Abstract

For ground metallic samples illuminated at various angles of incidence, optical transform patterns are determined theoretically and then verified both experimentally and using computer simulations. Surface roughness in the range from 0.025 to 3.2 μm is studied and means for categorizing surface roughness automatically are established. A noncontact optical method which provides a real-time display of Fourier transforms is compared to a computer-aided technique that models the optical system using profilometer data as an input. Also, the Fourier transforms for a periodic phase-reflection surface are presented at three angles of illumination to illustrate the effective increase in grating frequency and apparent decrease in roughness as the illumination angle is increased. Excellent results are obtained in accurately measuring roughened flat metallic surfaces remotely.

© 1987 Optical Society of America

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References

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  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 (1976).
    [CrossRef] [PubMed]
  2. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), pp. 9–10.
  3. W. Welford, “Review-Optical Estimation of Statistics of Surface Roughness from Light Scattering Measurements,” Opt. Quantum Electron. 9, 269 (1977).
    [CrossRef]
  4. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
    [CrossRef]
  5. E. Milana, F. Rasello, “An Optical Method for On-Line Evaluation of Machined Surface Finishing,” Opt. Acta 28, 111 (1981).
    [CrossRef]
  6. American Standard Association, “Physical Specimens of Surface Roughness and Lay,” ASA-B46.1-1962 (American Society of Mechanical Engineers, 1962).
  7. B. J. Pernick, “Surface Roughness Measurements with an Optical Fourier Spectrum Analyzer,” Appl. Opt. 18, 796 (1979).
    [CrossRef] [PubMed]
  8. R. C. Birkebak, “Optical and Mechanical RMS Surface Roughness Comparison,” Appl. Opt. 10, 1970 (1971).
    [CrossRef] [PubMed]
  9. E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the Finish of Diamond-Turned Metal Surfaces by Differential Light Scattering,” Opt. Eng. 16, 360 (1977).
    [CrossRef]
  10. J. Stover, S. Serati, “Calculation of Surface Statistics from Light Scatter,” Opt. Eng. 23, 406 (1984).
    [CrossRef]
  11. J. Ohtsubo, T. Asakura, “Measurement of Surface Roughness Properties Using Speckle Patterns with Non-Gaussian Statistics,” Opt. Commun. 25, 315 (1978).
    [CrossRef]
  12. D. Leger, E. Mathieu, J. Perrin, “Optical Surface Roughness Determination Using Speckle Correlation Technique,” Appl. Opt. 14, 872 (1975).
    [CrossRef] [PubMed]
  13. N. George, A. Jain, “Space and Wavelength Dependence of Speckle Intensity,” Appl. Phys. 4, 201 (1974).
    [CrossRef]
  14. T. Horiuchi, Y. Tomita, R. Kammel, “Surface Roughness Measurement with Speckle Intensity Distribution Detected Using a Linear Image Sensor,” Jpn. J. Appl. Phys. 21, L743 (1982).
    [CrossRef]
  15. T. Sawatari, “Optical Profile Transducer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 8 (1978).
  16. C. C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365 (1984).
  17. F. M. Smolka, T. P. Caudell, “A Non-Contact Method for Surface Profile Measurement and Angular Deflection Monitoring Using a Scanning Laser Beam,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 17 (1978).
  18. K. J. Allardyce, “Diffraction Pattern Analysis as a Method for Surface Roughness Measurement,” M. S. Thesis, U. Rochester (1985).
  19. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 5.
  20. L. Shirley, N. George, “Diffuser Transmission Functions and Far-Zone Speckle Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 556, 63 (1985).
  21. E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, NJ, 1974).

1985 (1)

L. Shirley, N. George, “Diffuser Transmission Functions and Far-Zone Speckle Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 556, 63 (1985).

1984 (2)

C. C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365 (1984).

J. Stover, S. Serati, “Calculation of Surface Statistics from Light Scatter,” Opt. Eng. 23, 406 (1984).
[CrossRef]

1982 (1)

T. Horiuchi, Y. Tomita, R. Kammel, “Surface Roughness Measurement with Speckle Intensity Distribution Detected Using a Linear Image Sensor,” Jpn. J. Appl. Phys. 21, L743 (1982).
[CrossRef]

1981 (1)

E. Milana, F. Rasello, “An Optical Method for On-Line Evaluation of Machined Surface Finishing,” Opt. Acta 28, 111 (1981).
[CrossRef]

1979 (2)

B. J. Pernick, “Surface Roughness Measurements with an Optical Fourier Spectrum Analyzer,” Appl. Opt. 18, 796 (1979).
[CrossRef] [PubMed]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

1978 (3)

T. Sawatari, “Optical Profile Transducer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 8 (1978).

F. M. Smolka, T. P. Caudell, “A Non-Contact Method for Surface Profile Measurement and Angular Deflection Monitoring Using a Scanning Laser Beam,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 17 (1978).

J. Ohtsubo, T. Asakura, “Measurement of Surface Roughness Properties Using Speckle Patterns with Non-Gaussian Statistics,” Opt. Commun. 25, 315 (1978).
[CrossRef]

1977 (2)

W. Welford, “Review-Optical Estimation of Statistics of Surface Roughness from Light Scattering Measurements,” Opt. Quantum Electron. 9, 269 (1977).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the Finish of Diamond-Turned Metal Surfaces by Differential Light Scattering,” Opt. Eng. 16, 360 (1977).
[CrossRef]

1976 (1)

1975 (1)

1974 (1)

N. George, A. Jain, “Space and Wavelength Dependence of Speckle Intensity,” Appl. Phys. 4, 201 (1974).
[CrossRef]

1971 (1)

Allardyce, K. J.

K. J. Allardyce, “Diffraction Pattern Analysis as a Method for Surface Roughness Measurement,” M. S. Thesis, U. Rochester (1985).

Asakura, T.

J. Ohtsubo, T. Asakura, “Measurement of Surface Roughness Properties Using Speckle Patterns with Non-Gaussian Statistics,” Opt. Commun. 25, 315 (1978).
[CrossRef]

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), pp. 9–10.

Bennett, J. M.

Birkebak, R. C.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, NJ, 1974).

Caudell, T. P.

F. M. Smolka, T. P. Caudell, “A Non-Contact Method for Surface Profile Measurement and Angular Deflection Monitoring Using a Scanning Laser Beam,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 17 (1978).

Church, E. L.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the Finish of Diamond-Turned Metal Surfaces by Differential Light Scattering,” Opt. Eng. 16, 360 (1977).
[CrossRef]

George, N.

L. Shirley, N. George, “Diffuser Transmission Functions and Far-Zone Speckle Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 556, 63 (1985).

N. George, A. Jain, “Space and Wavelength Dependence of Speckle Intensity,” Appl. Phys. 4, 201 (1974).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 5.

Horiuchi, T.

T. Horiuchi, Y. Tomita, R. Kammel, “Surface Roughness Measurement with Speckle Intensity Distribution Detected Using a Linear Image Sensor,” Jpn. J. Appl. Phys. 21, L743 (1982).
[CrossRef]

Huang, C. C.

C. C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365 (1984).

Jain, A.

N. George, A. Jain, “Space and Wavelength Dependence of Speckle Intensity,” Appl. Phys. 4, 201 (1974).
[CrossRef]

Jenkinson, H. A.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the Finish of Diamond-Turned Metal Surfaces by Differential Light Scattering,” Opt. Eng. 16, 360 (1977).
[CrossRef]

Kammel, R.

T. Horiuchi, Y. Tomita, R. Kammel, “Surface Roughness Measurement with Speckle Intensity Distribution Detected Using a Linear Image Sensor,” Jpn. J. Appl. Phys. 21, L743 (1982).
[CrossRef]

Leger, D.

Mathieu, E.

Milana, E.

E. Milana, F. Rasello, “An Optical Method for On-Line Evaluation of Machined Surface Finishing,” Opt. Acta 28, 111 (1981).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, T. Asakura, “Measurement of Surface Roughness Properties Using Speckle Patterns with Non-Gaussian Statistics,” Opt. Commun. 25, 315 (1978).
[CrossRef]

Pernick, B. J.

Perrin, J.

Rasello, F.

E. Milana, F. Rasello, “An Optical Method for On-Line Evaluation of Machined Surface Finishing,” Opt. Acta 28, 111 (1981).
[CrossRef]

Sawatari, T.

T. Sawatari, “Optical Profile Transducer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 8 (1978).

Serati, S.

J. Stover, S. Serati, “Calculation of Surface Statistics from Light Scatter,” Opt. Eng. 23, 406 (1984).
[CrossRef]

Shirley, L.

L. Shirley, N. George, “Diffuser Transmission Functions and Far-Zone Speckle Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 556, 63 (1985).

Smolka, F. M.

F. M. Smolka, T. P. Caudell, “A Non-Contact Method for Surface Profile Measurement and Angular Deflection Monitoring Using a Scanning Laser Beam,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 17 (1978).

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), pp. 9–10.

Stover, J.

J. Stover, S. Serati, “Calculation of Surface Statistics from Light Scatter,” Opt. Eng. 23, 406 (1984).
[CrossRef]

Tomita, Y.

T. Horiuchi, Y. Tomita, R. Kammel, “Surface Roughness Measurement with Speckle Intensity Distribution Detected Using a Linear Image Sensor,” Jpn. J. Appl. Phys. 21, L743 (1982).
[CrossRef]

Welford, W.

W. Welford, “Review-Optical Estimation of Statistics of Surface Roughness from Light Scattering Measurements,” Opt. Quantum Electron. 9, 269 (1977).
[CrossRef]

Zavada, J. M.

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the Finish of Diamond-Turned Metal Surfaces by Differential Light Scattering,” Opt. Eng. 16, 360 (1977).
[CrossRef]

Appl. Opt. (4)

Appl. Phys. (1)

N. George, A. Jain, “Space and Wavelength Dependence of Speckle Intensity,” Appl. Phys. 4, 201 (1974).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Horiuchi, Y. Tomita, R. Kammel, “Surface Roughness Measurement with Speckle Intensity Distribution Detected Using a Linear Image Sensor,” Jpn. J. Appl. Phys. 21, L743 (1982).
[CrossRef]

Opt. Acta (1)

E. Milana, F. Rasello, “An Optical Method for On-Line Evaluation of Machined Surface Finishing,” Opt. Acta 28, 111 (1981).
[CrossRef]

Opt. Commun. (1)

J. Ohtsubo, T. Asakura, “Measurement of Surface Roughness Properties Using Speckle Patterns with Non-Gaussian Statistics,” Opt. Commun. 25, 315 (1978).
[CrossRef]

Opt. Eng. (4)

C. C. Huang, “Optical Heterodyne Profilometer,” Opt. Eng. 23, 365 (1984).

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Measurement of the Finish of Diamond-Turned Metal Surfaces by Differential Light Scattering,” Opt. Eng. 16, 360 (1977).
[CrossRef]

J. Stover, S. Serati, “Calculation of Surface Statistics from Light Scatter,” Opt. Eng. 23, 406 (1984).
[CrossRef]

E. L. Church, H. A. Jenkinson, J. M. Zavada, “Relationship Between Surface Scattering and Microtopographic Features,” Opt. Eng. 18, 125 (1979).
[CrossRef]

Opt. Quantum Electron. (1)

W. Welford, “Review-Optical Estimation of Statistics of Surface Roughness from Light Scattering Measurements,” Opt. Quantum Electron. 9, 269 (1977).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng. (3)

F. M. Smolka, T. P. Caudell, “A Non-Contact Method for Surface Profile Measurement and Angular Deflection Monitoring Using a Scanning Laser Beam,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 17 (1978).

T. Sawatari, “Optical Profile Transducer,” Proc. Soc. Photo-Opt. Instrum. Eng. 153, 8 (1978).

L. Shirley, N. George, “Diffuser Transmission Functions and Far-Zone Speckle Patterns,” Proc. Soc. Photo-Opt. Instrum. Eng. 556, 63 (1985).

Other (5)

E. O. Brigham, The Fast Fourier Transform (Prentice-Hall, Englewood Cliffs, NJ, 1974).

American Standard Association, “Physical Specimens of Surface Roughness and Lay,” ASA-B46.1-1962 (American Society of Mechanical Engineers, 1962).

K. J. Allardyce, “Diffraction Pattern Analysis as a Method for Surface Roughness Measurement,” M. S. Thesis, U. Rochester (1985).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, 1968), Chap. 5.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), pp. 9–10.

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Figures (12)

Fig. 1
Fig. 1

Optical transform configuration for rough reflective surface (S) illuminated by a monochromatic plane wave at an angle θ. Incident plane wave W at I is perturbed to W′ at II and then Fourier transformed by a canonical processor.

Fig. 2
Fig. 2

Insert b from Fig. 1 showing an expanded view of rough surface h(x′,y′) and path differences Δl1 and Δl2. Segment ab is L1 and bc is L2 in Fig. 1.

Fig. 3
Fig. 3

Relative intensity in percent at fx = fy = vs the normalized surface roughness σ/λ, for normal illumination from Eq. (36) with the correlation length ξ0 along the surface as labeled.

Fig. 4
Fig. 4

Profilometer height measurements for ground metallic samples. Note that the scale of (b) rough covers ten times the range of (a) smooth.

Fig. 5
Fig. 5

Computer simulated transforms, using the exponential height dependence in Eq. (11), for eight ground metallic surfaces: (a)–(d) same scale; (e)–(h) one-tenth scale in ordinate.

Fig. 6
Fig. 6

Optoelectronic hybrid for roughness measurements with rough sample (object) and photodetector (in transform plane).

Fig. 7
Fig. 7

Experimental optical transforms of phase reflection gratings at various angles of illumination.

Fig. 8
Fig. 8

Optical transforms from the measuring system shown in Fig. 6 with the same set of ground metal surfaces used for Fig. 5.

Fig. 9
Fig. 9

Optical transforms at three angles of illumination for a single ground metallic sample of roughness σ = 0.1 μm.

Fig. 10
Fig. 10

Area from optical transforms as a function of normalized surface roughness σ/λ, for eight ground metallic samples.

Fig. 11
Fig. 11

Standard deviation of transform intensities vs normalized roughness σ/λ: ●, optical system and ▲, computer simulation.

Fig. 12
Fig. 12

Optical transform data at fx = fy = 0 for actual ground metallic surfaces vs normalized roughness σ/λ The theoretical curve with varying correlation length is plotted by the solid line.

Tables (1)

Tables Icon

Table I Quoted and Measured Values for the rms Heights (Roughness) of a Series of Eight Metallic Ground Surfaces Manufactured by Rubert & Co., Ltd.

Equations (39)

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σ rms = [ 1 N i = 1 N ( y i - y ¯ ) 2 ] 1 / 2 ,
σ rms < λ 8 cos θ ,
σ rms λ 0 or θ π 2 ,
L 3 + L 4 = ( L 1 + L 2 ) - ( Δ l 1 + Δ l 2 ) ,
Δ l 1 + Δ l 2 = 2 h ( x , y ) cos θ .
x cos θ - h ( x , y ) sin θ = x ,
y = y .
R ( x , y ) = exp [ + i 2 k h ( x , y ) cos θ ] ,
V 3 ( ξ , η ) = B - d x d y R ( x , y ) exp [ i 2 π ( ξ x + η y ) / ( F λ ) ] ,
f x = - ξ / ( F λ ) ,
f y = - η / ( F λ ) .
V 0 ( f x , f y ) = B spot d x d y exp { - i 2 π [ f x x + f y y - 2 h ( x , y ) / λ ] } .
cos θ d x d x , d y = d y .
V 3 ( ξ , η ) = B cos θ spot d x d y exp [ i 2 π h ( x , y ) × ( 2 cos θ / λ + f x sin θ ) ] exp [ - i 2 π ( f x cos θ x + f y y ) ] .
f x = f x 0 cos θ .
V 3 ( ξ , η ) = B spot d x d y exp [ i 4 π h ( x / cos θ , y ) cos θ / λ - i 2 π ( f x x + f y y ) ] .
h ( x , y ) = h 0 sin ( 2 π x / w ) ,
V 3 ( ξ , η ) = a 2 B - J n ( A ) J 1 ( 2 π a v ) / ( a v ) ,
A = 4 π h 0 cos θ / λ ,
B = [ i / ( λ F ) ] exp ( - i 4 π F / λ ) ,
v 2 = [ f x - n / ( w cos θ ) ] 2 + f y 2 .
f x = n w cos θ ,             n = 0 , ± 1 , ± 2 , .
D ( x , y ) = rect ( x D 1 ) rect ( y D 2 ) ,
V ( f x , f y ) = B - d x d y D ( x , y ) × exp { - i 2 π [ η h ( x ) + f x x + f y y ] } ,
V ( f x , f y ) = B D 2 sinc ( D 2 f y ) - d x rect ( x / D 1 ) × exp { - i 2 π [ η h ( x ) + f x x ] } .
U ( f x , f y ) = V ( f x , f y ) V * ( f x , f y ) ,
U ( f x f y ) = U 0 - d x d x rect ( x / D 1 ) rect ( x / D 2 ) × exp [ i 2 π f x ( x - x ) ] × exp [ - i 2 π η h ( x ) + i 2 π η h ( x ) ] ,
f ( h 1 , h 2 ; r 12 ) = exp { - ( h 1 2 - 2 r 12 h 1 h 2 + h 2 2 ) / [ 2 σ 2 ( 1 - r 12 2 ) ] } 2 π σ 2 ( 1 - r 12 2 ) 1 / 2 ,
< h 1 h 2 > / σ 2 = r 12 .
r 12 ( x - x ) = Λ ( x - x ξ 0 ) , r 12 ( x - x ) = { 1 - x - x ξ 0 , x - x ξ 0 1 , 0 , x - x ξ 0 > 1 ,
exp [ - i 2 π η h ( x ) + i 2 π η h ( x ) ] = exp [ - γ ( 1 - r 12 ) ] ,
γ = ( 4 π σ / λ ) 2 .
U ( f x , f y ) = U 0 - d x rect ( x / D 1 ) ( - d x × rect [ ( x + x ) / D 2 ] × exp { - γ [ 1 - Λ ( x / ξ 0 ) ] - i 2 π f x x } ) .
U ( f x , f y ) = U 0 [ D 1 2 sinc 2 ( D 1 f x ) - 2 ξ 0 D 1 sinc ( 2 ξ 0 f x ) ] exp ( - γ ) + U 0 ξ 0 D 1 [ 1 γ - i 2 π ξ 0 f x + 1 γ + i 2 π ξ 0 f x ] - U 0 ξ 0 D 1 [ exp ( i 2 π ξ 0 f x ) γ - i 2 π ξ 0 f x + exp ( - i 2 π ξ 0 f x ) γ + i 2 π ξ 0 f x ] exp ( - γ ) ,
U ( f x , f y ) = [ B D 1 D 2 sinc ( D 1 f x ) sinc ( D 2 f y ) ] 2 .
U n ( 0 , 0 ) = U ( 0 , 0 ) ( D 1 D 2 / λ F ) 2 ,
U n ( 0 , 0 ) = exp ( - γ ) ( 1 - 2 ξ 0 D 1 - 2 ξ 0 γ D 1 ) + 2 ξ 0 γ D 1 ,
f x = n N Δ X             n = - N 2 , , 0 , + N 2 ,
σ = [ 1 N i = 1 N ( I i - I ¯ ) 2 ] 1 / 2 ,

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