Abstract

An analysis of a surface flaw detection method is presented in which oblique illumination is combined with a high pass spatial filter to detect the light scattered from surface flaws. The effects of surface finishes of test samples (meteoric plates) are assessed statistically, and the sensitivity of the system is calculated. Data have been collected on diffraction patterns and surface scratch detection for three stainless steel plates having different surface finishes. The results agree with theoretical considerations and are quite promising.

© 1972 Optical Society of America

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References

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  1. R. L. Powell, K. A. Stetson, J. Opt. Soc. Am. 55, 612 (1966).
  2. J. E. Sollid, Appl. Opt. 8, 1587 (1969).
    [Crossref] [PubMed]
  3. E. Marom, Appl. Opt. 9, 1385 (1970).
    [Crossref] [PubMed]
  4. E. Marom, R. K. Mueller, Proc. of Air Force Conf. on Fatigue and Fracture of Aircraft Structures and Materials, AFFDL TR 70-144, 493, December1969 (Miami, Florida).
  5. M. Born, E. Wolf, Prinicples of Optics (Pergamon, New York, 1964).
  6. N. S. Kapany, T. Sawatari, B. G. Phillips, J. Opt. Soc. Am. 59, 5122A (1969).
  7. H. Ohzu, H. Kubota, Oyo Butsuri (Japan) 26, 3 96(18) (1957).

1970 (1)

1969 (2)

N. S. Kapany, T. Sawatari, B. G. Phillips, J. Opt. Soc. Am. 59, 5122A (1969).

J. E. Sollid, Appl. Opt. 8, 1587 (1969).
[Crossref] [PubMed]

1966 (1)

R. L. Powell, K. A. Stetson, J. Opt. Soc. Am. 55, 612 (1966).

1957 (1)

H. Ohzu, H. Kubota, Oyo Butsuri (Japan) 26, 3 96(18) (1957).

Born, M.

M. Born, E. Wolf, Prinicples of Optics (Pergamon, New York, 1964).

Kapany, N. S.

N. S. Kapany, T. Sawatari, B. G. Phillips, J. Opt. Soc. Am. 59, 5122A (1969).

Kubota, H.

H. Ohzu, H. Kubota, Oyo Butsuri (Japan) 26, 3 96(18) (1957).

Marom, E.

E. Marom, Appl. Opt. 9, 1385 (1970).
[Crossref] [PubMed]

E. Marom, R. K. Mueller, Proc. of Air Force Conf. on Fatigue and Fracture of Aircraft Structures and Materials, AFFDL TR 70-144, 493, December1969 (Miami, Florida).

Mueller, R. K.

E. Marom, R. K. Mueller, Proc. of Air Force Conf. on Fatigue and Fracture of Aircraft Structures and Materials, AFFDL TR 70-144, 493, December1969 (Miami, Florida).

Ohzu, H.

H. Ohzu, H. Kubota, Oyo Butsuri (Japan) 26, 3 96(18) (1957).

Phillips, B. G.

N. S. Kapany, T. Sawatari, B. G. Phillips, J. Opt. Soc. Am. 59, 5122A (1969).

Powell, R. L.

R. L. Powell, K. A. Stetson, J. Opt. Soc. Am. 55, 612 (1966).

Sawatari, T.

N. S. Kapany, T. Sawatari, B. G. Phillips, J. Opt. Soc. Am. 59, 5122A (1969).

Sollid, J. E.

Stetson, K. A.

R. L. Powell, K. A. Stetson, J. Opt. Soc. Am. 55, 612 (1966).

Wolf, E.

M. Born, E. Wolf, Prinicples of Optics (Pergamon, New York, 1964).

Appl. Opt. (2)

J. Opt. Soc. Am. (2)

N. S. Kapany, T. Sawatari, B. G. Phillips, J. Opt. Soc. Am. 59, 5122A (1969).

R. L. Powell, K. A. Stetson, J. Opt. Soc. Am. 55, 612 (1966).

Oyo Butsuri (Japan) (1)

H. Ohzu, H. Kubota, Oyo Butsuri (Japan) 26, 3 96(18) (1957).

Other (2)

E. Marom, R. K. Mueller, Proc. of Air Force Conf. on Fatigue and Fracture of Aircraft Structures and Materials, AFFDL TR 70-144, 493, December1969 (Miami, Florida).

M. Born, E. Wolf, Prinicples of Optics (Pergamon, New York, 1964).

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Figures (12)

Fig. 1
Fig. 1

Reflected wavefront for a step object; (a) for normal incidence of light (θ = 0) and (b) for oblique illumination (θ).

Fig. 2
Fig. 2

Schematic of oblique illumination technique. A, aperture; TO, test object; L, lens; O, modified object plane; I′, near field plane (Fresnel diffraction plane); P, far field plane (Fraunhofer plane). Solid line: specularly reflected ray; dotted line: light scattered from scratch.

Fig. 3
Fig. 3

Intensity ratio of central component (a) and scattered component (b) of diffraction pattern from rough surface.

Fig. 4
Fig. 4

Numerical example of output intensity for the system shown in Fig. 2. Solid line: no scratch on the tested surface; dotted line: scratch on the surface; solid-dotted line: nonscratch component for scratched surface. [Double dotted solid line: an extension of Eq. (17).]

Fig. 5
Fig. 5

Numerical example of system sensitivity to a scratch.

Fig. 6
Fig. 6

Mechanical traces of surface roughness for three steel plates (a) sample 1, (b) sample 2, and (c) sample 3.

Fig. 7
Fig. 7

Diffraction patterns and reflected beam pattern for different angles of incidence (a) sample 1, (b) sample 2, and (c) sample 3.

Fig. 8
Fig. 8

Photometric traces of diffraction patterns for various angles of incidence (sample 2). sample 3.

Fig. 9
Fig. 9

Experimental results for sample 1; output voltage vs number of scratches.

Fig. 10
Fig. 10

Experimental results for sample 2; output voltage vs number of scratches.

Fig. 11
Fig. 11

Experimental results for sample 3; output voltage vs number of scratches.

Fig. 12
Fig. 12

Relative sensitivity of the apparatus (for five scratches) vs incident angle θ. —□— sample 1; —○—sample 2; —Δ— sample 3.

Equations (27)

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ψ θ = ( 4 π / λ ) h cos θ ,
ψ θ = ( 4 π / λ ) g ( x , y ) cos θ .
x = X / cos θ ,   y = Y .
ψ θ = ( 4 π / λ ) g ( X , Y ) cos θ ,
g ( X , Y ) = g [ ( X / cos θ ) , y ] .
f ( X , Y ) = A 0 exp ( i ψ θ ) ,
F ( u , υ ) = F [ A 0 exp ( i ψ θ ) ] S ,
F [ 0 ] S = S 0 exp [ i ( 2 π / λ z 0 ) ( X u + Y υ ) ] d X d Y ,
lim S 1 S S g ( x , y ) d x d y = 0 ,
lim S 1 S S | g ( x , y ) | 2 d x d y = σ 2 ,
φ g g ( x , y ) = lim S 1 S S g ( x , y ) g * ( x x , y y ) d x d y = σ 2 exp [ ( x 2 / 2 ρ 1 2 ) ] exp [ ( y 2 / 2 ρ 2 2 ) ] ,
I ( u , υ ) | F ( u , υ ) | 2 .
| F | 2 α F ( f f * ) S .
I ( u , υ ) = K 0 | A 0 | 2 F { [ 1 ( 4 π λ cos ) 2 σ 2 ] + ( 4 π λ cos θ ) 2 σ 2 exp ( x 2 2 ρ 1 2 cos 2 y 2 2 ρ 2 2 ) } S =
= K 0 | A 0 | 2 { 2 π [ 1 ( 4 π λ cos θ ) 2 σ 2 ] δ ( 2 π λ z 0 u , 2 π λ z 0 υ ) + ( 4 π λ cos θ ) 2 σ 2 cos θ ρ 1 ρ 2 exp [ ρ 1 2 cos 2 θ 2 ( 2 π λ z 0 ) 2 × u 2 ρ 2 2 2 ( 2 π λ z 0 ) 2 υ 2 ] } ,
I out = p p s I ( u , υ ) d u d υ ,
I out = K 1 cos 3 θ l L l L exp [ α 1 2 ( cos 2 θ ) u 2 2 α 2 2 υ 2 2 ] d u d υ ,
I out = K 1 α 1 α 2 cos 2 θ [ erf ( L α 1 cos θ ) erf ( l α 1 cos θ ) ] × [ erf ( L α 2 ) erf ( l α 2 ) ] .
λ = 0.6 ( μ ) , σ = 0.1 ( μ ) , L = 40 mm , l = 0.5 mm , ρ = 1.0 ( μ ) .
f ( X , Y ) = f N ( X , Y ) + f S ( X , Y ) ,
I ( u , υ ) = | F ( u , υ ) | 2 = | F N | 2 + | F S | 2 + 2 Re ( F N * F S ) .
I out = I ( u , υ ) p p s = | F N | 2 p p s + | F S | 2 p p s + 2 Re ( F N * F S ) p p s ,
ϕ p p s = p p s ϕ d u d υ .
p p s cos ( ϕ N ϕ S ) d u d υ = 0
I out = | F N | 2 p p s + | F S | 2 p p s .
I out = ( 1 ) | F | 2 p p s + K S ( p p s ) ,
Δ = I out I out / I out

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