Abstract

The generation of diffractive elements of variable optical parameters and high diffraction efficiency is presented. It can be realized by a superposition of two conjugate kinoforms. In particular, the method gives rise to zone plates of variable focusing power as well as to circular and linear gratings of variable deflection angles. The theoretical description is illustrated by an experimental example of the blazed grating with a changeable period; some possible applications are mentioned.

© 1993 Optical Society of America

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References

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  1. A. W. Lohmann, D. P. Paris, “Variable Fresnel zone pattern,” Appl. Opt. 6, 1567–1570 (1967).
    [CrossRef] [PubMed]
  2. J. M. Burch, D. C. Williams, “Varifocal moiré zone plates for straightness measurement,” Appl. Opt. 16, 2445–2450 (1977).
    [CrossRef] [PubMed]
  3. S. Bara, Z. Jaroszewicz, A. Kolodziejczyk, V. Moreno, “Determination of basic grids for substrctive moire patterns,” Appl. Opt. 30, 1258–1262 (1991).
    [CrossRef] [PubMed]
  4. Z. Jaroszewicz, “A review of Fresnel zone plates moiré patterns obtained by translations,” Opt. Eng. 31, 458–464 (1992).
    [CrossRef]
  5. R. Smith, “Diffractive optical elements fabricated by electron beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of OSA 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper MB1.
  6. W. B. Herrmannsfeldt, M. J. Lee, J. J. Spranza, K. R. Trigger, “Precision alignment using a system of large rectangular Fresnel lenses,” Appl. Opt. 7, 995–1005 (1968).
    [CrossRef] [PubMed]
  7. P. W. Harrison, “A laser-based technique for alignment and deflection measurement,” Civ. Eng. Public Works Rev. 68, 224–227 (1973).
  8. B. M. New, “Versatile electrooptic alignment for field applications,” Appl. Opt. 13, 937–941 (1974).
    [CrossRef] [PubMed]
  9. P. W. Harrison, “Growth of practical laser-based alignment techniques,” in Proceedings, The Engineering Uses of Coherent Optics, E. R. Robertson, ed. (Cambridge U. Press, London, 1976).
  10. R. F. Stevens, “A zone plate interferometer for pointing,” NPL Rep. No. MOM 84 (National Physical Laboratory, Teddington, Middlesex, England, March1987).
  11. R. K. Ritt, Fourier Series (McGraw-Hill, New York, 1970), pp. 38–40.
  12. L. Song, R. A. Lessard, P. Galarneau, “Diffraction efficiency of a thin amplitude-phase holographic grating: a convolution approach,” J. Mod. Opt. 37, 1319–1328 (1990).
    [CrossRef]
  13. W-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 143–152.
    [CrossRef]
  14. M. Sypek, “A new technique for the measurement of phase retardation,” Opt. Laser Technol. 23, 42–44 (1991).
    [CrossRef]
  15. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, Tokyo, 1976), pp. 32–33.

1992 (1)

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

1991 (2)

1990 (1)

L. Song, R. A. Lessard, P. Galarneau, “Diffraction efficiency of a thin amplitude-phase holographic grating: a convolution approach,” J. Mod. Opt. 37, 1319–1328 (1990).
[CrossRef]

1977 (1)

1974 (1)

1973 (1)

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

1968 (1)

1967 (1)

Bara, S.

Burch, J. M.

Galarneau, P.

L. Song, R. A. Lessard, P. Galarneau, “Diffraction efficiency of a thin amplitude-phase holographic grating: a convolution approach,” J. Mod. Opt. 37, 1319–1328 (1990).
[CrossRef]

Harrison, P. W.

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

P. W. Harrison, “Growth of practical laser-based alignment techniques,” in Proceedings, The Engineering Uses of Coherent Optics, E. R. Robertson, ed. (Cambridge U. Press, London, 1976).

Herrmannsfeldt, W. B.

Jaroszewicz, Z.

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

S. Bara, Z. Jaroszewicz, A. Kolodziejczyk, V. Moreno, “Determination of basic grids for substrctive moire patterns,” Appl. Opt. 30, 1258–1262 (1991).
[CrossRef] [PubMed]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, Tokyo, 1976), pp. 32–33.

Kolodziejczyk, A.

Lee, M. J.

Lee, W-H.

W-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 143–152.
[CrossRef]

Lessard, R. A.

L. Song, R. A. Lessard, P. Galarneau, “Diffraction efficiency of a thin amplitude-phase holographic grating: a convolution approach,” J. Mod. Opt. 37, 1319–1328 (1990).
[CrossRef]

Lohmann, A. W.

Moreno, V.

New, B. M.

Paris, D. P.

Ritt, R. K.

R. K. Ritt, Fourier Series (McGraw-Hill, New York, 1970), pp. 38–40.

Smith, R.

R. Smith, “Diffractive optical elements fabricated by electron beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of OSA 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper MB1.

Song, L.

L. Song, R. A. Lessard, P. Galarneau, “Diffraction efficiency of a thin amplitude-phase holographic grating: a convolution approach,” J. Mod. Opt. 37, 1319–1328 (1990).
[CrossRef]

Spranza, J. J.

Stevens, R. F.

R. F. Stevens, “A zone plate interferometer for pointing,” NPL Rep. No. MOM 84 (National Physical Laboratory, Teddington, Middlesex, England, March1987).

Sypek, M.

M. Sypek, “A new technique for the measurement of phase retardation,” Opt. Laser Technol. 23, 42–44 (1991).
[CrossRef]

Trigger, K. R.

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, Tokyo, 1976), pp. 32–33.

Williams, D. C.

Appl. Opt. (5)

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).

J. Mod. Opt. (1)

L. Song, R. A. Lessard, P. Galarneau, “Diffraction efficiency of a thin amplitude-phase holographic grating: a convolution approach,” J. Mod. Opt. 37, 1319–1328 (1990).
[CrossRef]

Opt. Eng. (1)

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

Opt. Laser Technol. (1)

M. Sypek, “A new technique for the measurement of phase retardation,” Opt. Laser Technol. 23, 42–44 (1991).
[CrossRef]

Other (6)

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, Tokyo, 1976), pp. 32–33.

W-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 143–152.
[CrossRef]

R. Smith, “Diffractive optical elements fabricated by electron beam lithography,” in Diffractive Optics: Design, Fabrication, and Applications, Vol. 9 of OSA 1992 Technical Digest Series (Optical Society of America, Washington, D.C., 1992), paper MB1.

P. W. Harrison, “Growth of practical laser-based alignment techniques,” in Proceedings, The Engineering Uses of Coherent Optics, E. R. Robertson, ed. (Cambridge U. Press, London, 1976).

R. F. Stevens, “A zone plate interferometer for pointing,” NPL Rep. No. MOM 84 (National Physical Laboratory, Teddington, Middlesex, England, March1987).

R. K. Ritt, Fourier Series (McGraw-Hill, New York, 1970), pp. 38–40.

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Figures (3)

Fig. 1
Fig. 1

Graphic presentation of the displacements pointed out in the text. Point P′ of transmittance T1(r − Δr) is the counterpart of point P of transmittance T1(r) after proper displacement. The contours of these transmittances are indicated by dashed and solid lines, respectively: (a) translation, (b) rotation, (c) change of scale.

Fig. 2
Fig. 2

(a) Binary amplitude mask defined by Eq. (23). (b) Final transmittance formed by a mutual linear translation of the two identical masks shown in (a). (c) The same transmittance as presented in (b) but related to the greater displacements of the diffractive structures. The density of moiré fringes that is characteristic of the cylindrical zone plane is higher so that the focal distance of the resultant wave front decreases.

Fig. 3
Fig. 3

Upper bright spots of a deflected laser beam in the output plane refer to the following angles of rotation: (a) α = 15°, (b) α = 30°, (c) α = 45° (d) α = 60°,(e) α = 75° (f) α = 90°. The output plane was at a distance of 42 cm from that of the kinoforms. The centers of small additionally painted crosses indicate the position of an incident undeflected laser beam (a zero order is hardly visible). The remaining weak spots indicate additional diffraction orders and appear because of the limited diffraction efficiency of the kinoforms.

Equations (33)

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U ( r ) = exp [ i ϕ ( r ) ]
T 1 ( r ) = g 1 [ Φ ( r ) ] ,
0 g 1 ( Φ ) 1.
T 1 ( r ) = n = - + A n exp [ i n Φ ( r ) ] ,
A n = 1 2 π 0 2 π g 1 ( Φ ) exp ( - i n Φ ) d Φ .
n = - + A n 2 1 .
T 1 ( r - Δ r ) = g 1 [ Φ ( r ) - δ Φ ( r ) ] ,
δ Φ ( r ) = Φ Δ r ,
δ Φ ( r ) = Φ φ δ φ ,
δ Φ = Φ x Δ .
δ Φ = Φ θ α .
δ Φ = Φ r β r ,
T ( r ) = T 1 ( r ) T 1 ( r - Δ r ) = n A n A - n exp ( i n δ Φ ) + m - n A n A m exp [ i ( n + m ) Φ - i m δ Φ ] .
U 1 ( r ) = exp [ i δ Φ ( r ) ] ,
η = A 1 2 A - 1 2 ,
δ ϕ = S ( d φ ) = Φ φ d φ + 1 2 ! 2 Φ φ 2 ( d φ ) 2 + ,
{ 2 Φ φ 2 = const , n Φ φ n = 0 for n > 2 , d φ = const ( translations , rotations ) ,
{ n Φ φ n = 0 for n > 1 , d φ const ( changing of a scale ) .
δ Φ = S ( d φ / 2 ) + S ( - d φ / 2 ) = Φ φ d φ + 1 3 ! 3 Φ φ 3 ( d φ ) 3 2 2 + 1 5 ! 5 Φ φ 5 ( d φ ) 5 2 4 + .
{ 3 Φ φ 3 = const , n Φ φ n = 0 for n = 5 , 7 , , d φ = const ,
{ n Φ φ n = 0 for n = 3 , 5 , , d φ const .
δ Φ = 2 π y 2 d 2 + 2 π γ ,
Φ = 2 π y 2 d 2 Δ x + 2 π γ Δ x + f ( y ) ,
g 1 ( Φ ) = { 1 ( transparent part ) , - π / 2 + 2 π n < Φ < π / 2 + 2 π n ( n = 0 , ± 1 , ± 2 , ) 0 ( opaque part ) otherwise .
U * ( r ) = exp [ - i Φ ( r ) ] ,
T 2 ( r ) = g 2 [ Φ ( r ) ] = n = - + B n exp [ - i n Φ ( r ) ] ,
B n = 1 2 π 0 2 π g 2 ( Φ ) exp ( i n Φ ) d Φ ,
T ( r ) = T 1 ( r ) T 2 ( r - Δ r ) = n A n B n exp ( i n δ Φ ) + n m A n B m exp [ i ( n - m ) Φ + i m δ Φ ] .
T 2 ( r - Δ r ) = g 2 [ Φ ( r ) - δ Φ ( r ) ] = n B n exp { - i n [ Φ ( r ) - δ Φ ( r ) ] } .
η = A 1 2 B 1 2 ,
Φ = 2 π x / d .
δ Φ = 2 π y ( d 2 sin α ) .
α def = arcsin ( 2 sin α λ / d ) .

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