Abstract

A mathematical framework is derived for transfer-function analysis of magneto-optic data storage devices. The characteristics of the magneto-optic medium define what portions of the optical system transfer function are important. Several ways to improve the transfer function are analyzed, and several optical systems are compared in respect to relative contrast level versus frequency. Estimates of edge responses and two-point resolution are compared. The system that exhibits the best edge and two-point resolution is a self-masking medium. However, shading bands in the collection optics show excellent response.

© 1992 Optical Society of America

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  1. H. H. Hopkins, “Diffraction theory of laser read-out systems for optical video discs,” J. Opt. Soc. Am. 69, 4–24 (1979).
    [Crossref]
  2. J. Braat, “Optics of recording and read-out in optical disk systems,” Jpn. J. Appl. Phys. 28, 103–108 (1989).
  3. Y. Yamanaka, Y. Hirose, K. Kubota, “High density optical recording by superresolution,” Jpn. J. Appl. Phys. 28, 197–200 (1989).
  4. T. Suhara, H. Nishihara, “Possibility of super-resolution readout in integrated-optic disc pickup,” in Technical Digest of the International Symposium on Optical Memory, (Japan Society of Applied Physics, Kobe, Japan, 1989), pp. 97–8.
  5. A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).
  6. D. Treves, D. S. Bloomberg, “Signal, noise, and codes in optical memories,” Opt. Eng. 25, 881–891 (1986).
  7. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1986), pp. 509–532.
  8. H. M. Haskal, “Laser recording with truncated Gaussian beams,” Appl. Opt. 18, 2143–2146 (1979).
    [Crossref] [PubMed]
  9. T. Wilson, S. J. Hewlett, “Superresolution in confocal scanning microscopy,” Opt. Lett. 16, 1062–1064 (1991).
    [Crossref] [PubMed]
  10. M. Mansuripur, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication).

1991 (1)

1989 (2)

J. Braat, “Optics of recording and read-out in optical disk systems,” Jpn. J. Appl. Phys. 28, 103–108 (1989).

Y. Yamanaka, Y. Hirose, K. Kubota, “High density optical recording by superresolution,” Jpn. J. Appl. Phys. 28, 197–200 (1989).

1986 (1)

D. Treves, D. S. Bloomberg, “Signal, noise, and codes in optical memories,” Opt. Eng. 25, 881–891 (1986).

1979 (2)

Aratani, K.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

Bloomberg, D. S.

D. Treves, D. S. Bloomberg, “Signal, noise, and codes in optical memories,” Opt. Eng. 25, 881–891 (1986).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1986), pp. 509–532.

Braat, J.

J. Braat, “Optics of recording and read-out in optical disk systems,” Jpn. J. Appl. Phys. 28, 103–108 (1989).

Fukumoto, A.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

Haskal, H. M.

Hewlett, S. J.

Hirose, Y.

Y. Yamanaka, Y. Hirose, K. Kubota, “High density optical recording by superresolution,” Jpn. J. Appl. Phys. 28, 197–200 (1989).

Hopkins, H. H.

Kaneko, M.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

Kubota, K.

Y. Yamanaka, Y. Hirose, K. Kubota, “High density optical recording by superresolution,” Jpn. J. Appl. Phys. 28, 197–200 (1989).

Mansuripur, M.

M. Mansuripur, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication).

Nishihara, H.

T. Suhara, H. Nishihara, “Possibility of super-resolution readout in integrated-optic disc pickup,” in Technical Digest of the International Symposium on Optical Memory, (Japan Society of Applied Physics, Kobe, Japan, 1989), pp. 97–8.

Ohta, M.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

Suhara, T.

T. Suhara, H. Nishihara, “Possibility of super-resolution readout in integrated-optic disc pickup,” in Technical Digest of the International Symposium on Optical Memory, (Japan Society of Applied Physics, Kobe, Japan, 1989), pp. 97–8.

Treves, D.

D. Treves, D. S. Bloomberg, “Signal, noise, and codes in optical memories,” Opt. Eng. 25, 881–891 (1986).

Udagawa, T.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

Wilson, T.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1986), pp. 509–532.

Yamanaka, Y.

Y. Yamanaka, Y. Hirose, K. Kubota, “High density optical recording by superresolution,” Jpn. J. Appl. Phys. 28, 197–200 (1989).

Yoshimura, S.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

Appl. Opt. (1)

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

J. Braat, “Optics of recording and read-out in optical disk systems,” Jpn. J. Appl. Phys. 28, 103–108 (1989).

Y. Yamanaka, Y. Hirose, K. Kubota, “High density optical recording by superresolution,” Jpn. J. Appl. Phys. 28, 197–200 (1989).

Opt. Eng. (1)

D. Treves, D. S. Bloomberg, “Signal, noise, and codes in optical memories,” Opt. Eng. 25, 881–891 (1986).

Opt. Lett. (1)

Other (4)

M. Mansuripur, Optical Sciences Center, University of Arizona, Tucson, Ariz. 85721 (personal communication).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1986), pp. 509–532.

T. Suhara, H. Nishihara, “Possibility of super-resolution readout in integrated-optic disc pickup,” in Technical Digest of the International Symposium on Optical Memory, (Japan Society of Applied Physics, Kobe, Japan, 1989), pp. 97–8.

A. Fukumoto, K. Aratani, S. Yoshimura, T. Udagawa, M. Ohta, M. Kaneko, “Super resolution in a magneto-optical disk with an active mask,” in Optical Data Storage 1991, D. B. Carlin, D. H. Kaye, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1499, 216–225 (1991).

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Figures (12)

Fig. 1
Fig. 1

Magneto-optic readout configuration: PPBS, partially polarizing beam splitter; PBS, polarizing beam splitter; s and p; directions relative to the beam-splitter surface; x and y; global coordinates.

Fig. 2
Fig. 2

Unfolded optical system.

Fig. 3
Fig. 3

Positive and negative first diffraction orders for P2(σ) = δ(σ): (a) low spatial frequency, (b) high spatial frequency.

Fig. 4
Fig. 4

Same as Fig. 3 but for finite area P2(σ).

Fig. 5
Fig. 5

Calculation of the signal current isig(ys). νy, νy′, ν, and νΔ are different axes of spatial frequency, where ∑ and Δ correspond to sum and difference frequencies, respectively.

Fig. 6
Fig. 6

Optical system transfer function C(νy; νy′) for the case of two pinholes spaced distance s apart in the collection lens aperture P2(σ): curve A, reference with P2(σ); curve B, single pinhole at center of P2(σ); curve C, s/D = 20%; curve D, s/D = 40%; curve E s/D = 60%; curve F, s/D = 85%.

Fig. 7
Fig. 7

Optical system transfer function C(νy, νy′) for rectangularly obstructed P2(σ): curve A, s/D = 0 (open aperture), nonconfocal; curve B1, s/D = 25%, nonconfocal; curve B2, s/D = 25%, confocal; curve C1, s/D = 50%, nonconfocal; curve C2, s/D = 50%, confocal; curve D1, s/D = 75%, nonconfocal; curve D2, s/D = 75%, confocal.

Fig. 8
Fig. 8

Optical system transfer function C(νy, νy′) for the system of Yamanaka: curve A, open aperture P1(σ), R(rd) = 1; curve B, s/D = 20%, R(rd) = 1; curve C, s/D = 20%, detector slit width τ adjusted to pass only central lobe to detector.

Fig. 9
Fig. 9

Optical system transfer function C(νy, νy′) for the integrated-optic disk pickup system of Suhara and Nisihara: curve A, nonconfocal; curve B, confocal.

Fig. 10
Fig. 10

Optical system transfer function C(νy, νy′) for the self-masking medium scheme proposed by Fukumoto et al. The mask function m(r0) is defined by a circle of radius ρ and an offset of γ from the spot center. In our case, ρ = 0.68 μm and γ = 0.85 μm: curve A, m(r0) = 0 (no masking), nonconfocal; curve B, m(r0) = 1 inside the mask, nonconfocal; curve C, m(r0) = 1 inside the mask, confocal; curve D, m(r0) = 1 inside the mask, nonconfocal configuration and a shading band in P2(σ) with s/D = 25%; curve E, m(r0) = 1 inside the mask, shading band of s/D 50%.

Fig. 11
Fig. 11

Edge responses of several systems: curve A, reference system in which P1(σ) and P2(σ) are unobstructed and R(rd) = 1 (nonconfocal); curve B, shading band in P2(σ) at S/D = 25% and R(rd) = 1; curve C, shading band in P2(σ) at s/D = 50% and R(rd) = 1; curve D, Suhara and Nishihara waveguide coupler system; curve E, Fukumoto et al. system with an open P2(σ) and R(rd) = 1.

Fig. 12
Fig. 12

Two-point resolution of several systems: curve A, bit pattern on disk plane consists of two 1.56-μm-long marks separated by 0.52 μm; curve B, reference system response with an open P2(σ) and R(rd) = 1; curve C, Fukumoto et al. system with an open P2(σ) and R(rd) = 1; curve D, shading band of 50% in the collection optics and R(rd) = 1.

Equations (22)

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D = ρ [ 1 ± a exp ( - j Φ ) ± a exp ( - j Φ ) - 1 ] ,
U x ( r 0 ) = h ( r 0 ) = P 1 ( σ ) exp ( - σ 2 w 2 ) exp [ j ( k / f 0 ) σ · r 0 ] d σ ,
U x ( r 0 ; r s ) = h ( r 0 ) ρ ( r 0 - r s ) , U y ( r 0 ; r s ) = h ( r 0 ) ρ ( r 0 - r s ) × a ( r 0 - r s ) exp [ - j Φ ( r 0 - r s ) ] .
U x ( σ ; r s ) = h ( r 0 ) ρ ( r 0 - r s ) P 2 ( σ ) × exp [ - j ( k / f 0 ) σ · r 0 ] d r 0 , U y ( σ ; r s ) = h ( r 0 ) ρ ( r 0 - r s ) a ( r 0 - r s ) × exp [ - j Φ ( r 0 - r s ) ] P 2 ( σ ) × exp [ - j ( k / f 0 ) σ · r 0 ] d r 0 .
H = [ cos 2 θ sin 2 θ - sin 2 θ cos 2 θ ] ,
U x ( σ ; r s ) = η cos 2 θ U x - ( σ ; r s ) + sin 2 θ U y - ( σ ; r s ) , U y ( σ ; r s ) = - η sin 2 θ U x - ( σ ; r s ) + cos 2 θ U y - ( σ ; r s ) ,
i sig ( r s ) μ ( r 0 - r s ; r 0 - r s ) × h ( r 0 ) h * ( r 0 ) g ( r 0 ; r 0 ) d r 0 d r 0
μ ( r 0 ; r 0 ) = η { a ( r 0 ) exp [ - j Φ ( r 0 ) ] + a ( r 0 ) exp [ j Φ ( r 0 ) ] } ρ ( r 0 ) ρ * ( r 0 ) ,
g ( r 0 ; r 0 ) = P 2 ( σ ) P 2 * ( σ ) G d ( σ - σ ) × exp [ - j ( k / f 0 ) ( σ · r 0 - σ . r 0 ) ] d σ d σ .
G d ( σ ) = R ( r d ) exp [ - j ( k / f d ) σ · r d ] d r d .
i sig ( r s ) 2 η Re { [ a exp ( - j Φ ) ρ h ] [ ρ * h * ] } ,
i sig ( r s ) 2 η Re { a exp ( - j Φ ) R } h 2 ,
μ ( r 0 ; r 0 ) = M ( ν ; ν ) × exp [ 2 π j ( ν · r 0 + ν · r 0 ) ] d ν 0 d ν 0 .
M ( ν ; ν ) = Q ( ν ) V * ( - ν ) + Q * ( - ν ) V ( ν ) ,
Q ( ν ) = η a ( r 0 ) ρ ( r 0 ) × exp [ - j Φ ( r 0 ) exp ( - 2 π j ν · r 0 ) d r 0 ,
V ( ν ) = ρ ( r 0 ) exp ( - 2 π j ν · r 0 ) d r 0 .
i sig ( r s ) = C ( ν ; ν ) M ( ν ; ν ) × exp [ - 2 π j ( ν - ν ) · r s ] d ν d ν ,
C ( ν ; ν ) = h ( r 0 ) h * ( r 0 ) g ( r 0 ; r 0 ) × exp [ - 2 π j ( ν · r 0 - ν · r 0 ) ] d r 0 d r 0 = P 2 ( σ ) P 2 * ( σ ) P 1 × ( σ + λ f 0 ν ) P 1 * ( σ + λ f 0 ν ) G d ( σ - σ ) × exp ( - σ + λ f 0 ν 2 w 2 ) × exp ( - σ + λ f 0 ν 2 w 2 ) d σ d σ .
i sig ( r s ) = C ( ν Δ ; ν Σ ) M ( ν Δ ; ν Σ ) × exp ( - 2 π j ν Δ · r s ) d ν Δ d ν Σ = [ C ( ν Δ ; ν Σ ) M ( ν Δ ; ν Σ ) d ν Σ ] × exp ( - 2 π j ν Δ · r s ) d ν Δ = f ( ν Δ ) exp ( - 2 π j ν Δ · r s ) d ν Δ .
M ( ν ; ν ) = Q ( ν ) δ ( ν ) + Q * ( - ν ) δ ( ν ) .
P 1 ( σ ) = h ( r 0 ) [ 1 - m ( r 0 ) ] exp [ - j ( k / f 0 ) σ · r 0 ] d r 0 ,
SNR = P sig P elec + c shot P sum 1 / 2 + c las P sig + c disk P sig + c x y P sum ,

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