roughness values measured with tracing stylus instruments,” Wear 16, 325–335 (1970).
[CrossRef]

Other (1)

V. S. Luk’yanov, Y. A. Rudzit, Parameters of Surface Roughness (in Russian) (Publishing House of Standards, Moscow, 1979).

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Figures (5)

Fig. 1
Fig. 1

Scheme of profile tracing.

Fig. 2
Fig. 2

Part of original profile. The rms roughness is 0.05 µm and σ/ρc is 0.028.

Fig. 3
Fig. 3

Part of traced profile. The stylus tip radius is 2 µm. The fractional measuring error of rms roughness is 0.002.

Fig. 4
Fig. 4

Part of traced profile. The stylus tip radius is 10 µm. The fractional measuring error of rms roughness is 0.041.

Fig. 5
Fig. 5

Dependence of fractional measuring errors α on the ratios σ/r and σ/ρc: solid curve, σ/ρc = 0.048; dashed curve, σ/ρc = 0.028.

Tables (2)

Tables Icon

Table 1 Profile Lengths and Spacing between Data Points in Profiles

Tables Icon

Table 2 Values of Ratios σ/r and σ/ρc and Corresponding Values of rms Roughness and Stylus Tip Radii

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

ηξ=-r2-ξ21/2,
ηx0i×x1+r+h-y0x0i=lmin,
y1x1=y0x0i+r2-x0i-x121/2.
Bρ=σ21+γρ2,
yn=k=-ppckfn-k,
Ck=2σβ3/21--1k exp-β/2/β2+2πk2,

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