Abstract

A point-spread function (PSF) is commonly used as a model of an optical disk readout channel. However, the model given by the PSF does not contain the quadratic distortion generated by the photo-detection process. We introduce a model for calculating an approximation of the quadratic component of a signal. We show that this model can be further simplified when a read-only-memory (ROM) disk is assumed. We introduce an edge-spread function by which a simple nonlinear model of an optical ROM disk readout channel is created.

© 2002 Optical Society of America

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References

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  1. H. H. Hopkins, “Diffraction theory of laser read-out systems of optical video discs,” J. Opt. Soc. Am. 69, 4–24 (1979).
    [CrossRef]
  2. C. H. F. Veltzel, “Laser beam reading of video records,” Appl. Opt. 17, 2029–2038 (1978).
    [CrossRef]
  3. J. Braat, “Read-out of Optical discs,” in Principles of Optical Disc Systems, G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink (Adam Hilger Ltd., Bristol and Boston, 1985), pp. 7–87.
  4. S. Kubota, “Aplanatic condition required to reproduce jitter-free signals in an optical digital disk system,” Appl. Opt. 26, 3961–3972 (1987).
    [CrossRef] [PubMed]
  5. K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
    [CrossRef]
  6. L. Agarossi, S. Bellini, A. Canella, P. Migliorati, “A Volterra model for the high density optical disc,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 1998, Proc. IEEE3, 1605–1608 (1998).
  7. P. W. Nutter, C. D. Wright, “A new technique for the prediction and correction of nonlinearities in simulated optical readout waveforms,” in Technical Digest of Optical Data Storage 2001, T. Hurst, S. Kobayashi, eds., Proc. SPIE4342, 82–84 (2001).
  8. S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
    [CrossRef]

2000 (2)

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

1987 (1)

1979 (1)

1978 (1)

Agarossi, L.

L. Agarossi, S. Bellini, A. Canella, P. Migliorati, “A Volterra model for the high density optical disc,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 1998, Proc. IEEE3, 1605–1608 (1998).

Ahn, S. K.

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

Bellini, S.

L. Agarossi, S. Bellini, A. Canella, P. Migliorati, “A Volterra model for the high density optical disc,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 1998, Proc. IEEE3, 1605–1608 (1998).

Braat, J.

J. Braat, “Read-out of Optical discs,” in Principles of Optical Disc Systems, G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink (Adam Hilger Ltd., Bristol and Boston, 1985), pp. 7–87.

Canella, A.

L. Agarossi, S. Bellini, A. Canella, P. Migliorati, “A Volterra model for the high density optical disc,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 1998, Proc. IEEE3, 1605–1608 (1998).

Hineno, S.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Hopkins, H. H.

Jeong, S. Y.

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

Kato, Y.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Kim, H. N.

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

Kim, J. Y.

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

Kubota, S.

Matsumoto, Y.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Migliorati, P.

L. Agarossi, S. Bellini, A. Canella, P. Migliorati, “A Volterra model for the high density optical disc,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 1998, Proc. IEEE3, 1605–1608 (1998).

Nishi, N.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Nutter, P. W.

P. W. Nutter, C. D. Wright, “A new technique for the prediction and correction of nonlinearities in simulated optical readout waveforms,” in Technical Digest of Optical Data Storage 2001, T. Hurst, S. Kobayashi, eds., Proc. SPIE4342, 82–84 (2001).

Park, K. C.

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

Saito, K.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Toyota, K.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Uemura, K.

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Veltzel, C. H. F.

Wright, C. D.

P. W. Nutter, C. D. Wright, “A new technique for the prediction and correction of nonlinearities in simulated optical readout waveforms,” in Technical Digest of Optical Data Storage 2001, T. Hurst, S. Kobayashi, eds., Proc. SPIE4342, 82–84 (2001).

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Jpn. J. Appl. Phys. (2)

S. K. Ahn, H. N. Kim, S. Y. Jeong, K. C. Park, J. Y. Kim, “A nonlinearity compensated channel model and partial response maximum likelihood (PRML) simulator for the high density optical disc,” Jpn. J. Appl. Phys. 39, 824–829 (2000).
[CrossRef]

K. Saito, K. Uemura, Y. Kato, S. Hineno, Y. Matsumoto, N. Nishi, K. Toyota, “Optical disk readout analysis using an extended point spread function,” Jpn. J. Appl. Phys. 39, 693–697 (2000).
[CrossRef]

Other (3)

L. Agarossi, S. Bellini, A. Canella, P. Migliorati, “A Volterra model for the high density optical disc,” in Proceedings of the International Conference on Acoustics, Speech and Signal Processing, 1998, Proc. IEEE3, 1605–1608 (1998).

P. W. Nutter, C. D. Wright, “A new technique for the prediction and correction of nonlinearities in simulated optical readout waveforms,” in Technical Digest of Optical Data Storage 2001, T. Hurst, S. Kobayashi, eds., Proc. SPIE4342, 82–84 (2001).

J. Braat, “Read-out of Optical discs,” in Principles of Optical Disc Systems, G. Bouwhuis, J. Braat, A. Huijser, J. Pasman, G. van Rosmalen, K. S. Immink (Adam Hilger Ltd., Bristol and Boston, 1985), pp. 7–87.

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Figures (14)

Fig. 1
Fig. 1

Schematic representation of an optical pickup given by Hopkins’s scalar diffraction method.

Fig. 2
Fig. 2

Assuming that the shapes of pits are rectangular with pit width Pw, the complex reflectance of the disk (a) can be decomposed into the background (b) and the pit sequence (c).

Fig. 3
Fig. 3

PSF(x) when a DVD pickup (λ = 650 nm, NA = 0.6) is used to play back the signal.

Fig. 4
Fig. 4

Three-dimensional representation of w′ (x 1, x 2) and its contour plot. w′ (x 1, x 2) is almost zero when x 2 > 0.24 µm.

Fig. 5
Fig. 5

(a) Modulation signal m(x); (b) Signal md(x, x 2) calculated as the product of two signals m(x + x 2) and m*(x - x 2) [shown in (c)]. (d), md(x, x 2) becomes a series of negative pulses at each edge position of m(x).

Fig. 6
Fig. 6

ESF for a DVD equivalent optical pickup. We normalize the ESF by the peak-to-peak amplitude of the linear term I 1(x 0).

Fig. 7
Fig. 7

Calculation method given by Eq. (33) is illustrated. For the pit pattern (a), a series of delta functions (b) is generated, corresponding to all of the edge positions of the pits. The quadratic term (d) can be calculated as a convolution between the ESF (c) and the series of delta functions.

Fig. 8
Fig. 8

With the ESF, the optical disc channel can be modeled as shown. As in a conventional method, the linear term I 1(x 0) is obtained by simply convolving the PSF with the input signal. In the proposed model, the quadratic term I 2(x 0) can be obtained by convolving the ESF with a series of delta functions, which are extracted from the edges of the input signal.

Fig. 9
Fig. 9

Pit pattern used for the simulation. Open rectangles represent pits whose width is 0.26 µm. In this simulation, 3T, 5T and 11T pits and spaces are assumed within a total length of 5.32 µm.

Fig. 10
Fig. 10

Simulation results of Hopkins’s method (bold curve) and the ESF method (thin curve) agree very well. A slight difference is observed only around the 3T (shortest) pits.

Fig. 11
Fig. 11

To estimate the accuracy of the proposed model, we assumed the periodic pattern whose pits and spaces are equal distance of Ed. We used 0.26 µm as the pit width Pw.

Fig. 12
Fig. 12

Inverse-MSE measures as a function of the edge-to-edge distance Ed. The result from the proposed model I 0 + I 1(x 0) + I 2(x 0) is shown in the thick-solid curve, the linear model I 0 + I 1(x 0) is shown in the dashed curve. The thin-solid curve is the result of the modified ESF, which is optimized for the edge-to-edge distance Ed to be 0.36 µm.

Fig. 13
Fig. 13

When the edge-to-edge distance Ed becomes small, the trailing edge of m(x + x 2) and the leading edge of m(x - x 2) exchange their positions. This crossover of the pulse edges causes the polarity inversion of the multiplied signal md(x, x 2).

Fig. 14
Fig. 14

Conventional linear model (convolution with PSF) provides the signal shown as I 0 + I 1(x 0). If the quadratic term I 2(x 0) is taken into account, a positive level shift of the playback signal of longer (11T) pits and spaces is observed as a bold curve [labeled I 0 + I 1(x 0) + I 2(x 0)]. This level shift is the asymmetry often observed in an actual playback signal.

Equations (36)

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fx, y= Fu, vexp-2πiux+vydudv,
Gu, v, x0= rx-x0, yfx, y×exp-2πiux+vydxdy,
Ix0= Au, v|Gu, v, x0|2dudv,
rx, y=1-rectyPw+mxrectyPw,
Mξ= mxexp2πixξdx.
Gu, v, x0=Bu, v+ Fru-ξ, vMξ×exp2πix0ξdξ,
Fru, v= rectyPwfx, y×exp-2πiux+vydxdy,
Bu, v=F-u, -v-Pw  sincπPwv×F-u-v-vdv.
Ix0=I0+I1x0+I2x0,
I0= Au, vBu, vB*u, vdudv.
I1x0= Hζ1Mζ1exp2πix0ζ1dζ1+ H*ζ2M*ζ2exp-2πix0ζ2dζ2,
Hζ= Au, vB*u, vFru-ζ, vdudv.
I1x0=2Repsfx*mx|x=x0.
I2x0= Wζ1, ζ2Mζ1M*ζ2×exp2πix0ζ1-ζ2dζ1dζ2,
Wζ1, ζ2= Au, vFru-ζ1, v×Fr*u-ζ2, vdudv.
Wζ1, ζ2=W*ζ2, ζ1.
I2x0= wξ1, ξ2mx0-ξ1m*x0-ξ2dξ1dξ2,
wξ1, ξ2= Wζ1, ζ2exp2πiξ1ζ1-ξ2ζ2dζ1dζ2.
wξ1, ξ2=w*ξ2, ξ1.
ξ1=x1-x2ξ2=x1+x2.
I2x0=2  wx1, x2mdx0-x1, x2dx1dx2,
wx1, x2=wx1-x2, x1+x2,
mdx1, x2=mx1+x2m*x1-x2.
wx1, x2mdx1, x2=w*x1, -x2md*x1, -x2.
I2x0=4 x2=0+Re-wx1, x2×mdx0-x1, x2dx1dx2,
mx=1landexpiϕpit,
mdx, x2+md*x, -x2=2+2cos ϕ-1nrectx-xn2x2,
I2x0=4cos ϕ-1x2=0+Re-wx1, x2×nrectx0-x1-xn2x2dx1dx2+C0,
C0=4 x2=0-Rewx1, x2dx1dx2.
|wx1, x2|0, |x2|>Tmin2,
I2x04cos ϕ-1x2=0+Re-wx1, x2×rectx-x12x2dx1dx2* n δx-xnx=x0+C0.
esfx=2 x2=0x1=-x2x2Rewx+x1, x2dx1dx2,
I2x02cos ϕ-1esfx* n δx-xnx=x0+C0.
MSE10 log |Ix-Ix|2dx |Ix|2dx.
esfx=2 x2=0x1=-x3x3Rewx+x1, x2dx1dx2,
x3=x2,x2<Ed/2Ed/2-x2,x2Ed/2.

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