Abstract

Wide, nonperiodic stepped phase structures are studied to correct various parameter-dependent wave-front aberrations in optical systems. The wide nature of these phase structures makes them easy to manufacture with sufficient compensation of the wave-front aberrations. Wave-front aberration correction for both continuous and discrete parameter variations are studied. An analytical method is derived for the discrete parameter variations to find the optimal phase structure. Both theoretical and experimental results show that these nonperiodic phase structures can be used to make (1) lenses athermal (defocus and spherical aberration compensated), (2) lenses achromatic, (3) lenses with a large field of view, (4) lenses with a reduced field curvature, and (5) digital versatile disk objective lenses for optical recording that are compatible with compact disk readout.

© 2001 Optical Society of America

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References

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  1. A. I. Tudorovskii, “An objective with a phase plate,” Opt. Spectrosc. 6, 126–133 (1959).
  2. H. P. Herzig, ed., Micro-optics (Taylor & Francis, London, 1998).
  3. K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
    [Crossref]
  4. Y. G. Soskind, “Novel technique for passive athermalization of optical systems,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 194–204.
  5. J. M. Sasian, R. A. Chipman, “Staircase lens: a binary and diffractive field curvature corrector,” Appl. Opt. 32, 60–66 (1993).
    [Crossref] [PubMed]
  6. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 9.1.3, p. 463.
  7. T. Shimano, A. Arimoto, “Objective lens and optical head using the same,” European patent application EP 0865037A1 (16September1998).
  8. R. Katayama, Y. Komatsu, Y. Yamanaka, “Dual-wavelength optical head with a wavelength-selective filter for 0.6- and 1.2-mm-thick-substrate optical disks,” Appl. Opt. 38, 3778–3786 (1999).
    [Crossref]
  9. B. H. W. Hendriks, P. G. J. M. Nuyens, “Design and manufacturing of far-field high-NA objective lenses for optical recording,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 413–414 (1999).
    [Crossref]
  10. B. H. W. Hendriks, J. E. de Vries, H. P. Urbach, “Application of non-periodic phase structures in optical systems,” in Proceedings of the Second Conference on Optical Design and Fabrication 2000 (Optical Society of Japan, Tokyo, 2000), pp. 325–328.
  11. P. Smulders, J. P. Baartman, J. W. Aarts, B. H. W. Hendriks, “Two-element objective lens and spherical aberration correction for digital video recording (DVR),” in Optical Data Storage, D. G. Stinson, R. Katayama, eds., Proc. SPIE4090, 302–308 (2000).
  12. Ref. 6, p. 464.
  13. D. G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1969).
  14. M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

1999 (1)

1993 (1)

1959 (1)

A. I. Tudorovskii, “An objective with a phase plate,” Opt. Spectrosc. 6, 126–133 (1959).

Aarts, J. W.

P. Smulders, J. P. Baartman, J. W. Aarts, B. H. W. Hendriks, “Two-element objective lens and spherical aberration correction for digital video recording (DVR),” in Optical Data Storage, D. G. Stinson, R. Katayama, eds., Proc. SPIE4090, 302–308 (2000).

Abramowitz, M.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Arimoto, A.

T. Shimano, A. Arimoto, “Objective lens and optical head using the same,” European patent application EP 0865037A1 (16September1998).

Baartman, J. P.

P. Smulders, J. P. Baartman, J. W. Aarts, B. H. W. Hendriks, “Two-element objective lens and spherical aberration correction for digital video recording (DVR),” in Optical Data Storage, D. G. Stinson, R. Katayama, eds., Proc. SPIE4090, 302–308 (2000).

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 9.1.3, p. 463.

Chipman, R. A.

de Vries, J. E.

B. H. W. Hendriks, J. E. de Vries, H. P. Urbach, “Application of non-periodic phase structures in optical systems,” in Proceedings of the Second Conference on Optical Design and Fabrication 2000 (Optical Society of Japan, Tokyo, 2000), pp. 325–328.

Hendriks, B. H. W.

B. H. W. Hendriks, J. E. de Vries, H. P. Urbach, “Application of non-periodic phase structures in optical systems,” in Proceedings of the Second Conference on Optical Design and Fabrication 2000 (Optical Society of Japan, Tokyo, 2000), pp. 325–328.

P. Smulders, J. P. Baartman, J. W. Aarts, B. H. W. Hendriks, “Two-element objective lens and spherical aberration correction for digital video recording (DVR),” in Optical Data Storage, D. G. Stinson, R. Katayama, eds., Proc. SPIE4090, 302–308 (2000).

B. H. W. Hendriks, P. G. J. M. Nuyens, “Design and manufacturing of far-field high-NA objective lenses for optical recording,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 413–414 (1999).
[Crossref]

Iwaki, M.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[Crossref]

Katayama, R.

Komatsu, Y.

Luenberger, D. G.

D. G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1969).

Maruyama, K.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[Crossref]

Nuyens, P. G. J. M.

B. H. W. Hendriks, P. G. J. M. Nuyens, “Design and manufacturing of far-field high-NA objective lenses for optical recording,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 413–414 (1999).
[Crossref]

Ogawa, R.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[Crossref]

Sasian, J. M.

Shimano, T.

T. Shimano, A. Arimoto, “Objective lens and optical head using the same,” European patent application EP 0865037A1 (16September1998).

Smulders, P.

P. Smulders, J. P. Baartman, J. W. Aarts, B. H. W. Hendriks, “Two-element objective lens and spherical aberration correction for digital video recording (DVR),” in Optical Data Storage, D. G. Stinson, R. Katayama, eds., Proc. SPIE4090, 302–308 (2000).

Soskind, Y. G.

Y. G. Soskind, “Novel technique for passive athermalization of optical systems,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 194–204.

Stegun, I. A.

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

Tudorovskii, A. I.

A. I. Tudorovskii, “An objective with a phase plate,” Opt. Spectrosc. 6, 126–133 (1959).

Urbach, H. P.

B. H. W. Hendriks, J. E. de Vries, H. P. Urbach, “Application of non-periodic phase structures in optical systems,” in Proceedings of the Second Conference on Optical Design and Fabrication 2000 (Optical Society of Japan, Tokyo, 2000), pp. 325–328.

Wakamiya, S.

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[Crossref]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 9.1.3, p. 463.

Yamanaka, Y.

Appl. Opt. (2)

Opt. Spectrosc. (1)

A. I. Tudorovskii, “An objective with a phase plate,” Opt. Spectrosc. 6, 126–133 (1959).

Other (11)

H. P. Herzig, ed., Micro-optics (Taylor & Francis, London, 1998).

K. Maruyama, M. Iwaki, S. Wakamiya, R. Ogawa, “A hybrid achromatic objective lens for optical data storage,” in International Conference on Applications of Optical Holography, T. Honda, ed., Proc. SPIE2577, 123–129 (1995).
[Crossref]

Y. G. Soskind, “Novel technique for passive athermalization of optical systems,” in Diffractive Optics and Micro-Optics, Postconference Digest, Vol. 43 of OSA Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 2000), pp. 194–204.

B. H. W. Hendriks, P. G. J. M. Nuyens, “Design and manufacturing of far-field high-NA objective lenses for optical recording,” in 18th Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, T. Asakura, eds., Proc. SPIE3749, 413–414 (1999).
[Crossref]

B. H. W. Hendriks, J. E. de Vries, H. P. Urbach, “Application of non-periodic phase structures in optical systems,” in Proceedings of the Second Conference on Optical Design and Fabrication 2000 (Optical Society of Japan, Tokyo, 2000), pp. 325–328.

P. Smulders, J. P. Baartman, J. W. Aarts, B. H. W. Hendriks, “Two-element objective lens and spherical aberration correction for digital video recording (DVR),” in Optical Data Storage, D. G. Stinson, R. Katayama, eds., Proc. SPIE4090, 302–308 (2000).

Ref. 6, p. 464.

D. G. Luenberger, Optimization by Vector Space Methods (Wiley, New York, 1969).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), Chap. 9.1.3, p. 463.

T. Shimano, A. Arimoto, “Objective lens and optical head using the same,” European patent application EP 0865037A1 (16September1998).

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Figures (15)

Fig. 1
Fig. 1

Lens system with a NPS in front.

Fig. 2
Fig. 2

Experimental results of the change in the lowest-order spherical wave-front aberration as a function of the temperature for the Philips glass/2P DVD objective lens (NA of 0.65) with and without NPS present.

Fig. 3
Fig. 3

Plot of the OPD as a function of the relative pupil coordinate ρ for the lens system when the temperature has changed by ΔT = 30 K (a) with no NPS present and (c) with NPS present. (b) The contribution to the wave front of the NPS.

Fig. 4
Fig. 4

Interferograms of the NA of 0.85 objective without NPS present for (a) λ = 404 nm and (b) λ = 409 nm and with NPS present for (c) λ = 404 nm and (d) λ = 409 nm.

Fig. 5
Fig. 5

Experimental and theoretical results of the change in defocus wave-front aberration OPDrms as a function of the wavelength for the NPS tabulated in Table 2.

Fig. 6
Fig. 6

Schematic ray trace through a lens containing a NPS. The height of the steps is exaggerated; it is generally small compared with the physical dimensions of the lens.

Fig. 7
Fig. 7

Schematic drawing of the coordinate system in which (x, y, z) is a point on the surface of the lens. Furthermore, ψ is the rotation angle of the lens around the y axis.

Fig. 8
Fig. 8

Calculated coma wave-front error at a 2° field (a) with no NPS present and (c) with NPS present. (b) The phase introduced by the NPS.

Fig. 9
Fig. 9

Experimental and theoretical results of the change in defocus wave-front aberration OPDrms as a function of the field angle for the NPS tabulated in Table 2.

Fig. 10
Fig. 10

Function f(ρ) and the stepped phase distribution that is due to the NPS.

Fig. 11
Fig. 11

Plot of the OPD in the CD configuration in the case (a) with no NPS present and (c) with NPS present. (b) The contribution to the wave front of the NPS.

Fig. 12
Fig. 12

Plot of the OPD in the CD configuration with Δz = 2.065-µm defocus in the case (a) with no NPS present and (c) with NPS present. (b) The contribution to the wave front of the NPS.

Fig. 13
Fig. 13

Photograph of the actuator with DVD objective and NPS used in the experiments.

Fig. 14
Fig. 14

Readout eye patterns, after equalization, obtained with the NPS: (a) DVD eye pattern with 8.9% jitter, (b) CD eye pattern with 4.0% jitter, (c) CD-R 1× eye pattern with 7.5% jitter.

Fig. 15
Fig. 15

Radial and tangential tilt windows for the DVD objective with NPS in the CD configuration.

Tables (5)

Tables Icon

Table 1 Zone Widths and Height Distribution of the NPS for the Athermalization of the Philips Glass/2P DVD Objective

Tables Icon

Table 2 Step Height and Zone Width Distribution of the NPS Compensating for Defocus

Tables Icon

Table 3 Step Width and Height Distribution of the NPS to Improve the Field of View of a Lens

Tables Icon

Table 4 Added Phase for the CD Configurationa

Tables Icon

Table 5 Example of the Determination of CF k for the Case Discussed in Subsection 3.Ba

Equations (58)

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h=λn-1,
ΔΦj=2πmjΔhh+Δnn-1,
Δh=αhΔT,
Δn=βΔT,
ΔΦj=2πα+βn-1 mjΔT.
ΔΦj=-0.001216mjΔT.
ΔΦj=-2πmjΔλλ-Δnn-1.
ΔΦj=-0.01693mjΔλ,
OPDθ=hjn1-sin2 θn21/2-cos θ,
x, y, z=R sin ζ cos φ, R sin ζ sin φ, R cos ζ,
θ=π-ζ.
x=R sin ζ cos φ cos ψ-R cos ζ sin ψ, y=R sin ζ sin φ, z=R sin ζ cos φ sin ψ+R cos ζ cos ψ.
x, y, z=R sin ζ cos φ, R sin ζ sin φ, R cos ζ,
z=R sin ζ cos φ sin ψ+R cos ζ cos ψ, Rψ sin ζ cos φ+R cos ζ, R cosζ-ψ cos φ.
ζ=ζ-ψ cos φ,
θ=θ+ψ cos φ.
ΔOPDψ=hjψ cos φ sin θ1-cos θn1-sin2 θn21/2.
hj=mjλn1-sin2 θn21/2-cos θ,
ΔΦrel=2πλ ΔOPDψ=2πmjψ sin θ cos φn.
ΔΦrel=2πmjrψ cos φnR.
ΔΦj=2πmjr¯jψ cos φnR.
Φlens=2π0.4ρ-0.6ρ3cos φ,
ΔΦj2π=0.016mjρ¯j cos φ.
ΔΦj=πmjn θ2,
2πfρ=2πλ Wρ.
OPDf2=2 01 fρ2ρdρ-2 01 fρρdρ2,
Fρ1,, ρN=OPD2fρ-i=1N+1 ai1ρi-1,ρiρ
1a,bρ=1a<ρ<b=0elsewhere,
Liρ1,, ρN=ρi-ρi-1,  i=1,, N+1.
Fρ1,, ρN
Liρ1,, ρN0,  i=1,, N+1.
Fρi=-4ai-ai+1fρiρi+2ai2-ai+12ρi+8ai-ai+1ρi01 fρρdρ-4 j=1N+1ai-ai+1ajρiρj2-ρj-12,
Liρj=-1when j=i-11when j=i0elsewhere.
Fρ1o,, ρNo+i=1N+1 μiLiρ1o,, ρNo=0,
μi0,  i=1,, N+1,
μiLiρ1o,, ρNo=0,  i=1,, N+1.
4ai-ai+1ρio-fρio+ai+ai+12+2 01 fρρdρ-j=1N+1 ajρjo2-ρj-1o2=μi+1-μi, i=1,, N,
μi0,  i=1,, N+1,
μiρio-ρi-1o=0,  i=1,, N+1.
fρio=ai+ai+12+2 01 fρρdρ-j=1N+1 ajρjo2-ρj-1o2.
Wρ=3.132ρ2-ρ4λ
Wadd=-12Δzρ2NA2,
fρ=Wρ/λ-12ρ2ΔzNA2/λ.
FΔz=0.
2 01 fρρ-2ρ3dρ+j=1N+1 ajρj4-ρj2-ρj-14-ρj-12=0.
CF=b0+1b1+1b2+1b3+1b4+b0+1b1+1b2+1b3+ .
CFk=b0+1b1+1b2+1b3+1bkb0, b1, b2,, bk=AkBk,
Ak=bkAk-1+Ak-2,
Bk=bkBk-1+Bk-2,
a0=h1h2,
b0=Inta0,
a1=a0-b0,
b1=Int1a1,
a2=1a1-b1.
bk=Int1ak,
ak+1=1ak-bk,
CFk-h1h20.005
h1h2CFk=AkBk,

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