Abstract

Computer-designed linear and circular zone plates are considered that utilize a π-phase jump in order to create destructive interference in the focus. Intensity distributions in the focal plane as well as along the optical axis are calculated for a few examples. A significant decrease of the black spot diameter in comparison with the dimensions of the ordinary focal spot is obtained. Further reduction is achieved when the central region of the zone plate is obstructed. Some applications to alignment and the schlieren technique are suggested. Experimental results that confirm the calculated distributions are presented.

© 1992 Optical Society of America

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References

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  1. M. J. Simpson, A. G. Michette, “Imaging properties of modified Fresnel zone plates,” Opt. Acta 31, 403–413 (1984).
    [CrossRef]
  2. V. P. Koronkevitch, “Computer synthesis of diffraction optical elements,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, Boston, 1989), p. 277.
  3. V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).
  4. J. Ojeda-Castaneda, P. Andrés, M. Martinez-Corral, “Zero axial irradiance by annular screens with angular variation,” (submitted to Appl. Opt.).
    [PubMed]
  5. L. Cheng, G. G. Siu, “Asymmetric apodization,” Meas. Sci. Technol. 2, 198–202 (1991).
    [CrossRef]
  6. H. Wolter, “Schlieren-Phasenkontrastund Lichtschittver-fahren,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 555.
    [CrossRef]
  7. J. Ojeda-Castaneda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 251.
  8. B. G. Whitford, “Two-aperture method of producing light beams with odd-symmetry for alignment and straightness measurements,” Appl. Opt. 11, 2069–2074 (1972) and references therein.
    [CrossRef] [PubMed]
  9. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 402.
  10. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986), p. 284.
  11. A. I. Mahan, C. V. Bitterli, S. M. Cannon, “Far-field diffraction patterns of single and multiple apertures bounded by arcs and radii of concentric circles,” J. Opt. Soc. Am. 54, 721–729 (1964).
    [CrossRef]
  12. M. Sypek, “Phase retardation measurements for simple kinoform technology,” in Holography ’89, Y. N. Denisyuk, T. H. Jeong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1183, 695–698 (1990).
    [CrossRef]
  13. D. J. Stigliani, R. Mitra, R. G. Sermonin, “Resolving power of a zone plate,” J. Opt. Soc. Am. 57, 610–613 (1967).
    [CrossRef]
  14. P. D. Kearney, A. G. Klein, “Resolving power of zone plates,” J. Mod. Opt. 36, 361–367 (1989).
    [CrossRef]

1991 (1)

L. Cheng, G. G. Siu, “Asymmetric apodization,” Meas. Sci. Technol. 2, 198–202 (1991).
[CrossRef]

1989 (1)

P. D. Kearney, A. G. Klein, “Resolving power of zone plates,” J. Mod. Opt. 36, 361–367 (1989).
[CrossRef]

1984 (1)

M. J. Simpson, A. G. Michette, “Imaging properties of modified Fresnel zone plates,” Opt. Acta 31, 403–413 (1984).
[CrossRef]

1972 (1)

1967 (1)

1964 (1)

Andrés, P.

J. Ojeda-Castaneda, P. Andrés, M. Martinez-Corral, “Zero axial irradiance by annular screens with angular variation,” (submitted to Appl. Opt.).
[PubMed]

Bitterli, C. V.

Cannon, S. M.

Cheng, L.

L. Cheng, G. G. Siu, “Asymmetric apodization,” Meas. Sci. Technol. 2, 198–202 (1991).
[CrossRef]

Churn, E. G.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Kearney, P. D.

P. D. Kearney, A. G. Klein, “Resolving power of zone plates,” J. Mod. Opt. 36, 361–367 (1989).
[CrossRef]

Klein, A. G.

P. D. Kearney, A. G. Klein, “Resolving power of zone plates,” J. Mod. Opt. 36, 361–367 (1989).
[CrossRef]

Korolkov, V. P.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Koronkevitch, V. P.

V. P. Koronkevitch, “Computer synthesis of diffraction optical elements,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, Boston, 1989), p. 277.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Mahan, A. I.

Martinez-Corral, M.

J. Ojeda-Castaneda, P. Andrés, M. Martinez-Corral, “Zero axial irradiance by annular screens with angular variation,” (submitted to Appl. Opt.).
[PubMed]

Michette, A. G.

M. J. Simpson, A. G. Michette, “Imaging properties of modified Fresnel zone plates,” Opt. Acta 31, 403–413 (1984).
[CrossRef]

Mikhaltsova, I. A.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Mitra, R.

Ojeda-Castaneda, J.

J. Ojeda-Castaneda, P. Andrés, M. Martinez-Corral, “Zero axial irradiance by annular screens with angular variation,” (submitted to Appl. Opt.).
[PubMed]

J. Ojeda-Castaneda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 251.

Palchikova, I. G.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 402.

Poleshchuk, A. G.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Sedukhin, A. G.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Sermonin, R. G.

Simpson, M. J.

M. J. Simpson, A. G. Michette, “Imaging properties of modified Fresnel zone plates,” Opt. Acta 31, 403–413 (1984).
[CrossRef]

Siu, G. G.

L. Cheng, G. G. Siu, “Asymmetric apodization,” Meas. Sci. Technol. 2, 198–202 (1991).
[CrossRef]

Sokolov, A. P.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986), p. 284.

Stigliani, D. J.

Sypek, M.

M. Sypek, “Phase retardation measurements for simple kinoform technology,” in Holography ’89, Y. N. Denisyuk, T. H. Jeong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1183, 695–698 (1990).
[CrossRef]

Whitford, B. G.

Wolter, H.

H. Wolter, “Schlieren-Phasenkontrastund Lichtschittver-fahren,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 555.
[CrossRef]

Yurlov, Y. I.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

Appl. Opt. (1)

J. Mod. Opt. (1)

P. D. Kearney, A. G. Klein, “Resolving power of zone plates,” J. Mod. Opt. 36, 361–367 (1989).
[CrossRef]

J. Opt. Soc. Am. (2)

Meas. Sci. Technol. (1)

L. Cheng, G. G. Siu, “Asymmetric apodization,” Meas. Sci. Technol. 2, 198–202 (1991).
[CrossRef]

Opt. Acta (1)

M. J. Simpson, A. G. Michette, “Imaging properties of modified Fresnel zone plates,” Opt. Acta 31, 403–413 (1984).
[CrossRef]

Other (8)

V. P. Koronkevitch, “Computer synthesis of diffraction optical elements,” in Optical Processing and Computing, H. H. Arsenault, T. Szoplik, B. Macukow, eds. (Academic, Boston, 1989), p. 277.

V. P. Koronkevitch, V. P. Korolkov, A. G. Poleshchuk, I. G. Palchikova, Y. I. Yurlov, I. A. Mikhaltsova, E. G. Churn, A. P. Sokolov, A. G. Sedukhin, “Kinoforms: technologies, new elements, and optical systems,” preprint N421 (Institute of Automation and Electrometry, Siberian Branch of the USSR Academy of Science, Novosibirsk, 1989).

J. Ojeda-Castaneda, P. Andrés, M. Martinez-Corral, “Zero axial irradiance by annular screens with angular variation,” (submitted to Appl. Opt.).
[PubMed]

H. Wolter, “Schlieren-Phasenkontrastund Lichtschittver-fahren,” in Handbuch der Physik, S. Flügge, ed. (Springer-Verlag, Berlin, 1956), Vol. 24, p. 555.
[CrossRef]

J. Ojeda-Castaneda, “Foucault, wire, and phase modulation tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1978), p. 251.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968), p. 402.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, 1986), p. 284.

M. Sypek, “Phase retardation measurements for simple kinoform technology,” in Holography ’89, Y. N. Denisyuk, T. H. Jeong, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1183, 695–698 (1990).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Ordinary linear ZP, Pt(x) = rect(x/A): (a) calculated intensity distribution across the focal line; (b) zone patterns; (c) experimentally obtained focal line.

Fig. 2
Fig. 2

Linear zone plate with a phase jump running through the middle, Pt(x) = rect[(x + A/4)/A/2] − rect[(xA/4)/A/2]: (a) calculated intensity distribution across the focal line; (b) zone patterns; (c) experimentally obtained focal line.

Fig. 3
Fig. 3

Ordinary circular Fresnel zone plate, Pt(r) = circ(2r/A): (a) calculated intensity distribution across the focal spot; (b) zone patterns; (c) experimentally obtained focal spot.

Fig. 4
Fig. 4

Circular Fresnel ZP with a phase jump at the r = 2 A / 4 , P t ( r ) = circ ( 2 r / A ) 2 circ ( 2 2 r / A ): (a) calculated intensity distribution across the focal spot; (b) zone patterns; (c) experimentally obtained focal spot; (d) calculated intensity distribution across the focal spot with an obstruction ratio of G = 0.5; (e) calculated intensity distribution across the focal spot with an obstruction ratio of G = 0.9; (f) relation between G and the height of the first maximum of the focal spot intensity distribution; (g) relation between G and the position of the first maximum and the HW.

Fig. 5
Fig. 5

Circular Fresnel zone plate with a phase jump at y = 0, Pt(r) = circ(2r/A)sgn(y): (a) calculated intensity distribution along the line x = 0; (b) zone patterns; (c) experimentally obtained focal spot; (d) calculated intensity distribution along the line x = 0 with an obstruction ratio of G = 0.5; (e) calculated intensity distribution along the line x = 0 with an obstruction ratio of G = 0.9; (f) relation between G and the height of the first maximum of the intensity distribution in the focal spot; (g) relation between G and the position of the first maximum and the HW.

Equations (22)

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U ( x 0 , f ) = C 1 ( λ f ) 1 / 2 P t ( x ) exp ( 2 π i x f x ) d x ,
C 1 = exp [ i ( k x 0 2 / 2 f + k f π / 4 ) ]
U ( 0 , z ) = C 2 ( λ z ) 1 / 2 P t ( x ) exp [ i k x 2 2 ( 1 / f 1 / z ) ] d x ,
I ( x 0 , f ) = I 0 sinc 2 ( t ) ,
I ( 0 , z ) = 2 f | f z | [ S 2 ( γ ) + C 2 ( γ ) ] ,
P t ( x ) = rect ( x + A / 4 A / 2 ) rect ( x A / 4 A / 2 ) .
I ( x 0 , f ) = I 0 sinc 2 ( t / 2 ) sin 2 ( π t / 2 ) ,
I ( 0 , z ) = 0 .
U ( ρ , f ) = 2 π C 3 λ f 0 x P t ( r ) J 0 ( 2 π r ρ ) r d r ,
U ( 0 , z ) = 2 π C 4 λ z 0 x P t ( r ) exp [ i k r 2 / 2 ( 1 / f 1 / z ) ] r d r ,
I ( ρ , f ) = I 0 J 1 2 ( π t ) / ( π t ) 2 ,
I ( 0 , z ) = I 0 ( f z ) 2 sinc 2 [ A 2 ( 1 / f 1 / z ) / 8 λ ] .
I ( ρ , f ) = I 0 [ J 1 ( π t ) / π t J 1 ( π t / 2 ) / ( π t / 2 ) ] 2 .
I ( 0 , z ) = I 0 ( f z ) 2 sinc 2 [ A 2 ( 1 / f 1 / z ) / 16 λ ] × sin 2 [ π A 2 ( 1 / f 1 / z ) / 16 λ ] .
I ( ρ , f ) = I 0 { J 1 ( π t ) π t [ 2 ( 1 + G 2 ) ] 1 / 2 J 1 [ ( 1 + G 2 2 ) 1 / 2 π t ] π t + G J 1 ( G π t ) π t } 2 .
I ( ρ , f ) = I 0 16 ( Δ A A ) 4 [ π t J 1 ( π t ) ] 2 .
U ( x 0 , y 0 , f ) = C π i f y { A / 2 A / 2 cos [ 2 π ( A 2 / 4 x 2 ) 1 / 2 f y ] × exp ( 2 π i x f x ) d x A sinc ( A f x ) }
I ( y 0 , f ) = 256 π 2 I 0 [ n = 1 n 2 4 n 2 1 J 2 n ( π t ) π t ] 2 ,
I ( y 0 , f ) = I 0 4 π 2 [ k = 1 ( 1 ) k ( π t ) 2 k 1 2 2 k k ! 2 ( 2 k + 1 ) ! 2 k ! ] 2 .
I ( y 0 , f ) = I 0 4 π 2 [ k = 1 ( 1 ) k ( 1 G 2 k + 1 ) ( π t ) 2 k 1 2 2 k k ! 2 ( 2 k + 1 ) ! 2 k ! ] 2 .
I ( y 0 , f ) = I 0 4 π 2 ( Δ A A ) 2 [ k = 1 ( 1 ) k ( π t ) 2 k 1 2 2 k k ! 2 ( 2 k ! ) 2 ] 2 ,
I ( x 0 , x 0 , f ) = I 0 4 π 2 1 π 2 t 2 { 2 π t [ sin 2 ( π t 2 ) sin 2 ( G π t 2 ) ] + 0 1 [ G cos ( G π t 1 s 2 ) sin ( G π t s ) cos ( π t 1 s 2 ) sin ( π t s ) d s } 2 .

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