Abstract

Projection fringe interferometry provides a useful technique for nondestructive surface analysis. Two beam interferometric fringes were projected onto a block of aluminum whose surface had various types of grooves cut into it. The fringes were digitized and analyzed via an automatic fringe tracking algorithm. Three-dimensional topographical maps of the surface’s microstructure are presented together with a statistical analysis of surface parameters including average roughness, height distributions, and the autocorrelation function.

© 1988 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. H. Rowe, W. T. Welford, “Surface Topography of Nonoptical Surfaces by Projected Interference Fringes,” Nature London 216, 786 (1967).
    [CrossRef]
  2. W. T. Welford, “Some Applications of Projected Interference Fringes,” Opt. Acta 16, 331 (1969).
  3. S. H. Rowe, “Projected Interference Fringes in Holographic Interferometry,” J. Opt. Soc. Am. 61, 1599 (1971).
    [CrossRef]
  4. A. J. MacGovern, “Projected Fringes and Holography,” Appl. Opt. 11, 2972 (1972).
    [CrossRef] [PubMed]
  5. K. Leonhardt, “The Interference of Two Obliquely Intersecting Beams,” Optik 41, 344 (1974).
  6. O. D. D. Soares, “Non-optical Surface Topography by Projected Interference Fringes,” Port. Phys. 13, 217 (1982).
  7. O. D. D. Soares, S. P. Almeida, “Projection Interference Microscope,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 32 (1983).
  8. S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).
  9. R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Microtopography by Automated Processing of Projected Interference Fringes,” Proc. Soc. Photo-Opt. Instrum. Eng. 42, 863 (1987).
  10. R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Micro-Metrology by Image Processing of Patterns from Collimated Interference Fringe Illumination,” in OPTICS-ECOOSA, Birmingham, U.K., 22–25 Mar. 1988.
  11. S. P. Almeida, R. W. Wygant, O. D. D. Soares, “Automatic Surface Analysis with Fringe Projection,” Proc. Soc. Photo-Opt. Instrum. Eng. 08, 952 (1988).
  12. N. George, “About Speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 5, 153 (1983).

1988 (1)

S. P. Almeida, R. W. Wygant, O. D. D. Soares, “Automatic Surface Analysis with Fringe Projection,” Proc. Soc. Photo-Opt. Instrum. Eng. 08, 952 (1988).

1987 (1)

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Microtopography by Automated Processing of Projected Interference Fringes,” Proc. Soc. Photo-Opt. Instrum. Eng. 42, 863 (1987).

1986 (1)

S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).

1983 (2)

O. D. D. Soares, S. P. Almeida, “Projection Interference Microscope,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 32 (1983).

N. George, “About Speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 5, 153 (1983).

1982 (1)

O. D. D. Soares, “Non-optical Surface Topography by Projected Interference Fringes,” Port. Phys. 13, 217 (1982).

1974 (1)

K. Leonhardt, “The Interference of Two Obliquely Intersecting Beams,” Optik 41, 344 (1974).

1972 (1)

1971 (1)

1969 (1)

W. T. Welford, “Some Applications of Projected Interference Fringes,” Opt. Acta 16, 331 (1969).

1967 (1)

S. H. Rowe, W. T. Welford, “Surface Topography of Nonoptical Surfaces by Projected Interference Fringes,” Nature London 216, 786 (1967).
[CrossRef]

Almeida, S. P.

S. P. Almeida, R. W. Wygant, O. D. D. Soares, “Automatic Surface Analysis with Fringe Projection,” Proc. Soc. Photo-Opt. Instrum. Eng. 08, 952 (1988).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Microtopography by Automated Processing of Projected Interference Fringes,” Proc. Soc. Photo-Opt. Instrum. Eng. 42, 863 (1987).

S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).

O. D. D. Soares, S. P. Almeida, “Projection Interference Microscope,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 32 (1983).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Micro-Metrology by Image Processing of Patterns from Collimated Interference Fringe Illumination,” in OPTICS-ECOOSA, Birmingham, U.K., 22–25 Mar. 1988.

Bernardo, L. M.

S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).

George, N.

N. George, “About Speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 5, 153 (1983).

Leonhardt, K.

K. Leonhardt, “The Interference of Two Obliquely Intersecting Beams,” Optik 41, 344 (1974).

MacGovern, A. J.

Rowe, S. H.

S. H. Rowe, “Projected Interference Fringes in Holographic Interferometry,” J. Opt. Soc. Am. 61, 1599 (1971).
[CrossRef]

S. H. Rowe, W. T. Welford, “Surface Topography of Nonoptical Surfaces by Projected Interference Fringes,” Nature London 216, 786 (1967).
[CrossRef]

Soares, O. D. D.

S. P. Almeida, R. W. Wygant, O. D. D. Soares, “Automatic Surface Analysis with Fringe Projection,” Proc. Soc. Photo-Opt. Instrum. Eng. 08, 952 (1988).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Microtopography by Automated Processing of Projected Interference Fringes,” Proc. Soc. Photo-Opt. Instrum. Eng. 42, 863 (1987).

S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).

O. D. D. Soares, S. P. Almeida, “Projection Interference Microscope,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 32 (1983).

O. D. D. Soares, “Non-optical Surface Topography by Projected Interference Fringes,” Port. Phys. 13, 217 (1982).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Micro-Metrology by Image Processing of Patterns from Collimated Interference Fringe Illumination,” in OPTICS-ECOOSA, Birmingham, U.K., 22–25 Mar. 1988.

Welford, W. T.

W. T. Welford, “Some Applications of Projected Interference Fringes,” Opt. Acta 16, 331 (1969).

S. H. Rowe, W. T. Welford, “Surface Topography of Nonoptical Surfaces by Projected Interference Fringes,” Nature London 216, 786 (1967).
[CrossRef]

Wygant, R. W.

S. P. Almeida, R. W. Wygant, O. D. D. Soares, “Automatic Surface Analysis with Fringe Projection,” Proc. Soc. Photo-Opt. Instrum. Eng. 08, 952 (1988).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Microtopography by Automated Processing of Projected Interference Fringes,” Proc. Soc. Photo-Opt. Instrum. Eng. 42, 863 (1987).

S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Micro-Metrology by Image Processing of Patterns from Collimated Interference Fringe Illumination,” in OPTICS-ECOOSA, Birmingham, U.K., 22–25 Mar. 1988.

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

S. P. Almeida, R. W. Wygant, L. M. Bernardo, O. D. D. Soares, “Analysis of Microscopic Surfaces by Projection Interference Fringes,” J. Opt. Soc. Am. A 3(13), P42 (1986).

Nature London (1)

S. H. Rowe, W. T. Welford, “Surface Topography of Nonoptical Surfaces by Projected Interference Fringes,” Nature London 216, 786 (1967).
[CrossRef]

Opt. Acta (1)

W. T. Welford, “Some Applications of Projected Interference Fringes,” Opt. Acta 16, 331 (1969).

Optik (1)

K. Leonhardt, “The Interference of Two Obliquely Intersecting Beams,” Optik 41, 344 (1974).

Port. Phys. (1)

O. D. D. Soares, “Non-optical Surface Topography by Projected Interference Fringes,” Port. Phys. 13, 217 (1982).

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

O. D. D. Soares, S. P. Almeida, “Projection Interference Microscope,” Proc. Soc. Photo-Opt. Instrum. Eng. 429, 32 (1983).

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Microtopography by Automated Processing of Projected Interference Fringes,” Proc. Soc. Photo-Opt. Instrum. Eng. 42, 863 (1987).

S. P. Almeida, R. W. Wygant, O. D. D. Soares, “Automatic Surface Analysis with Fringe Projection,” Proc. Soc. Photo-Opt. Instrum. Eng. 08, 952 (1988).

N. George, “About Speckle,” Proc. Soc. Photo-Opt. Instrum. Eng. 5, 153 (1983).

Other (1)

R. W. Wygant, S. P. Almeida, O. D. D. Soares, “Surface Micro-Metrology by Image Processing of Patterns from Collimated Interference Fringe Illumination,” in OPTICS-ECOOSA, Birmingham, U.K., 22–25 Mar. 1988.

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 (8)

Fig. 1
Fig. 1

Geometrical relationships between experimental parameters.

Fig. 2
Fig. 2

Interference fringes projected onto an aluminum block with machined grooves.

Fig. 3
Fig. 3

Digital image obtained from the photograph of Fig. 2. Image is magnified and rotated 90° counterclockwise relative to that of Fig. 2.

Fig. 4
Fig. 4

Bias intensity of the interference obtained from image of Fig. 3.

Fig. 5
Fig. 5

Interferogram of Fig. 2 after noise reduction and bias intensity flattening.

Fig. 6
Fig. 6

Symbolic fringe extrema pattern derived from image of Fig. 5.

Fig. 7
Fig. 7

Surface calculated from images of Figs. 5 and 6.

Fig. 8
Fig. 8

Autocorrelation function of surface of Fig. 7.

Equations (18)

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

I ( x ) = c E 2 [ 1 + cos [ ( k 1 - k 2 ) · x ] ] ,
d = λ / 2 sin ϕ .
d β = d / cos β = λ / 2 sin ϕ cos β .
d γ = d β cos γ = λ cos γ / 2 sin ϕ cos β .
δ γ = - Δ z ( x 1 , y 1 ; x 2 , y 2 ) sin ( β - γ ) / cos β .
δ γ / d γ = - 2 Δ z sin ϕ sin ( β - γ ) / λ cos γ .
Δ z = - λ ( δ γ / d γ ) cos γ / 2 sin ϕ sin ( β - γ ) .
d min = 2 h λ / ( 8 h - λ ) .
( Δ z ) / Δ z = ( δ γ ) / δ γ + ( d γ ) / d γ + ( δ ) cos ( β - γ ) - tan γ + ( ϕ ) cos ϕ + ( ϕ ) cos ( β - γ ) ,
I ( x , y ) = S ( x , y ) { A ( x , y ) + B ( x , y ) cos [ Φ ( x , y ) ] } + E ( x , y ) .
I ( x , y ) = ξ = x - Δ x x + Δ x η = y - Δ y y + Δ y W ( ξ - x , η - y ) I ( ξ , η ) = ξ η W ( ξ - x , η - y ) ( S ( ξ , η ) · { A ( ξ , η ) + B ( ξ , η ) cos [ Φ ( ξ , η ) ] } + E ( ξ , η ) ) { A ( x , y ) + B ( x , y ) cos [ Φ ( x , y ) ] } · ξ η W ( ξ - x , η - y ) S ( ξ , η ) + ξ η W ( - x , - y ) E ( ξ , η ) A ( x , y ) + B ( x , y ) cos [ Φ ( x , y ) ] .
( x , y ) { R x = δ x , y [ - p / 2 , p / 2 ] } .
I ( x , y ) = ( ξ , η ) R { A ( ξ , η ) + B ( ξ , η ) cos [ Φ ( ξ , η ) ] } A ( x , y ) .
R α = ( 1 N 2 { i , j = 1 N [ z ( i , j ) - z ¯ ] 2 } ) 1 / 2 ,
R α = [ i , j = 1 z ( i , j ) - z ¯ ] / N 2 .
skew = ( { i , j = 1 N [ z ( i , j ) - z ¯ ] 3 } / N 2 ) / σ 3 .
kurtosis = ( { i , j = 1 N [ z ( i , j ) - z ¯ ] 4 } / N 2 ) / σ 4 .
C ( x , y ) = 1 n k = 1 n { [ z ( i k , j k ) - z ¯ ] [ z ( i k + x , j k + y ) - z ¯ ] / σ 2 } .

Metrics