Abstract

A Fourier-transform holographic optical element is described that has low aberrations over an extended range of spatial frequencies. The design is based on a relatively simple analytic solution involving optimization by minimizing the output wave-front deviations. We recorded the holographic element with the aid of a computer-generated hologram which was placed in one of the recording beams. The optimized element demonstrated much lower aberrations, over a 6° field, than the comparable spherical holographic lens.

© 1984 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. K. M. Leung, S. M. Arnold, J. C. Lindquist, “Using E-Beam Written Computer-Generated Holograms to Test Aspheric Wavefronts,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 161 (1981).
  2. H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).
  3. K. Biedermann, O. Holmgren, “Large-Size Distortion-Free Computer-Generated Holograms in Photoresist,” Appl. Opt. 16, 2014 (1977).
    [CrossRef] [PubMed]
  4. S. Lowenthal, P. Chavel, “Reduction of the Number of Samples in Computer Holograms for Image Processing,” Appl. Opt. 13, 718 (1974).
    [CrossRef] [PubMed]
  5. Y. Ishii, K. Murata, “Reflection Holographic Lens Having Nonspherical Wavefront Designed by a Microcomputer,” Opt. Commun. 47, 303 (1983).
    [CrossRef]
  6. R. C. Fairchild, J. R. Fienup, “Computer-Originated Hologram Lens,” Opt. Eng. 21, 133 (1982).
  7. K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded with Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208 (1983).
    [CrossRef]
  8. J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
    [CrossRef]

1983

Y. Ishii, K. Murata, “Reflection Holographic Lens Having Nonspherical Wavefront Designed by a Microcomputer,” Opt. Commun. 47, 303 (1983).
[CrossRef]

K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded with Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208 (1983).
[CrossRef]

1982

R. C. Fairchild, J. R. Fienup, “Computer-Originated Hologram Lens,” Opt. Eng. 21, 133 (1982).

1981

K. M. Leung, S. M. Arnold, J. C. Lindquist, “Using E-Beam Written Computer-Generated Holograms to Test Aspheric Wavefronts,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 161 (1981).

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

1977

1974

1967

J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

Arnold, S. M.

K. M. Leung, S. M. Arnold, J. C. Lindquist, “Using E-Beam Written Computer-Generated Holograms to Test Aspheric Wavefronts,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 161 (1981).

Biedermann, K.

Burch, J. J.

J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

Caulfield, H. J.

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

Chavel, P.

Dvore, D.

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

Epstein, A.

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

Fairchild, R. C.

R. C. Fairchild, J. R. Fienup, “Computer-Originated Hologram Lens,” Opt. Eng. 21, 133 (1982).

Fienup, J. R.

K. A. Winick, J. R. Fienup, “Optimum Holographic Elements Recorded with Nonspherical Wave Fronts,” J. Opt. Soc. Am. 73, 208 (1983).
[CrossRef]

R. C. Fairchild, J. R. Fienup, “Computer-Originated Hologram Lens,” Opt. Eng. 21, 133 (1982).

Holmgren, O.

Ishii, Y.

Y. Ishii, K. Murata, “Reflection Holographic Lens Having Nonspherical Wavefront Designed by a Microcomputer,” Opt. Commun. 47, 303 (1983).
[CrossRef]

Leung, K. M.

K. M. Leung, S. M. Arnold, J. C. Lindquist, “Using E-Beam Written Computer-Generated Holograms to Test Aspheric Wavefronts,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 161 (1981).

Lindquist, J. C.

K. M. Leung, S. M. Arnold, J. C. Lindquist, “Using E-Beam Written Computer-Generated Holograms to Test Aspheric Wavefronts,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 161 (1981).

Loomis, J. S.

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

Lowenthal, S.

Mueller, P.

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

Murata, K.

Y. Ishii, K. Murata, “Reflection Holographic Lens Having Nonspherical Wavefront Designed by a Microcomputer,” Opt. Commun. 47, 303 (1983).
[CrossRef]

Winick, K. A.

Appl. Opt.

J. Opt. Soc. Am.

Opt. Commun.

Y. Ishii, K. Murata, “Reflection Holographic Lens Having Nonspherical Wavefront Designed by a Microcomputer,” Opt. Commun. 47, 303 (1983).
[CrossRef]

Opt. Eng.

R. C. Fairchild, J. R. Fienup, “Computer-Originated Hologram Lens,” Opt. Eng. 21, 133 (1982).

Proc. IEEE

J. J. Burch, “A Computer Algorithm for the Synthesis of Spatial Frequency Filters,” Proc. IEEE 55, 599 (1967).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

K. M. Leung, S. M. Arnold, J. C. Lindquist, “Using E-Beam Written Computer-Generated Holograms to Test Aspheric Wavefronts,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 161 (1981).

H. J. Caulfield, P. Mueller, D. Dvore, A. Epstein, J. S. Loomis, “Computer Holograms for Optical Testing,” Proc. Soc. Photo-Opt. Instrum. Eng. 306, 154 (1981).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Illumination of the element by a plane wave with direction cosine a/f.

Fig. 2
Fig. 2

Spot diagrams for the on-axis elements: (a) spherical holographic lens; (b) quadratic holographic lens.

Fig. 3
Fig. 3

Reconstruction system in the off-axis configuration.

Fig. 4
Fig. 4

Spot diagrams for the off-axis spherical holographic lens.

Fig. 5
Fig. 5

Spot diagrams for the off-axis quadratic holographic lens.

Fig. 6
Fig. 6

Schematic diagram of the recording setup.

Fig. 7
Fig. 7

Photograph taken in the focal plane of the elements: (a) distribution in the spherical lens focal plane; (b) distribution in the quadratic lens focal plane.

Equations (37)

Equations on this page are rendered with MathJax. Learn more.

ψ in = a f x ,
ψ d = - ( x - a ) 2 + f 2 .
T ( x ) = 1 2 + 1 2 cos [ 2 π λ ψ h ( x ) ] ,
ψ out = ψ in - ψ h = a f x - ψ h ( x ) .
E 2 = a 1 a 2 x 1 ( a ) x 2 ( a ) ( ψ d - ψ out ) 2 d x d a .
E 2 = a 1 a 2 x 1 ( a ) x 2 ( a ) ( ψ d - ψ in + ψ h + ϕ ) 2 d x d a .
e 2 ( x ) = a 1 ( x ) a 2 ( x ) ( ψ d - ψ in + ψ h + ϕ ^ ) 2 d a ,
e 2 ( a ) = x 1 ( a ) x 2 ( a ) ( ψ d - ψ in + ψ ^ h + ϕ ) 2 d x ,
ψ ^ h ( x ) = - 1 a 2 ( x ) - a 1 ( x ) a 1 ( x ) a 2 ( x ) [ ψ d - ψ in + ϕ ^ ( a ) ] d a ,
ϕ ^ ( a ) = - 1 x 2 ( a ) - x 1 ( a ) x 1 ( a ) x 2 ( a ) [ ψ d - ψ in + ψ ^ h ( x ) ] d x .
F u 1 ( u 2 - u 1 ) u 1 u 2 F d u ,
ψ ^ h ( x ) = [ ( x - a ) 2 + f 2 ] 1 / 2 a + a x f a - ϕ ^ a ,
ϕ ^ ( a ) = [ ( x - a ) 2 + f 2 ] 1 / 2 x + a x f x - ψ ^ h x .
ψ ^ h = f + x 2 2 f + a 2 2 f a - p ( x - a ) a - ϕ ^ a ,
ϕ ^ = f + x 2 2 f x + a 2 2 f - p ( x - a ) x - ψ ^ h x .
ψ ^ h = x 2 2 f - p ( x - a ) a - x 2 2 f x a + p ( x - a ) x a + ψ ^ h x a .
p ( x - a ) a = 1 2 w x - w x + w p ( x - a ) d a = - 1 2 w P ( x - a ) ] x - w x + w = - P ( - 2 w ) 2 w ,
p ( x - a ) a = 1 2 w P ( 2 w ) .
p ( x - a ) x = 1 2 w a - w a + w p ( x - a ) d x = 1 2 w P ( 2 w ) ,
p ( x - a ) x a = 1 2 w P ( 2 w ) .
ψ ^ h = x 2 2 f - x 2 2 f x a + ψ ^ h x a ,
ψ ^ h - x 2 2 f = ψ ^ h - x 2 2 f x a .
ψ ^ h - x 2 2 f = constant .
ψ ^ h = x 2 2 f .
ψ h ( x , y ) = - x 2 + y 2 2 f .
ψ out = - ( x - α f ) 2 + ( y - β f ) 2 2 f + constant ,
p = x + d k x k z ,
k x = x ( - x 2 2 f ) = - x f .
p 2 = 1 2 w - w + w ( x + d k x k z ) 2 d x ,
p 2 = 1 2 w - w + w x 2 d x + d 2 2 w - w + w ( k x k z ) 2 d x + 2 d 2 w - w + w x k x k z d x .
p 2 d = 0 ,
d min = - - w + w x k x k z d x - w + w ( k x k z ) 2 d x .
d min f = - w + w x 2 1 - ( x f ) 2 d x - w + w x 2 1 - ( x f ) 2 d x .
ψ h = - x 2 2 f - ρ x ,
T ( x , y ) = ½ + ½ cos [ 2 π λ ( x 2 + y 2 + f s 2 - 1 2 f q ( x 2 + y 2 ) + c x ) ]
U m = exp [ i 2 π λ ( x 2 + y 2 + f s 2 - 1 2 f q ( x 2 + y 2 ) - ρ x ) ] ,
T ( x , y ) = ½ + ½ cos [ 1 2 f q ( x 2 + y 2 ) + ρ x ] .

Metrics