Abstract

Methods of geometrical optics are used in deriving a simple expression for the focus error signal in terms of the parameters of an astigmatic system. The extent of validity of this result is then examined by comparison with diffraction calculations. Diffraction analysis also permits the study of push–pull tracking error signal from pregrooved disk surfaces.

© 1987 Optical Society of America

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References

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  1. G. Bouwhuis, J. J. M. Braat, “Recording and Reading of Information on Optical Disks,” in Applied Optics and Optical Engineering, Vol. 9, R. Shannon, J. C. Wyant, Eds. (Academic, New York, 1983).
    [CrossRef]
  2. W. H. Meiklejohn, “Magneto-optics: A Thermomagnetic Recording Technology,” IEEE Proc. 74, 1570 (1986).
    [CrossRef]
  3. M. Yamamoto, A. Watabe, H. Ukita, “Optical Pregroove Dimensions: Design Considerations,” Appl. Opt. 25, 4031 (1986).
    [CrossRef] [PubMed]
  4. T. Murakami, K. Taira, M. Mori, “Magnetooptic Erasable Disk Memory with Two Optical Heads,” Appl. Opt. 25, 3986 (1986).
    [CrossRef] [PubMed]
  5. S. L. DeVore, “Radial Error Signal Simulation for Optical Disk Drives,” Appl. Opt. 25, 4001 (1986).
    [CrossRef] [PubMed]
  6. D. K. Cohen, W. H. Gee, M. Ludeke, J. Lewkowicz, “Automatic Focus Control: The Astigmatic Lens Approach,” Appl. Opt. 23, 565 (1984).
    [CrossRef] [PubMed]
  7. J. J. M. Braat, G. Bouwhuis, “Position Sensing in Video Disk Readout,” Appl. Opt. 17, 2013 (1978).
    [CrossRef] [PubMed]
  8. M. Mansuripur, “Distribution of Light at and Near the Focus of High Numerical Aperture Objectives,” J. Opt. Soc. Am. A 3, 2086 (1986).
    [CrossRef]

1986 (5)

1984 (1)

1978 (1)

Bouwhuis, G.

J. J. M. Braat, G. Bouwhuis, “Position Sensing in Video Disk Readout,” Appl. Opt. 17, 2013 (1978).
[CrossRef] [PubMed]

G. Bouwhuis, J. J. M. Braat, “Recording and Reading of Information on Optical Disks,” in Applied Optics and Optical Engineering, Vol. 9, R. Shannon, J. C. Wyant, Eds. (Academic, New York, 1983).
[CrossRef]

Braat, J. J. M.

J. J. M. Braat, G. Bouwhuis, “Position Sensing in Video Disk Readout,” Appl. Opt. 17, 2013 (1978).
[CrossRef] [PubMed]

G. Bouwhuis, J. J. M. Braat, “Recording and Reading of Information on Optical Disks,” in Applied Optics and Optical Engineering, Vol. 9, R. Shannon, J. C. Wyant, Eds. (Academic, New York, 1983).
[CrossRef]

Cohen, D. K.

DeVore, S. L.

Gee, W. H.

Lewkowicz, J.

Ludeke, M.

Mansuripur, M.

Meiklejohn, W. H.

W. H. Meiklejohn, “Magneto-optics: A Thermomagnetic Recording Technology,” IEEE Proc. 74, 1570 (1986).
[CrossRef]

Mori, M.

Murakami, T.

Taira, K.

Ukita, H.

Watabe, A.

Yamamoto, M.

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of the astigmatic focus-error-detection system. When the disk surface has grooves of depth λ/8, the same system yields the track error signal in the push–pull mode. Note that δ, the distance between S and the focal point of L1, is twice the actual separation of the disk from the objective's focal plane.

Fig. 2
Fig. 2

(a) FES vs Δ as obtained from geometrical optics considerations leading to Eq. (3). Although the plot is obtained for the specific values of α = 100 and β = 10 it is typical of all other values of α and β. The maximum of FES occurs at Δmax = 1/(α + β), while its minimum occurs at Δmin = −1/(αβ). The zero-crossings occur at Δ = 0 and Δ = 1/β. (b) Derivative of FES with respect to Δ for α = 100 and β = 10. The extrema of this curve occur at Δ0, Δ1, and Δ2 which are related to α and β through Eq. (5).

Fig. 3
Fig. 3

Distribution of the reflected light intensity at various cross sections of the system of Fig. 1 with parameters specified in Table I. The assumed incident beam at L1 has a Gaussian amplitude distribution with 1/e radius equal to 2.2 mm (same as the radius of L1). The disk is in the focal plane of the objective, and the focused spot is ontrack: (a) intensity distribution at the disk surface; (b) intensity distribution at the plane of the objective lens L1; (c) intensity distribution at the plane of the astigmatic lens L2; (d) intensity distribution at the plane of the photodetectors.

Fig. 4
Fig. 4

Same as Fig. 3 but for the disk being out-of-focus by +5λ. The plus indicates that the disk is far from the lens.

Fig. 5
Fig. 5

Same as Fig. 3 but for the disk being out-of-focus by +3λ.

Fig. 6
Fig. 6

Same as Fig. 3 but for the disk being out-of-focus by −3λ.

Fig. 7
Fig. 7

Focus error signal vs focus error distance for the system of Fig. 1 with parameters of Table I. The broken curve is the geometric result of Eq. 3, while the solid curve is obtained from diffraction calculations. The × points represent the focus error signal when in the diffraction calculations the spot is assumed offtrack by various amounts.

Fig. 8
Fig. 8

Intensity distribution after reflection from the disk: (a) at the plane of the objective lens and (b) at the plane of the detectors. The disk is in the focal plane of L1, but the focused spot is offtrack by −0.6 μm.

Fig. 9
Fig. 9

Same as Fig. 8 but for an offtrack distance of +0.45 μm.

Fig. 10
Fig. 10

Same as Fig. 8 but for an offtrack distance of +0.15 μm.

Fig. 11
Fig. 11

Track error signal vs position of the spot as obtained from diffraction calculations. The solid curve corresponds to situations where the disk is in-focus. The points indicated by ×, +, and * represent TES when the disk is out-of-focus by −3λ, +3λ, and +6λ, respectively.

Fig. 12
Fig. 12

Intensity distribution after reflection from the disk: (a) at the plane of the objective lens and (b) at the plane of the detectors. The disk is out-of-focus by −3λ, and the focused spot is offtrack by +0.6 μm.

Tables (1)

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Table I Numerical Values of the System Parameters used in the Computations

Equations (7)

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d = 2 f 1 f 2 f 1 + f 2 ,
FES = h 2 w 2 h 2 + w 2
F E S = 2 α ( 1 β Δ ) Δ 1 2 β Δ + ( α 2 + β 2 ) Δ 2 .
d d Δ F E S = 2 α [ 1 2 β Δ ( α 2 β 2 ) Δ 2 ] [ 1 2 β Δ + ( α 2 β 2 ) Δ 2 ] 2 .
Δ n = β + 2 α cos ( { 2 n π + arccos [ 2 α β / ( α 2 + β 2 ) ] } / 3 ) β 2 α 2 ; n = 0 , 1 , 2.
FES = ( Q 1 + Q 3 ) ( Q 2 + Q 4 ) Q 1 + Q 2 + Q 3 + Q 4 ,
TES = ( Q 1 + Q 2 ) ( Q 3 + Q 4 ) Q 1 + Q 2 + Q 3 + Q 4 .

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