Abstract

Analytical expressions for the primary wave-front aberrations of an actively tilted two-lens objective are derived, and expressions for the higher-order wave-front aberrations for disk tilt of this lens system are presented. This analysis is important because the two-lens objective opens the way to achieving higher-numerical-aperture systems for optical recording with acceptable tolerances that cannot be achieved with a single-lens objective. To test whether the conclusions drawn from the analytically derived results remain valid for high numerical apertures, we compare the results with those obtained by ray tracing: It is shown not only that the two-lens system is tolerant of disk-thickness variations and decentering of the lenses but that it can also be made tolerant of disk tilt when the lens facing the disk is actively tilted.

© 1998 Optical Society of America

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References

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  1. See, for instance, the Proceedings of the Joint Magneto-Optical Recording International Symposium/International Symposium on Optical Memory ’97, Yamagata, Japan, J. Magn. Jpn.22, Suppl. S2, 1–236 (1998)/Jpn. J. Appl. Phys. 37, 2079–2280 (1998).
  2. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
    [CrossRef]
  3. K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
    [CrossRef]
  4. W. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1991).
  5. B. H. W. Hendriks, “Tilt tolerant high-numerical-aperture two-lens objective for optical recording,” in Proceedings of the International Optical Design Conference ’98, L. Gardner, K. P. Thompson, eds., Proc. SPIE3482, 90–95 (1998).
    [CrossRef]
  6. Ref. 4, pp. 158–161.
  7. S. M. Mansfield, W. R. Studenmund, G. S. Kino, K. Osato, “High-numerical-aperture lens system for optical storage,” Opt. Lett. 18, 305–307 (1993).
    [CrossRef] [PubMed]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).
  9. J. Braat, “Analytical expression for the aberration coefficients of a tilted plane-parallel plate,” Appl. Opt. 36, 8459–8466 (1997).
    [CrossRef]
  10. Y. V. Martynov, B. H. W. Hendriks, F. Zijp, J. Aarts, J.-P. Baartman, G. E. van Rosmalen, J. J. H. B. Schleipen, H. van Houten have submitted the following paper to the Japanese Journal of Applied Physics: “High numerical aperture optical recording: active tilt correction or thin cover layer?”

1997

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

J. Braat, “Analytical expression for the aberration coefficients of a tilted plane-parallel plate,” Appl. Opt. 36, 8459–8466 (1997).
[CrossRef]

1993

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Braat, J.

Hendriks, B. H. W.

B. H. W. Hendriks, “Tilt tolerant high-numerical-aperture two-lens objective for optical recording,” in Proceedings of the International Optical Design Conference ’98, L. Gardner, K. P. Thompson, eds., Proc. SPIE3482, 90–95 (1998).
[CrossRef]

Ichimura, I.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

Iwasa, N.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Kino, G. S.

Kiyoku, H.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Maeda, F.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

Mansfield, S. M.

Matsushita, T.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Nagahama, S.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Nakamura, S.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Osato, K.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

S. M. Mansfield, W. R. Studenmund, G. S. Kino, K. Osato, “High-numerical-aperture lens system for optical storage,” Opt. Lett. 18, 305–307 (1993).
[CrossRef] [PubMed]

Senoh, M.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Studenmund, W. R.

Sugimoto, Y.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Watanabe, T.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

Welford, W.

W. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1991).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Yamada, T.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

Yamamoto, K.

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

Appl. Opt.

Jpn. J. Appl. Phys.

S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, Y. Sugimoto, H. Kiyoku, “High-power, long-lifetime InGaN multi-quantum-well-structure laser diodes,” Jpn. J. Appl. Phys. 36, L1059–L1061 (1997).
[CrossRef]

K. Yamamoto, K. Osato, I. Ichimura, F. Maeda, T. Watanabe, “0.8-numerical-aperture two-element objective lens for the optical disk,” Jpn. J. Appl. Phys. 36, 456–459 (1997).
[CrossRef]

Opt. Lett.

Other

See, for instance, the Proceedings of the Joint Magneto-Optical Recording International Symposium/International Symposium on Optical Memory ’97, Yamagata, Japan, J. Magn. Jpn.22, Suppl. S2, 1–236 (1998)/Jpn. J. Appl. Phys. 37, 2079–2280 (1998).

W. Welford, Aberrations of Optical Systems (Hilger, Bristol, UK, 1991).

B. H. W. Hendriks, “Tilt tolerant high-numerical-aperture two-lens objective for optical recording,” in Proceedings of the International Optical Design Conference ’98, L. Gardner, K. P. Thompson, eds., Proc. SPIE3482, 90–95 (1998).
[CrossRef]

Ref. 4, pp. 158–161.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).

Y. V. Martynov, B. H. W. Hendriks, F. Zijp, J. Aarts, J.-P. Baartman, G. E. van Rosmalen, J. J. H. B. Schleipen, H. van Houten have submitted the following paper to the Japanese Journal of Applied Physics: “High numerical aperture optical recording: active tilt correction or thin cover layer?”

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Figures (8)

Fig. 1
Fig. 1

Optical pickup consisting of a two-lens objective in front of a disk. The NA is defined by NA = n 5 sin θ. Furthermore, n 1, n 3, and n 5 are the refractive indices of lens 1, lens 2, and the disk, respectively. Lens 2 is tilted by an angle α; the disk, by angle β. The axis of rotation is perpendicular to the paper.

Fig. 2
Fig. 2

Incident pencil of rays, virtually focused at F, refracted by two surfaces. Fαβ is the sagittal paraxial focus of the pencil. The ray ABF αβ is the reference ray, and PQR is a general ray of the pencil. The system models the last part of the optical lens system shown in Fig. 1 when lens 2 is tilted by an angle α and the disk is tilted by angle β.

Fig. 3
Fig. 3

Analytically calculated OPDrms as a function of the tilt angle α of lens 2 when the disk is tilted by an angle β = 1° and where d 4 = 50 μm, d 5 = 0.6 mm, n 3 = 1.486, and n 5 = 1.581. For a discussion of the results obtained by ray tracing, see Section 5.

Fig. 4
Fig. 4

Analytically calculated OPDrms as a function of the tilt angle α of lens 2 for four values of d 4 when the disk is tilted by an angle β = 1° and where d 5 = 0.6 mm, n 3= 1.486, and n 5 = 1.581.

Fig. 5
Fig. 5

Analytically calculated OPDrms as a function of the tilt angle α of lens 2 for three values of d 5 when the disk is tilted by an angle β = 1° and where d 4 = 50 μm, n 3 = 1.486, and n 5 = 1.581.

Fig. 6
Fig. 6

Calculated proportionality constant μ as a function of d 4/d 5 for three values of n 3 when n 5 = 1.581.

Fig. 7
Fig. 7

Ray-trace plot of the two-lens system with a 50-μm air gap. F and P are the focal and the principal points, respectively.

Fig. 8
Fig. 8

Schematic drawing of the last part of the two-lens system when lens 2 is decentered by a distance δy (exaggerated in the figure) in the y direction. Both (a) the original pencil of rays and (b) the temporarily enlarged pencil used to derive the primary aberrations are shown.

Tables (4)

Tables Icon

Table 1 Lens Parameters as a Function of d4 for Solutions Near Λ ≈ Λ c

Tables Icon

Table 2 Lens Parameters as a Function of d4 for Solutions Near Λ ≈ Λ h

Tables Icon

Table 3 Comparison between Third-Order Theory and Numerical Ray-Traced Results

Tables Icon

Table 4 15-mλ OPDrms Tolerances of the Two-Lens Systems as Defined in Table 3 (Ray Trace)

Equations (47)

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d 3 n 3 + d 4 + d 5 n 5 = 1 K 1 1 - d 1 n 1 + d 2 K 1 1 - Λ ,
Λ = K 2 d 3 n 3 + d 4 + d 5 n 5 .
Φ = 2 NA K 1 1 - Λ .
F = 1 - Λ K 1 .
W S = - NA 4 8 1 - Λ 4 K 1 1 n 1 - 1 2 n 1 2 + 8 G n 1 - 1 K 1 3 + 1 - 1 n 1 2 1 - d 1 n 1   K 1 - 1 - n 3 n 3 - 1   Λ 2 × 1 - 1 n 3 2 - Λ Λ K 2 + 1 - 1 n 3 2 d 4 + 1 n 5 2 - 1 n 3 2 d 5 n 5 ,
W C = - NA 3 η 2 1 - Λ 2 1 n 1 - 1 n 1 2 - 1 - 1 n 1 2 × 1 - d 1 n 1   K 1 + 1 - n 3 n 3 - 1   Λ 1 - 1 n 3 2 - Λ × 1 + d 1 n 1 + d 2 K 2 n 3 - 1 × K 1 Λ K 2 1 - Λ - 1 - 1 n 3 2 d 4 + 1 n 5 2 - 1 n 3 2 d 5 n 5 1 - d 1 n 1 + d 2 K 2 K 1 1 - Λ ,
G = G 0 + G 1 ,
G 0 = - K 1 3 8 n 1 - 1 1 n 1 - 1 2 n 1 2 + 1 - 1 n 1 2 × 1 - d 1 n 1   K 1 ,
W S = - NA 4 8 8 G 1 n 1 - 1 1 - Λ 4 K 1 4 - 1 - n 3 n 3 - 1   Λ 2 1 - 1 n 3 2 - Λ Λ K 2 + 1 - 1 n 3 2   d 4 + 1 n 5 2 - 1 n 3 2 d 5 n 5 .
W S d 5 = - NA 4 8 n 5 - 32 K 2 G 1 n 1 - 1 1 - Λ 3 K 1 4 + 2 n 3 n 3 - 1 × 1 - n 3 n 3 - 1   Λ 1 - 1 n 3 2 - Λ Λ + 1 - n 3 n 3 - 1   Λ 2 Λ - 1 - n 3 n 3 - 1   Λ 2 × 1 - 1 n 3 2 - Λ + 1 n 5 2 - 1 n 3 2 .
d 2 d 5 = - 1 n 5 1 - Λ 2
W δ y = 1 2   δ y NA 3 n 3 n 3 - 1 2   Λ Λ - n 3 - 1 n 3 × Λ + 1 n 3 2 - 1 - K 2 d 4 1 n 3 2 - 1 + d 5 n 5 1 n 3 2 - 1 n 5 2 ,
W β = - 1 2 NA 3 β   d 5 n 5 1 - 1 n 5 2 .
W α ,   β = 1 2 NA 3 n 3 α d 4 + d 5 n 5 1 - 1 n 3 2 - 1 2 NA 3 d 5 n 5 n 3 - 1 α + β 1 - 1 n 5 2 .
W S = 0 ,
W S d 5 = 0 ,
W C = 0 ,
W δ y = 0 ,
W α ,   β = 0 ,
α = μ β ,
μ = 1 - n 3 + 1 + n 5 d 4 d 5 n 5 2 n 3 n 3 2 - 1 n 5 2 - 1 - 1 .
n 5 d 4 d 5 = n 3 2 n 5 2 n 5 2 - 1 n 3 2 - 1 - 1 ,
1 - 2 Λ + Λ 2 - 1 n 5 2 = 0 .
Λ = 1 - 1 n 5 .
0 = d 3 n 5 3 - d 3 n 5 2 n 3 + n 5 d 5 - 1 + 2 n 5 + n 5 - d 3 - d 4 + 2 d 4 n 5 n 3 2 + n 5 d 3 - d 4 n 5 - d 5 - 1 + n 5 + n 5 2 n 3 3 + - d 5 + d 4 n 5 - 2 n 5 3 n 3 4 + d 5 + d 4 n 5 3 n 3 5 .
Λ c = 1 - 1 n 3 ,
Λ h = 1 - 1 n 3 2 .
W = FPQR - FABF α β .
W = n 3 2 d 4 + d 5 n 5 1 - 1 + tan 2   θ 0 1 / 2 - d 4 1 - 1 + tan 2   θ 1 1 / 2 - n 5 d 5 1 - cos   θ 2 + n 5 n 3 d 4 + d 5 n 5 tan   θ 0 - d 4   tan   θ 1 sin   θ 2 + β - α n 3 d 4 + d 5 n 5 tan   θ 0 - d 4 tan   θ 1 × 1 + tan 2   θ 1 1 / 2 - n 5   sin   θ 2 tan   θ 1 - β - α d 5   sin   θ 2 ,
n 3   sin   θ 0 = sin   θ 1 ,
sin θ 1 - β + α = n 5   sin   θ 2 ,
NA = n 3   sin θ 0 + α .
NA ˜ = NA 1 + δ y h 3 ,
h 3 = Λ NA K 2 .
W I NA ˜ NA 4 W I 0 = 1 8 NA ˜ 4 1 - n 3 n 3 - 1   Λ 2 1 - 1 n 3 2 - Λ Λ K 2 + 1 n 3 2 - 1 d 4 + 1 n 3 2 - 1 n 5 2 d 5 n 5
W II NA ˜ NA 3 W II 0 = - 1 2 NA ˜ 3 δ y 1 - Λ n 3 n 3 - 1   Λ - 1 1 - 1 n 3 2 - Λ - K 2 Λ 1 n 3 2 - 1 d 4 - K 2 Λ 1 n 3 2 - 1 n 5 2 d 5 n 5 ,
W x ,   y = W I x 2 + y 2 2 h 3 + δ y 4 + W II y x 2 + y 2 h 3 + δ y 3 + O δ y 2 ,
x = x ,
y = y + δ y ,
x 2 + y 2 h 3 2 .
W x ,   y = W I 0 x 2 + y 2 2 h 3 4 + W II 0 - 4 W I 0 K 2 δ y Λ NA × y x 2 + y 2 h 3 3 + O δ y 2 .
W 51 = 1 8 NA 5 n 3 α d 4 3 - 2 n 3 2 - 1 n 3 4 + d 5 n 5 3 n 5 4 - 2 n 3 2 n 5 2 - 1 n 3 4 - β - α d 5 n 5 - 3 n 5 4 + 2 n 5 2 + 1 .
W 71 = 1 16 NA 7 n 3 α d 4 5 - 3 n 3 2 - 1 n 3 4 - 1 n 3 6 + d 5 n 5 5 n 5 6 - 3 n 3 2 n 5 4 - 1 n 3 4 n 5 2 - 1 n 3 6 - β - α d 5 n 5 - 5 n 5 6 + 3 n 5 4 + 1 n 5 2 + 1 .
A 31 = 1 3   W 31 + 2 5   W 51 + 2 5   W 71 + 8 21   W 91 + 5 14   W 11,1 + 1 3   W 13,1 + 14 45   W 15,1 + 16 55   W 17,1 + 3 11   W 19,1 + ,
A 51 = 1 10   W 51 + 6 35   W 71 + 3 14   W 91 + 5 21   W 11,1 + 1 4   W 13,1 + 14 45   W 15,1 + 14 55   W 17,1 + 36 143   W 19,1 + ,
A 71 = 1 35   W 71 + 4 63   W 91 + 2 21   W 11,1 + 4 33   W 13,1 + 14 99   W 15,1 + 112 715   W 17,1 + 24 143   W 19,1 + ,
OPD rms = n = 1 A 2 n + 1,1 2 4 n + 4 1 / 2 .

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