Abstract

We report a novel aspheric holographic optical element, the holographic axilens, for achieving extended focal depth while keeping high lateral resolution. The element is designed according to special optimization techniques and recorded as a computer-generated hologram. The results for a specific element, which has a depth of focus of 30 mm, a lateral resolution of 80 μm, a focal length of 1250 mm, and a diameter of 12.5 mm at a wavelength of 633 nm, are presented.

© 1991 Optical Society of America

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References

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  1. G. Bickel, G. Hausler, M. Maul, Opt. Eng. 24, 975 (1985).
  2. J. Ojeda-Castaneda, R. Ramos, A. Noyola Isgleas, Appl. Opt. 27, 2583 (1988).
    [CrossRef] [PubMed]
  3. J. H. Mcleod, J. Opt. Soc. Am. 44, 592 (1954).
    [CrossRef]
  4. A. Vasara, J. Turunen, A. T. Friberg, J. Opt. Soc. Am. A 6, 1748 (1989).
    [CrossRef] [PubMed]
  5. J. W. GoodmanIntroduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.
  6. G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

1989

1988

1985

G. Bickel, G. Hausler, M. Maul, Opt. Eng. 24, 975 (1985).

1954

Bickel, G.

G. Bickel, G. Hausler, M. Maul, Opt. Eng. 24, 975 (1985).

Friberg, A. T.

Goodman, J. W.

J. W. GoodmanIntroduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.

Hausler, G.

G. Bickel, G. Hausler, M. Maul, Opt. Eng. 24, 975 (1985).

Maul, M.

G. Bickel, G. Hausler, M. Maul, Opt. Eng. 24, 975 (1985).

Mcleod, J. H.

Noyola Isgleas, A.

Ojeda-Castaneda, J.

Ramos, R.

Swanson, G. J.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Turunen, J.

Vasara, A.

Veldkamp, W. B.

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

G. Bickel, G. Hausler, M. Maul, Opt. Eng. 24, 975 (1985).

G. J. Swanson, W. B. Veldkamp, Opt. Eng. 28, 605 (1989).

Other

J. W. GoodmanIntroduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 64.

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Figures (4)

Fig. 1
Fig. 1

Geometrical parameters and schematic distribution of rays with an input plane wave focused by an axilens.

Fig. 2
Fig. 2

Calculated intensity distribution as a function of the axial distance around the focal region for the axilens and a spherical holographic lens.

Fig. 3
Fig. 3

Calculated intensity distribution at different distances z from the axilens: dashed curve, z = 1235 mm; solid curve, z = 1250 mm; dashed–dotted curve, z = 1265 mm.

Fig. 4
Fig. 4

Photographs of the focused spots (top) and the intensity cross sections (bottom) at several distances from the axilens: (a) z = 1235 mm, (b) z = 1250 mm, (c) z = 1265 mm.

Equations (11)

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δ z = 4 ( δ x ) 2 λ ,
ϕ ( r ) = 2 π λ r 2 + f 2 ,
ϕ ( r ) = 2 π λ r 2 2 f ,
ϕ ( r ) = 2 π λ r 2 2 f ( r ) ,
ϕ ( r ) = π λ r a .
f ( r ) = f 0 + a r b ,
δ f ( r ) = 2 a r δ r .
f ( r ) = f 0 + a r 2 .
a = δ z g R 2 .
ϕ ( r ) = π λ r 2 f 0 + δ z g R 2 r 2 .
I ( z , r ) = ( 2 π λ z ) 2 | 0 R exp { i 2 π } [ r 2 / 2 λ z - ϕ ( r ) ] } × J 0 ( 2 π r r / λ z ) r d r | 2 ,

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