Abstract

During the study of laser-scattering properties of machined surfaces, an interesting reflective characteristic has been observed. For a certain range of angles of incidence a stationary reflective pattern has been observed regardless of the angle of incidence. We explain the same by using geometric optics. The intensities calculated from the model are found to be in good agreement with the experimentally measured intensity of the scattered pattern.

© 1998 Optical Society of America

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References

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  1. L. H. Tanner, “The use of laser light in the study of metal surfaces,” Opt. Laser Technol. 8, 113–116 (1976).
    [CrossRef]
  2. J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
    [CrossRef]
  3. L. Cuthbert, V. M. Huynh, “Statistical analysis of optical Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
    [CrossRef]
  4. K. I. Jolic, C. R. Nagarajah, W. Thompson, “Noncontact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
    [CrossRef]
  5. B. B. Batchelor, “Interactive image analysis as a prototyping tool for industrial inspection,” IEE J. Comput. Digital Technol. 2, 61–70 (1979).
    [CrossRef]
  6. R. M. Bytchkov, V. P. Koronkevitch, Yu. V. Chugui, “Threaded article parameter measurement by spatial spectra analysis,” Appl. Opt. 18, 197–200 (1979).
    [CrossRef] [PubMed]
  7. B. J. Stossel, N. George, “Recognition of threaded objects by spatial spectrum analysis,” Appl. Opt. 30, 1379–1387 (1991).
    [CrossRef] [PubMed]
  8. D. Mansfield, I. Bell, I. Buehring, J. Harding, “Apparatus and method using optical diffraction to measure surface roughness,” U.S. patent5,488,476 (30January1996).
  9. C. Babu Rao, A. V. Ananta Lakshmi, B. Raj, “Laser scattering studies on ground surface standards,” in Proceedings of the National Laser Symposium, Dehradun, India (Instruments Research and Development Establishment, Dehradun, India, 1995), pp. 310–311.
  10. V. Zalipaev, “Optical properties of an echelette grating in the short-wave approximation,” Opt. Lett. 22, 1–3 (1997).
    [CrossRef] [PubMed]
  11. M. C. Hutley, Diffraction Gratings (Academic, London, 1992).

1997 (1)

1994 (1)

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Noncontact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

1992 (1)

L. Cuthbert, V. M. Huynh, “Statistical analysis of optical Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

1991 (1)

1987 (1)

J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

1979 (2)

B. B. Batchelor, “Interactive image analysis as a prototyping tool for industrial inspection,” IEE J. Comput. Digital Technol. 2, 61–70 (1979).
[CrossRef]

R. M. Bytchkov, V. P. Koronkevitch, Yu. V. Chugui, “Threaded article parameter measurement by spatial spectra analysis,” Appl. Opt. 18, 197–200 (1979).
[CrossRef] [PubMed]

1976 (1)

L. H. Tanner, “The use of laser light in the study of metal surfaces,” Opt. Laser Technol. 8, 113–116 (1976).
[CrossRef]

Ananta Lakshmi, A. V.

C. Babu Rao, A. V. Ananta Lakshmi, B. Raj, “Laser scattering studies on ground surface standards,” in Proceedings of the National Laser Symposium, Dehradun, India (Instruments Research and Development Establishment, Dehradun, India, 1995), pp. 310–311.

Babu Rao, C.

C. Babu Rao, A. V. Ananta Lakshmi, B. Raj, “Laser scattering studies on ground surface standards,” in Proceedings of the National Laser Symposium, Dehradun, India (Instruments Research and Development Establishment, Dehradun, India, 1995), pp. 310–311.

Batchelor, B. B.

B. B. Batchelor, “Interactive image analysis as a prototyping tool for industrial inspection,” IEE J. Comput. Digital Technol. 2, 61–70 (1979).
[CrossRef]

Bell, I.

D. Mansfield, I. Bell, I. Buehring, J. Harding, “Apparatus and method using optical diffraction to measure surface roughness,” U.S. patent5,488,476 (30January1996).

Buckthal, J. E.

J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Buehring, I.

D. Mansfield, I. Bell, I. Buehring, J. Harding, “Apparatus and method using optical diffraction to measure surface roughness,” U.S. patent5,488,476 (30January1996).

Bytchkov, R. M.

Chugui, Yu. V.

Cuthbert, L.

L. Cuthbert, V. M. Huynh, “Statistical analysis of optical Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

George, N.

Harding, J.

D. Mansfield, I. Bell, I. Buehring, J. Harding, “Apparatus and method using optical diffraction to measure surface roughness,” U.S. patent5,488,476 (30January1996).

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, London, 1992).

Huynh, V. M.

L. Cuthbert, V. M. Huynh, “Statistical analysis of optical Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

Jolic, K. I.

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Noncontact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Koronkevitch, V. P.

Kusy, R. P.

J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Mansfield, D.

D. Mansfield, I. Bell, I. Buehring, J. Harding, “Apparatus and method using optical diffraction to measure surface roughness,” U.S. patent5,488,476 (30January1996).

Mayhew, M. J.

J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Nagarajah, C. R.

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Noncontact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Raj, B.

C. Babu Rao, A. V. Ananta Lakshmi, B. Raj, “Laser scattering studies on ground surface standards,” in Proceedings of the National Laser Symposium, Dehradun, India (Instruments Research and Development Establishment, Dehradun, India, 1995), pp. 310–311.

Stossel, B. J.

Tanner, L. H.

L. H. Tanner, “The use of laser light in the study of metal surfaces,” Opt. Laser Technol. 8, 113–116 (1976).
[CrossRef]

Thompson, W.

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Noncontact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Whitley, J. O.

J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Zalipaev, V.

Appl. Opt. (2)

IEE J. Comput. Digital Technol. (1)

B. B. Batchelor, “Interactive image analysis as a prototyping tool for industrial inspection,” IEE J. Comput. Digital Technol. 2, 61–70 (1979).
[CrossRef]

Meas. Sci. Technol. (2)

L. Cuthbert, V. M. Huynh, “Statistical analysis of optical Fourier transform patterns for surface texture assessment,” Meas. Sci. Technol. 3, 740–745 (1992).
[CrossRef]

K. I. Jolic, C. R. Nagarajah, W. Thompson, “Noncontact, optically based measurement of surface roughness of ceramics,” Meas. Sci. Technol. 5, 671–684 (1994).
[CrossRef]

Opt. Laser Technol. (2)

L. H. Tanner, “The use of laser light in the study of metal surfaces,” Opt. Laser Technol. 8, 113–116 (1976).
[CrossRef]

J. O. Whitley, R. P. Kusy, M. J. Mayhew, J. E. Buckthal, “Surface roughness of stainless steel and electroformed nickel standards using a He–Ne laser,” Opt. Laser Technol. 19, 189–196 (1987).
[CrossRef]

Opt. Lett. (1)

Other (3)

M. C. Hutley, Diffraction Gratings (Academic, London, 1992).

D. Mansfield, I. Bell, I. Buehring, J. Harding, “Apparatus and method using optical diffraction to measure surface roughness,” U.S. patent5,488,476 (30January1996).

C. Babu Rao, A. V. Ananta Lakshmi, B. Raj, “Laser scattering studies on ground surface standards,” in Proceedings of the National Laser Symposium, Dehradun, India (Instruments Research and Development Establishment, Dehradun, India, 1995), pp. 310–311.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the experimental setup.

Fig. 2
Fig. 2

Scattering patterns of different turned surfaces at normal incidence.

Fig. 3
Fig. 3

Scattering pattern from the surface SN11 as a function of angle of incidence.

Fig. 4
Fig. 4

Ray diagram when (a) i ≤ (3ϕ/2) - π and (b) i > (3ϕ/2) - π.

Fig. 5
Fig. 5

Schematic diagram explaining the contribution of an incident wave front to (a) I a and I b , (b) L and S patterns.

Fig. 6
Fig. 6

Intensities of various scattering patterns as a function of incident angle. L, R, single reflection patterns; S, stationary pattern. The solid curves calculated from theory and data points are experimental.

Equations (9)

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

i a = i + π / 2 - ϕ / 2 .
i b = i - π / 2 - ϕ / 2 .
i b n = i a n - 1 - ϕ ,
i a n = i b n - 1 - ϕ .
I a = PO / PQ × I = sin ϕ / 2 - i / sin ϕ / 2 - i + sin ϕ / 2 + i × I .
I b = QO / PQ × I = sin ϕ / 2 + i / sin ϕ / 2 - i + sin ϕ / 2 + i × I .
I S = OA / OA × I a = sin i - 3 ϕ / 2 + π / sin ϕ / 2 - i × I a .
I L = AA / OA × I a = sin ϕ / 2 - i - sin i - 3 ϕ / 2 + π / sin ϕ / 2 - i × I a .
I R = I b .

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