Abstract

We present equilateral hyperbolic zone plates with variable focal length, which are formed as moiré patterns by a mutual rotation of two identical basic grids. Among others, all principal zone plates, except of the spherical one, can be used as these basic transmittances. Three most important advantages of the proposed moiré zone plates are: a constant aperture of the created element during the mutual movement of basic grids, lack of aberrations due to their undesired mutual lateral displacements and high diffraction efficiency of the binary phase version. To obtain clearer moiré fringe pattern, a radial carrier frequency can be added additionally to the transmittances of basic grids. The destructive interference between both arms of the focal cross of the equilateral hyperbolic moiré zone plate can be obtained by a constant phase shift introduced in the transmittances of the basic grids. Potential applications of discussed elements are indicated, including the most promising one in the three-point alignment technique.

© 2005 Optical Society of America

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References

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  1. L.W. Alvarez, ཿTwo-element variable-power spherical lens,ཿ U.S. patent 3,305,294 (February 21, 1967).
  2. A.W. Lohmann, ཿImprovements relating to lenses and to variable optical lens systems formed of such lenses,ཿ British patent 998, 191 (May 29, 1964).
  3. A.W. Lohmann and D.P. Paris, ཿVariable Fresnel zone pattern,ཿ Appl. Opt. 6, 1567-1570 (1967).
    [CrossRef] [PubMed]
  4. J.M. Burch and D.C. Williams, ཿVarifocal moiré zone plates for straightness measurement,ཿ Appl. Opt. 16, 2445-2450 (1977).
    [CrossRef] [PubMed]
  5. D.C. Williams and A.B. Penfold, ཿThree-point alignment in non-ideal situations,ཿ in 18th Proceedings of International Congress of the International Federation of Surveyors (Toronto, 1986) 10, 331-345.
  6. A.W. Lohmann, ཿA new class of varifocal lenses,ཿ Appl. Opt. 9, 1669-1671 (1970).
    [CrossRef] [PubMed]
  7. A. Kolodziejczyk and Z. Jaroszewicz, ཿDiffractive elements of variable optical power and high diffraction efficiency,ཿ Appl. Opt. 32, 4317-4322 (1993).
    [CrossRef] [PubMed]
  8. I.M. Barton, S.N. Dixit, L.J. Summers, Ch.A. Thompson, K. Avicola, and J. Wilhelmsen ཿDiffractive Alvarez lens,ཿ Opt. Lett. 25, 1-3 (2000).
    [CrossRef]
  9. Y. Toyohara, M. Itoh, and T. Yatagai, ཿVariable aberration generator using moiré patterns,ཿ in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, G. kos, T. Lippényi, G. Lupkovics, and A. Podmaniczky, eds., Proc. SPIE 1983, 155-156 (1993).
  10. N. Lopez-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, ཿGeneration of third-order spherical and coma aberrations by use of radially symmetrical fourth-order lenses,ཿ J. Opt. Soc. Am. A 15, 2563-2571 (1998).
    [CrossRef]
  11. I.A. Palusinski, J.M. Sasian, and J.E. Greivenkamp, ཿLateral-shift variable aberration generators,ཿ Appl. Opt. 38, 86-90 (1999).
    [CrossRef]
  12. P.W. Harrison, ཿA laser-based technique for alignment and deflection measurement,ཿ Civ. Eng. Public Works Rev. 68, 224-227 (1973).
  13. W.B. Hermannsfeldt, M.J. Lee, J.J. Spranza, and K.R. Trigger, ཿPrecision alignment using a system of large rectangular Fresnel lenses,ཿ Appl. Opt. 7, 995-1005 (1968).
    [CrossRef]
  14. R.E. Ruland, ཿA summary of ground motion effects at SLAC resulting from the Oct. 17th 1989 earthquake,ཿ in Proceedings of the 2nd International Workshop on Accelerator Alignment, F. Löffler, ed., (Hamburg, 1990), 131-155.
  15. A.-H. Maeng, K.-W. Seo, and S.-Ch. Lee, ཿSurvey & alignment of Pohang light source,ཿ in Proceedings of the 4th International Workshop on Accelerator Alignment, K. Endo, ed., (Tsukuba, 1995), 67-76.
  16. R.E. Ruland, ཿAlignment considerations for the next linear collider,ཿ in Proceedings of the 4th International Workshop on Accelerator Alignment, K. Endo, ed., (Tsukuba, 1995), 451-458.
  17. A. Seryi ཿSLAC tunnel motion and analysis,ཿ in Proceedings of the 22nd Advanced ICFA Beam Dynamics Workshop on Ground Motion in Future Accelerators, A. Seryi, ed., (Stanford, 2000), 281-293.
  18. S. Wang, D. Zhao, X. Jiang, and F. Huang, ཿLaser safety monitoring considerations for the largest dam by means of the generalized three-point methodཿ Opt. Las. Technol. 33, 153-156 (2001).
    [CrossRef]
  19. C. Gomez-Reino, J. M. Cuadrado, and M. V. Perez, ཿElliptical and hyperbolic zone plates,ཿ Appl. Opt. 19, 1541 1545 (1980).
    [CrossRef] [PubMed]
  20. J.M. Cuadrado, C. Gomez-Reino, and M.V. Perez, ཿZone plates produced by cylindrical wavefronts recording and reconstruction,ཿ Opt. Acta 29, 717-723 (1982).
    [CrossRef]
  21. Z. Jaroszewicz, ཿFresnel zone plate moiré patterns and its metrological applications,ཿ in International Colloquium on Diffractive Optical Elements, J. Nowak and M. Zajac, eds., Proc. SPIE 1574, 154-158 (1991).
    [CrossRef]
  22. S. Bará, Z. Jaroszewicz, A. Kolodziejczyk, and V. Moreno, ཿDetermination of basic grids for subtractive moiré patterns,ཿ Appl. Opt. 30, 1258-1262 (1991).
    [CrossRef] [PubMed]
  23. Z. Jaroszewicz, ཿA review of Fresnel zone plate moiré patterns obtained by translations,ཿ Opt. Eng. 31, 458- 464 (1992).
    [CrossRef]
  24. P.S. Theocaris, Moire Fringes in Strain Analysis (Pergamon, London, 1969).
  25. K. Patorski, Kujawiñska M, Handbook of the Moire Fringe Technique (Elsevier, Amsterdam, 1993).
  26. Y. Vladimirsky and H.W.P. Koops, ཿMoiré method and zone plate pattern inaccuracies,ཿ J. Vac. Sci. Technol. B 6, 2142-2146 (1988).
    [CrossRef]
  27. Z. Jaroszewicz, A. Kolodziejczyk, R. Henao, and S. Bará, ཿVarifocal equilateral hyperbolic zone plates obtained by rotational moiré,ཿ in 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, J. Nowak, M. Zajac, and J. Masajada, eds., Proc. SPIE 5259, 88-91 (2003).
    [CrossRef]
  28. Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, and J. Sochacki: "Generalized zone plates focusing light into arbitrary line segments", J. Mod. Opt. 40, 601-612 (1993).
    [CrossRef]
  29. J. Ojeda-Castañeda and G. Ramirez ཿZone plates for zero axial irradiance,ཿ Opt. Lett. 18, 87ཿ89 (1993).
    [CrossRef] [PubMed]
  30. J.F. Barrera, A. Kolodziejczyk, and C.A. Rodriguez, ཿFeatures of phase wavefront binary encoding and their potential utilization for alignment purposes,ཿ Rev. Colomb. Fis. 34, 196-200 (2002).
  31. M. Sypek, ཿLight propagation in the Fresnel region. New numerical approach,ཿ Opt. Commun. 116, 43ཿ48 (1995).
    [CrossRef]

22nd Advanced ICFA Beam Dynamics '00 (1)

A. Seryi ཿSLAC tunnel motion and analysis,ཿ in Proceedings of the 22nd Advanced ICFA Beam Dynamics Workshop on Ground Motion in Future Accelerators, A. Seryi, ed., (Stanford, 2000), 281-293.

2nd Int'l Wkshp on Accelerator Alignment (1)

R.E. Ruland, ཿA summary of ground motion effects at SLAC resulting from the Oct. 17th 1989 earthquake,ཿ in Proceedings of the 2nd International Workshop on Accelerator Alignment, F. Löffler, ed., (Hamburg, 1990), 131-155.

4th Int'l Wkshp on Accelerator Alignment (2)

A.-H. Maeng, K.-W. Seo, and S.-Ch. Lee, ཿSurvey & alignment of Pohang light source,ཿ in Proceedings of the 4th International Workshop on Accelerator Alignment, K. Endo, ed., (Tsukuba, 1995), 67-76.

R.E. Ruland, ཿAlignment considerations for the next linear collider,ཿ in Proceedings of the 4th International Workshop on Accelerator Alignment, K. Endo, ed., (Tsukuba, 1995), 451-458.

Appl. Opt. (8)

Civ. Eng. Public Works Rev. (1)

P.W. Harrison, ཿA laser-based technique for alignment and deflection measurement,ཿ Civ. Eng. Public Works Rev. 68, 224-227 (1973).

ICIFS 1986 (1)

D.C. Williams and A.B. Penfold, ཿThree-point alignment in non-ideal situations,ཿ in 18th Proceedings of International Congress of the International Federation of Surveyors (Toronto, 1986) 10, 331-345.

J. Mod. Opt. (1)

Z. Jaroszewicz, A. Kolodziejczyk, D. Mouriz, and J. Sochacki: "Generalized zone plates focusing light into arbitrary line segments", J. Mod. Opt. 40, 601-612 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. B (1)

Y. Vladimirsky and H.W.P. Koops, ཿMoiré method and zone plate pattern inaccuracies,ཿ J. Vac. Sci. Technol. B 6, 2142-2146 (1988).
[CrossRef]

Opt. Acta (1)

J.M. Cuadrado, C. Gomez-Reino, and M.V. Perez, ཿZone plates produced by cylindrical wavefronts recording and reconstruction,ཿ Opt. Acta 29, 717-723 (1982).
[CrossRef]

Opt. Commun. (1)

M. Sypek, ཿLight propagation in the Fresnel region. New numerical approach,ཿ Opt. Commun. 116, 43ཿ48 (1995).
[CrossRef]

Opt. Eng. (1)

Z. Jaroszewicz, ཿA review of Fresnel zone plate moiré patterns obtained by translations,ཿ Opt. Eng. 31, 458- 464 (1992).
[CrossRef]

Opt. Las. Technol. (1)

S. Wang, D. Zhao, X. Jiang, and F. Huang, ཿLaser safety monitoring considerations for the largest dam by means of the generalized three-point methodཿ Opt. Las. Technol. 33, 153-156 (2001).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (3)

Z. Jaroszewicz, ཿFresnel zone plate moiré patterns and its metrological applications,ཿ in International Colloquium on Diffractive Optical Elements, J. Nowak and M. Zajac, eds., Proc. SPIE 1574, 154-158 (1991).
[CrossRef]

Z. Jaroszewicz, A. Kolodziejczyk, R. Henao, and S. Bará, ཿVarifocal equilateral hyperbolic zone plates obtained by rotational moiré,ཿ in 13th Polish-Czech-Slovak Conference on Wave and Quantum Aspects of Contemporary Optics, J. Nowak, M. Zajac, and J. Masajada, eds., Proc. SPIE 5259, 88-91 (2003).
[CrossRef]

Y. Toyohara, M. Itoh, and T. Yatagai, ཿVariable aberration generator using moiré patterns,ཿ in Optics as a Key to High Technology: 16th Congress of the International Commission for Optics, G. kos, T. Lippényi, G. Lupkovics, and A. Podmaniczky, eds., Proc. SPIE 1983, 155-156 (1993).

Rev. Colomb. Fis. (1)

J.F. Barrera, A. Kolodziejczyk, and C.A. Rodriguez, ཿFeatures of phase wavefront binary encoding and their potential utilization for alignment purposes,ཿ Rev. Colomb. Fis. 34, 196-200 (2002).

Other (4)

P.S. Theocaris, Moire Fringes in Strain Analysis (Pergamon, London, 1969).

K. Patorski, Kujawiñska M, Handbook of the Moire Fringe Technique (Elsevier, Amsterdam, 1993).

L.W. Alvarez, ཿTwo-element variable-power spherical lens,ཿ U.S. patent 3,305,294 (February 21, 1967).

A.W. Lohmann, ཿImprovements relating to lenses and to variable optical lens systems formed of such lenses,ཿ British patent 998, 191 (May 29, 1964).

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Figures (5)

Fig. 1.
Fig. 1.

A superposition of two binary amplitude elliptic ZP’s with fX =600 mm and fY =1500 mm for λ=632.8 nm rotated mutually by an angle of 2θ 0=0.075π rad creates the moiré EHZP oriented perpendicularly with fM =4284 mm (left); the focal pattern in the distance fM =4284 mm formed by the moiré EHZP made from the binary phase versions of the basic grids (right).

Fig. 2.
Fig. 2.

A superposition of two binary amplitude elliptic ZP’s with fX =600 mm and fY =1500 mm for λ=632.8 nm, rotated mutually by an angle of 2θ 0=0.075π rad, one of them shifted from the centre, creates the displaced moiré EHZP oriented perpendicularly with fM =4284 mm (left); the focal pattern in the distance fM =4284 mm formed by the moiré EHZP made from the binary phase versions of the basic grids (right).

Fig. 3.
Fig. 3.

The binary amplitude cylindrical ZP with fX =fBG =1000 mm for λ=632.8 nm and radial carrier frequency α=-0.005 (left); the moiré EHZP oriented perpendicularly with fM =4284 mm created by superposition of two such binary amplitude cylindrical ZP’s with radial carrier frequency α=-0.0075 rotated mutually by an angle of 2θ 0=0.075π rad (right).

Fig. 4.
Fig. 4.

A superposition of two binary amplitude cylindrical ZP’s shown in Fig. 3, rotated mutually by an angle of 2θ 0=0.075π rad, one of them shifted from the centre, creates the aberrated moiré EHZP oriented perpendicularly with fM =4284 mm (left); the focal pattern in the distance fM =4284 mm formed by the moiré EHZP made from the binary phase versions of the basic grids (right).

Fig. 5.
Fig. 5.

A superposition of two binary amplitude elliptic ZP’s with fX =600 mm and fY =1500 mm for λ=632.8 nm rotated mutually by an angle of 2θ 0=0.075π rad, one of them with phase shift equal to π/2, creates the moiré EHZP oriented perpendicularly with fM =4284 mm and with phase shift equal to π/2 (left); the focal pattern in the distance fM =4284 mm formed by the moiré EHZP with the initial phase shift equal to π/2 made from the binary phase versions of the basic grids (right).

Equations (11)

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Φ ( r ) Δ r = Ψ ( r ) ,
Φ ( r , θ ) θ Δ θ = Ψ ( r , θ ) ,
Ψ ( r , θ ) = r 2 sin ( 2 θ ) 2 λ f M = n ,
Φ ( r , θ ) = r 2 cos 2 ( θ ) 2 λ f BG + f ( r ) + c = m ,
m 1 m 2 = n ,
Ψ ( r , θ ) = r 2 sin ( 2 θ ) 2 λ f M = n , where f M = f BG sin ( 2 θ 0 )
Φ ( x , y ) = x 2 2 λ f x + y 2 2 λ f y = m , where f x = f BG ( a 1 ) , f y = f BG a .
Φ ( r , θ ) = r 2 cos 2 ( θ ) 2 λ f BG + a r 2 2 λ f BG + α r = m , where
Ψ ( x , y ) = π ( x 2 y 2 ) λ f M + π 2 ,
c 1 c 2 =π/2, where
η TOT = η + 1 + η 1 = 2 ( 2 π ) 4 = 32.85 % ,

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