Abstract

The depth of focus of light patterns can be extended, within given tolerances, beyond the classical limits. For a quantitative evaluation we introduce a degree of depth-of-focus extension and a three-dimensional energy-distribution efficiency. The basic limitations involved in depth-of-focus extension are discussed. A coherent system in which the input is optimized for a desired output pattern is presented. An example of a pattern containing diffraction-limited line segments and a 4 times improvement in depth of focus is demonstrated. This task is much more difficult than generating patterns of isolated light spots in which the depth of focus is extended beyond an order of magnitude.

© 1998 Optical Society of America

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References

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).
  2. M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
    [CrossRef]
  3. H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
    [CrossRef]
  4. S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
    [CrossRef]
  5. R. Piestun, J. Shamir, “Control of wave-front propagation with diffractive elements,” Opt. Lett. 19, 771–773 (1994).
    [CrossRef] [PubMed]
  6. B. Salik, J. Rosen, A. Yariv, “Nondiffracting images under coherent illumination,” Opt. Lett. 17, 1743–1745 (1995).
    [CrossRef]
  7. F. Wyrowski, O. Bryngdahl, “Speckle-free reconstruction in digital holography,” J. Opt. Soc. Am. A 2, 693–697 (1985).
  8. See, for example, R. Piestun, B. Spektor, J. Shamir, “Wave fields in three dimensions: analysis and synthesis,”J. Opt. Soc. Am. A 13, 1837–1848 (1996), and references therein.
  9. M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).
  10. V. P. Koronkevitch, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik (Stuttgart) 87, 91–93 (1991).
  11. E. Marom, N. Konforti, D. Mendelovic, J. Katz, “Extended confinement beam generation,” in Proceedings of the Sixteenth Congress of the International Commission on Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 526–527 (1993).

1996 (1)

1995 (1)

1994 (1)

1992 (1)

S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
[CrossRef]

1991 (2)

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

V. P. Koronkevitch, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik (Stuttgart) 87, 91–93 (1991).

1985 (1)

1982 (1)

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

1981 (1)

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Bryngdahl, O.

Fujisawa, T.

S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
[CrossRef]

Fukuda, H.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Golub, M. A.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

Inoue, S.

S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
[CrossRef]

Karpeev, S. V.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Katz, J.

E. Marom, N. Konforti, D. Mendelovic, J. Katz, “Extended confinement beam generation,” in Proceedings of the Sixteenth Congress of the International Commission on Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 526–527 (1993).

Konforti, N.

E. Marom, N. Konforti, D. Mendelovic, J. Katz, “Extended confinement beam generation,” in Proceedings of the Sixteenth Congress of the International Commission on Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 526–527 (1993).

Koronkevitch, V. P.

V. P. Koronkevitch, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik (Stuttgart) 87, 91–93 (1991).

Levenson, M. D.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

Marom, E.

E. Marom, N. Konforti, D. Mendelovic, J. Katz, “Extended confinement beam generation,” in Proceedings of the Sixteenth Congress of the International Commission on Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 526–527 (1993).

Mendelovic, D.

E. Marom, N. Konforti, D. Mendelovic, J. Katz, “Extended confinement beam generation,” in Proceedings of the Sixteenth Congress of the International Commission on Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 526–527 (1993).

Ogawa, Y.

S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
[CrossRef]

Okazaki, S.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Palchikova, I. G.

V. P. Koronkevitch, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik (Stuttgart) 87, 91–93 (1991).

Piestun, R.

Prokhorov, A. M.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Rosen, J.

Salik, B.

Shamir, J.

Simpson, R. A.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

Sisakyan, I. N.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Soifer, V. A.

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Spektor, B.

Tamaushi, S.

S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
[CrossRef]

Terasawa, T.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Viswanathan, N. S.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

Wyrowski, F.

Yariv, A.

IEEE Trans. Electron. Devices (1)

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. B (2)

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus and resolution enhancement,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

S. Inoue, T. Fujisawa, S. Tamaushi, Y. Ogawa, “Optimization of partially coherent optical system for optical lithography,” J. Vac. Sci. Technol. B 10, 3004–3007 (1992).
[CrossRef]

Opt. Lett. (2)

Optik (Stuttgart) (1)

V. P. Koronkevitch, I. G. Palchikova, “Kinoforms with increased depth of focus,” Optik (Stuttgart) 87, 91–93 (1991).

Sov. Technol. Phys. Lett. (1)

M. A. Golub, S. V. Karpeev, A. M. Prokhorov, I. N. Sisakyan, V. A. Soifer, “Focusing light into a specified volume by computer synthesized hologram,” Sov. Technol. Phys. Lett. 7, 264–266 (1981).

Other (2)

E. Marom, N. Konforti, D. Mendelovic, J. Katz, “Extended confinement beam generation,” in Proceedings of the Sixteenth Congress of the International Commission on Optics: Optics as a Key to High Technology, G. Akos, T. Lippenyi, G. Lupkovics, A. Podmaniczky, eds., Proc. SPIE1983, 526–527 (1993).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1996).

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Figures (3)

Fig. 1
Fig. 1

(a) General system for DOF extension. (b) Coherent system proposed for pattern generation.

Fig. 2
Fig. 2

Pattern composed of line segments: (a) Transverse intensity profile with a minimum relative error for κ ≈ 3.6. The distances are in units of δx = λ/NA. In the upper right-hand corner we show the desired pattern. (b) Relative error in the generated patterns as a function of the axial distance in units of δz = λ/(2NA2) for different degrees of DOF extension κ. (c) Three-dimensional energy efficiency η3D and the product κη3D as functions of κ.

Fig. 3
Fig. 3

Pattern composed of light spots: (a) Transverse intensity profile calculated at different planes separated in depth by distances Δz = 5λ/(2NA2). (b) Relative error in the generated pattern (solid curve) as a function of the axial distance in units of δz = λ/(2NA2). Comparison with a classical design for a single plane (dotted curve).

Equations (10)

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δ x = k 1 λ / NA ,     δ z = k 2 λ / NA 2 ,
RE z = I x ,   y ,   z - α I 0 x ,   y α I 0 x ,   y ,
RE z =   w x ,   y I x ,   y ,   z - α I 0 x ,   y 2 d x d y 1 / 2   w x ,   y α I 0 x ,   y 2 d x d y 1 / 2 .
α z =   w x ,   y I 2 x ,   y ,   z d x d y   w x ,   y I x ,   y ,   z I 0 x ,   y d x d y .
F = z | RE z ,
DOF = F d z .
κ = DOF k 2 λ / NA 2 .
η 3 D = F d z   P d x d yI x ,   y ,   z F d z   - d x d yI i x ,   y ,
U x ,   y ,   z     V 1 λ f exp - j π x 2 + y 2 z λ f 2 g x ,   y ,
U x ,   y ,   z     exp j π x 2 + y 2 λ f + z V 1 λ f + z × exp - j π x 2 + y 2 z λ f f + z g x ,   y .

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