Abstract

We present an optical technique for measuring irregularities on a small local surface (≈λ/100). This new technique uses a narrow laser beam as a local probe. The probe beam interferes with a reference beam. We use a 90° phase delay on the reference beam to increase the sensitivity. We show that if the test surface vibrates laterally, the collected power of the interferogram encodes as amplitude modulations, on a sinusoidal temporal carrier, the local surface irregularities.

© 1998 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. M. Bennett, “Measurement of the rms roughness, autocovariance function and other statistical properties of optical surfaces using a FECO scanning interferometer,” Appl. Opt. 15, 2705–2721 (1976).
    [CrossRef] [PubMed]
  2. J. Mignot, C. Gorecki, “Measurement of surface roughness comparison between a defect of focus optical technique and the classical stylus technique,” Wear 87, 39–49 (1993).
    [CrossRef]
  3. J. C. Stover, S. A. Serati, “Calculation of surface statistics from light scatter,” Opt. Eng. 23, 406–412 (1984).
    [CrossRef]
  4. G. E. Sommargren, “Optical heterodyne profilometry,” Appl. Opt. 20, 610–618 (1981).
    [CrossRef] [PubMed]
  5. W. M. Shi, S.-P. Lim, K. S. Lee, “Surface roughness classification using pattern recognition theory,” Opt. Eng. 34, 1756–1760 (1995).
    [CrossRef]

1995 (1)

W. M. Shi, S.-P. Lim, K. S. Lee, “Surface roughness classification using pattern recognition theory,” Opt. Eng. 34, 1756–1760 (1995).
[CrossRef]

1993 (1)

J. Mignot, C. Gorecki, “Measurement of surface roughness comparison between a defect of focus optical technique and the classical stylus technique,” Wear 87, 39–49 (1993).
[CrossRef]

1984 (1)

J. C. Stover, S. A. Serati, “Calculation of surface statistics from light scatter,” Opt. Eng. 23, 406–412 (1984).
[CrossRef]

1981 (1)

1976 (1)

Bennett, J. M.

Gorecki, C.

J. Mignot, C. Gorecki, “Measurement of surface roughness comparison between a defect of focus optical technique and the classical stylus technique,” Wear 87, 39–49 (1993).
[CrossRef]

Lee, K. S.

W. M. Shi, S.-P. Lim, K. S. Lee, “Surface roughness classification using pattern recognition theory,” Opt. Eng. 34, 1756–1760 (1995).
[CrossRef]

Lim, S.-P.

W. M. Shi, S.-P. Lim, K. S. Lee, “Surface roughness classification using pattern recognition theory,” Opt. Eng. 34, 1756–1760 (1995).
[CrossRef]

Mignot, J.

J. Mignot, C. Gorecki, “Measurement of surface roughness comparison between a defect of focus optical technique and the classical stylus technique,” Wear 87, 39–49 (1993).
[CrossRef]

Serati, S. A.

J. C. Stover, S. A. Serati, “Calculation of surface statistics from light scatter,” Opt. Eng. 23, 406–412 (1984).
[CrossRef]

Shi, W. M.

W. M. Shi, S.-P. Lim, K. S. Lee, “Surface roughness classification using pattern recognition theory,” Opt. Eng. 34, 1756–1760 (1995).
[CrossRef]

Sommargren, G. E.

Stover, J. C.

J. C. Stover, S. A. Serati, “Calculation of surface statistics from light scatter,” Opt. Eng. 23, 406–412 (1984).
[CrossRef]

Appl. Opt. (2)

Opt. Eng. (2)

J. C. Stover, S. A. Serati, “Calculation of surface statistics from light scatter,” Opt. Eng. 23, 406–412 (1984).
[CrossRef]

W. M. Shi, S.-P. Lim, K. S. Lee, “Surface roughness classification using pattern recognition theory,” Opt. Eng. 34, 1756–1760 (1995).
[CrossRef]

Wear (1)

J. Mignot, C. Gorecki, “Measurement of surface roughness comparison between a defect of focus optical technique and the classical stylus technique,” Wear 87, 39–49 (1993).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Schematic diagram of the optical setup. Lenses L1 and L2 have the same focal length f. Lenses L1 and L2 perform the Fourier transform of the object and the reference beam, respectively. BS, beam splitter; M, mirror. The phase plate introduces a 90° delay in the reference beam to increase sensitivity. The output is proportional to the surface irregularities of the object.

Fig. 2
Fig. 2

Experimental roughness values obtained for three different arbitrary points of the object. The abscissa represents 22 measurements obtained in a length of 4 μm of the object that was scanned. The interval between each measured point is 0.1818 ± 0.02 nm. On the linear ordinate scale 1 represents λ/600.

Fig. 3
Fig. 3

Plot of Eq. (22) for several values of the amplitude of vibration of the object δ0. The values chosen for visualization purposes are as follows: f 0 = 5 × 104, f s = 0.05, A = 1. (a) δ0 = λ/50, (b) δ0 = λ/10, (c) δ0 = λ/5, (d) δ0 = λ/2. The value of x = 7.00.

Equations (22)

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

Ψ x ,   y ;   x 0 ,   y 0 = P π r 0 2 1 / 2 exp - x - x 0 2 + y - y 0 2 r 0 2 .
Ψ r x ,   y ;   x 0 ,   y 0 ;   t = Ψ x ,   y ;   x 0 ,   y 0 exp j 2 kh x ,   y ;   t .
Ψ r x ,   y ;   x 0 ,   y 0 ;   t = Ψ x ,   y ;   x 0 ,   y 0 1 + j 2 kh x ,   y ;   t .
Ψ f ξ ,   η ;   x 0 ,   y 0 ;   t = 1 j λ f - -   Ψ r x ,   y ;   x 0 ,   y 0 ;   t × exp - j   2 π λ f x ξ + y η d x d y .
Ψ f ξ ,   η ;   x 0 ,   y 0 ;   t = P π r 0 2 1 / 2 1 j λ f × π r 0 2 exp - j   2 π λ f x 0 ξ + y 0 η exp - ξ 2 + η 2 R 0 2 + j 2 k   - - exp - x - x 0 2 + y - y 0 2 r 0 2 h x ,   y ;   t exp - j   2 π λ f x ξ + y η d x d y ,
Ψ R ξ ,   η ;   x 0 ,   y 0 = P π r 0 2 1 / 2 1 j λ f j π r 0 2 × exp - j   2 π λ f x 0 ξ + y 0 η exp - ξ 2 + η 2 R 0 2 .
I ξ ,   η ;   x 0 ,   y 0 ;   t = Ψ f + Ψ R Ψ f + Ψ R * = | Ψ f | 2 + | Ψ R | 2 + 2   Re Ψ f Ψ R * ,
P D x 0 ,   y 0 ;   t = - -   I ξ ,   η ;   x 0 ,   y 0 ;   t d ξ d η .
P D x 0 ,   y 0 ;   t = P π r 0 2 π r 0 2 2 + 4 k   - - × exp - 2   x - x 0 2 + y - y 0 2 r 0 2 h x ,   y ;   t d x d y .
T x ,   y = P   4 k π r 0 2 exp - 2   x 2 + y 2 r 0 2 .
P D x 0 ,   y 0 ;   t = P 2 + - - × T x - x 0 ,   y - y 0 h x ,   y ;   t d x d y .
h x ,   y ;   t = h x + δ 0   cos 2 π f s t ,   y .
h x ,   y ;   t = h x ,   y + h x ,   y x   δ 0   cos 2 π f s t .
P D x 0 ,   y 0 ;   t = P 2 + - -   T x - x 0 ,   y - y 0 × h x ,   y d x d y + δ 0   cos 2 π f s t - - × T x - x 0 ,   y - y 0 h x ,   y x d x d y .
P Dt x 0 ,   y 0 ;   t = 8 P λ r 0 2   δ 0   cos 2 π f s t - - × exp - 2   x - x 0 2 + y - y 0 2 r 0 2 × h x ,   y x d x d y .
P Dt x 0 ,   y 0 ;   t = 8 P λ r 0 2   δ 0 × cos 2 π f s t x 0 - r 0 2 x 0 + r 0 2 y 0 - r 0 2 y 0 + r 0 2 h x ,   y x d x d y .
P Dt x 0 ,   y 0 ;   t = 8 P λ r 0 2   δ 0 × cos 2 π f s t x 0 - r 0 2 x 0 + r 0 2 y 0 - r 0 2 y 0 + r 0 2 d f x d x   g y d x d y .
P Dt x 0 ,   y 0 ;   t = 8 P λ r 0 2   δ 0   cos 2 π f s t f x 0 - r 0 2 - f x 0 + r 0 2 G x 0 - r 0 2 - G x 0 + r 0 2 .
P Dt x 0 ,   y 0 ;   t = 16 P λ   δ 0   cos 2 π f s t h x ,   y x | x = x 0 ,   y = y 0 .
h x ,   y ,   t = h x + δ 0   cos 2 π   f s t .
h x ,   y = A   cos 2 π x / d .
h x ,   y ,   t = A   cos 2 π x + δ 0   cos 2 π f s t / d .

Metrics