Abstract

The relationship between the defect signal which causes read error and the defect factor involved in the optical disk was extensively analyzed. This analysis dealt with the effect of an opaque foreign substance contained in the disk substrate covering the reflective layer, particularly by using wave optics where the defect signal was two-dimensionally represented. Using this generalized concept for the defect signal analysis, the relationships between the foreign substance and defect signal and defect rate were clarified.

© 1988 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 30–56.
  2. H. Kubota, Wave Optics (Iwanami, Tokyo, 1971), pp. 242–244, in Japanese.
  3. H. H. Hopkins, “Diffraction Theory of Laser Read-Out Systems for Optical Video Discs,” J. Opt. Soc. Am. 69, 4 (1979).
    [CrossRef]

1979 (1)

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 30–56.

Hopkins, H. H.

Kubota, H.

H. Kubota, Wave Optics (Iwanami, Tokyo, 1971), pp. 242–244, in Japanese.

J. Opt. Soc. Am. (1)

Other (2)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 30–56.

H. Kubota, Wave Optics (Iwanami, Tokyo, 1971), pp. 242–244, in Japanese.

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Figures (11)

Fig. 1
Fig. 1

Sectional plane of an optical disk and causes of defect errors.

Fig. 2
Fig. 2

Analytical model. Light propagation from the aperture plane to the recording plane and back. On the incident and reflecting paths, a part of the light is intercepted by an opaque circular foreign substance: λ = 830 nm; f = 4.26 mm; a = 2.13 mm.

Fig. 3
Fig. 3

Intensity distributions from the aperture plane to the recording plane and back. Light is reflected by the pregrooved recording plane (pG = 1.6 μm, wG = 0.59 μm, dG = λ/8) and intercepted on the incident and reflecting paths by an opaque foreign substance d in diameter and located at the coordinates (x0,y0,z). (a) Intensity distribution across a plane immediately behind the objective lens. (b) Intensity distribution on the incident path across a plane, parallel to the recording plane at distance z = 8 μm. (c) Intensity distribution focused onto the recording plane after being intercepted by the opaque foreign substance: d = 3.2 μm; (x0,y0,z) = 0, 0, 8 μm. (d) Intensity distribution after propagating over distance z = 8 μm from the recording plane: d = 3.2 μm; (x0,y0,z) = 0, 0, 8 μm. (e) Intensity distribution across a plane immediately in front of the aperture plane: d = 160 μm; (x0,y0,z) = 0, 200, 800 μm. (f) Intensity distribution across a plane immediately in front of the aperture plane. The light is not intercepted, that is, the opaque foreign substance is d = 0 μm in diameter. (g) Intensity distribution collimated by the objective lens: d = 160 μm; (x0,y0,z) = 0, 200, 800 μm.

Fig. 4
Fig. 4

Defect amplitude distribution and theoretical defect signals: z = 800 μm; d/z = 0.4; x1 = 0 μm; n = 0, 125; pG = 1.6 μm; wG = 0.70 μm; dG = λ/8; N.A. = 0.5; f = 4.26 mm; λ = 830 nm.

Fig. 5
Fig. 5

Measured defect signals: RG = 0.5 V; vD = 4 m/s. The signals were distorted and leaned to the left because of the frequency characteristic of the signal amplifier: (a) the beam spot was scanning on the center of the foreign substance. (b) The beam spot was scanning along the groove situated 125 tracks away from the center of the foreign substance.

Fig. 6
Fig. 6

Volume of defect amplitude distribution vs area of the opaque circular foreign substance for various d/z values.

Fig. 7
Fig. 7

Defect region for z = 800 μm, d/z = 0.4, RS/RG = 0.2.

Fig. 8
Fig. 8

Normalized threshold voltage RS/RG vs the area of defect region for various values of z and d/z.

Fig. 9
Fig. 9

Area of defect region SD as a function of z for various values of d: RS/RG = 0.2.

Fig. 10
Fig. 10

Area enclosed by the function SD = f(RS/RG,d,z) and the two coordinate axes as a function of d for various values of RS/RG.

Fig. 11
Fig. 11

Defect rate as a function of normalized threshold voltage RS/RG.

Equations (35)

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g P ( u , v ) = { 1 inside the lens aperture ( u 2 + v 2 a 2 ) , 0 other than above ( u 2 + v 2 > a 2 ) ,
g 1 ( u , v ) = g 0 ( u , v ) g P ( u , v ) exp [ i κ ( f - r 0 ) ] ,
g 0 ( u , v ) = exp [ - ( u 2 + v 2 ) ln 2 / 2 a 2 ] ,
g 2 ( ξ , η ) = 1 / i λ · - g 1 ( u , v ) exp ( i κ r ) / r d u d v ,
g 2 ( ξ , η ) = 1 / i λ · - g 3 ( x , y ) exp ( i κ ρ ) / ρ d x d y ,
r = ( f 2 + u 2 + v 2 ) 1 / 2 + ( ξ 2 + η 2 ) / 2 f - ( u ξ + v η ) / f , ρ = ( z 2 + x 2 + y 2 ) 1 / 2 + ( ξ 2 + η 2 ) / 2 z - ( x ξ + y η ) / z .
g 2 ( ξ , η ) = 1 / i λ z · exp [ i κ ( ξ 2 + η 2 ) / 2 z ] · F κ ξ / z , κ η / z { g 3 ( x , y ) exp [ i κ ( z 2 + x 2 + y 2 ) 1 / 2 ] } ,
F f x , f y { g ( x , y ) } = - g ( x , y ) exp [ - i ( f x x + f y y ) ] d x d y ,
g ( x , y ) = 1 / ( 2 π ) 2 · - F f x , f y { g ( x , y ) } × exp { i ( f x x + f y y ) } d f x d f y .
g 3 ( x , y ) = j / λ z · exp [ - i κ ( z 2 + x 2 + y 2 ) 1 / 2 ] · F - κ x / z - κ y / z { g 2 ( ξ , η ) exp [ - i κ ( ξ 2 + η 2 ) / 2 z ] } .
g 2 ( ξ , η ) = 1 / i λ f · exp { i κ [ f + ( ξ 2 + η 2 ) / 2 f ] } · F κ ξ / f , κ η / f [ g 0 ( u , v ) g P ( u , v ) ] .
g 3 ( x , y ) = 1 / λ 2 z f · exp { i κ [ f - ( z 2 + x 2 + y 2 ) 1 / 2 ] } · F - κ x / z , - κ y / z { F κ ξ / f , κ η / f [ g 0 ( u , v ) g P ( u , v ) ] × exp [ i κ ( ξ 2 + η 2 ) ( 1 / f - 1 / z ) / 2 ] } .
g F ( x , y ) = { 0 inside a foreign substance ( x - x 0 ) 2 + ( y - y 0 ) 2 d 2 / 4 , 1 other than above ( x - x 0 ) 2 + ( y - y 0 ) 2 > d 2 / 4 ,
g 4 ( ξ , η ) = 1 / i λ · - g 3 ( x , y ) g F ( x , y ) exp ( i κ ρ ) / ρ d x d y = 1 / i λ z · exp [ i κ ( ξ 2 + η 2 ) / 2 z ] · F κ ξ / z , κ η / z { [ g 3 ( x , y ) g F ( x , y ) ] × exp [ i κ ( z 2 + x 2 + y 2 ) 1 / 2 ] } .
g G ( ξ , η ) = { 1 n p G + w G / 2 ξ n p G - w G / 2 , exp ( 2 i k d G ) n p G - ω G / 2 > ξ > ( n - 1 ) p G + w G / 2 ,
g 5 ( x , y ) = 1 / i λ · - g 4 ( ξ , η ) g G ( ξ , η ) exp ( i κ ρ ) / ρ d ξ d η = 1 / i λ z · exp [ i κ ( z 2 + x 2 + y 2 ) 1 / 2 ] · F κ x / z , κ y / z { g 4 ( ξ , η ) g G ( ξ , η ) × exp [ i κ ( ξ 2 + η 2 ) / 2 z ] } .
g G ( ξ , η ) = n = - + a n exp ( i · 2 π n ξ / p G ) ,
a n = { ɛ + ( 1 - ɛ ) exp ( 2 i δ ) ( n = 0 ) , [ 1 - exp ( 2 i δ ) ] sin ( n π ɛ ) / n π ( n 0 ) , ɛ = w G / p G , δ = κ d G .
g 5 ( x , y ) = 1 / i λ z · exp [ i k ( z 2 + x 2 + y 2 ) 1 / 2 ] · n = - + a n - g 4 ( ξ , η ) exp { i κ [ ( ξ 2 + η 2 ) / 2 - ( x - n λ z / p G ) ξ - y η ] / z } d ξ d η = n = - + a n g 5 F ( x - n λ z / p G , y ) ,
g 5 F ( x , y ) = 1 / i λ z · exp [ i k ( z 2 + x 2 + y 2 ) 1 / 2 ] · F κ x / z , κ y / z { g 4 ( ξ , η ) exp [ i k ( ξ 2 + η 2 ) / 2 z ] } ;
g 5 ( x , y ) g F ( x , y ) = 1 / i λ · - g 6 ( ξ , η ) exp ( i κ ρ ) / ρ d ξ d η ,
g 7 ( u , v ) = 1 / i λ · - + g 6 ( ξ , η ) exp ( i κ r ) / r d ξ d η .
g 7 ( u , v ) = 1 / λ 2 z f · exp [ i k ( f 2 + u 2 + v 2 ) 1 / 2 ] · F κ u / f , κ v / f { F - κ ξ / z , - κ η / z { g 5 ( x , y ) g F ( x , y ) × exp [ - i κ ( z 2 + x 2 + y 2 ) 1 / 2 ] } · exp [ i κ ( ξ 2 + η 2 ) ( 1 / f - 1 / z ) / 2 ] } .
g 8 ( u , v ) = g 7 ( u , v ) g P ( u , v ) exp [ i κ ( f - r 0 ) ] ,
R D ( x 0 , y 0 , z , d ) = - + g 8 ( u , v ) 2 d u d v .
ψ D ( x 0 , y 0 ) = 1 - R D ( x 0 , y 0 ) / R G ,
ψ D ( x 0 , y 0 ) = 1 - R D ( x 0 , y 0 z , d ) / R G ,
S ( t ) = ψ D ( x 1 + n p G , v D t ) ,
- + ψ D ( x 0 , y 0 ) d x 0 d y 0 .
ψ D ( x 0 , y 0 ) R S / R G .
0 + f ( R S / R G , d , z ) d z .
n S / t S A D · 0 + f ( R S / R G , d , z ) d z ,
d 1 d 2 N ( x ) d x ,
n S ρ s · 0 + N ( x ) [ 0 + f ( R S / R G , x , z , ) d z ] d x ,
log 10 N ( x ) = { 8.8 - 5.9 x ( x 1.0 μ m ) , 3.2 - 0.5 x ( 1.0 μ m < x ) .

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