Abstract

The efficiency and aberration of partitioned-field uniaxial volume holographic compound lenses are theoretically and experimentally studied. These systems increase the image fields of holographic volume lenses, limited by the angular selectivity that is typical of these elements. At the same time, working with uniaxial systems has led to a decrease in aberration because two recording points (that behave as aberration-free points) are used. The extension of the image field is experimentally proved.

© 2002 Optical Society of America

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References

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  1. J. Atencia, A. M. López, M. Quintanilla, “HOE recording with non-spherical waves,” J. Opt. A 3, 53–60 (2001).
    [CrossRef]
  2. M. Quintanilla, I. Arias, “Holographic imaging lenses. Composite lens with high efficiency,” J. Opt. 21, 67–72 (1990).
    [CrossRef]
  3. R. R. A. Syms, L. Solymar, “The effect of angular selectivity on the monochromatic imaging performance of volume holographic lenses,” Opt. Acta 30, 1303–1318 (1983).
    [CrossRef]
  4. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  5. J. Atencia, I. Arias, M. Quintanilla, A. García, A. M. López, “Field improvement in a uniaxial centered lens composed of two stacked-volume holographic elements,” Appl. Opt. 38, 4011–4018 (1999).
    [CrossRef]
  6. A. M. López, J. Atencia, I. Arias, M. Quintanilla, “Field improvement in optical uniaxial centered systems composed of holographic elements,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 177–186 (2000).
    [CrossRef]
  7. E. N. Leith, J. Upatnieks, “Zone plate with aberration correction,” J. Opt. Soc. Am. 57, 699 (1967).
    [CrossRef]
  8. M. Quintanilla, A. M. de Frutos, “Holographic lenses aberration balancing by angular selectivity,” Opt. Pura Apl. 20, 21–26 (1987).
  9. E. B. Champagne, “Nonparaxial imaging, magnification, and aberration properties in holography,” J. Opt. Soc. Am. 57, 51–55 (1967).
    [CrossRef]
  10. H. H. Hopkins, Wave Theory of Aberrations (Oxford University, Oxford, UK, 1950).
  11. S. K. Case, “Coupled wave theory of multiply exposed thick holographic gratings,” J. Opt. Soc. Am. 65, 724–729 (1975).
    [CrossRef]
  12. M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
    [CrossRef]
  13. T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
    [CrossRef]
  14. R. R. A. Syms, “Vector effects in holographical optical elements,” Opt. Acta 32, 1413–1425 (1985).
    [CrossRef]
  15. R. R. A. Syms, L. Solymar, “Analysis of volume holographical cylindrical lenses,” J. Opt. Soc. Am. 72, 179–86 (1982).
    [CrossRef]
  16. A. Fimia, A. Beléndez, I. Pascual, “Silver halide (sensitized) gelatin in Agfa-Gevaert plates: the optimized procedure,” J. Mod. Opt. 38, 2043–2051 (1991).
    [CrossRef]
  17. R. A. Ferrante, “Silver halide gelatin frequency response,” Appl. Opt. 23, 4180–4181 (1984).
    [CrossRef] [PubMed]
  18. J. N. Latta, “Computer-based analysis of holography using ray tracing,” Appl. Opt. 10, 2698–2710 (1971).
    [CrossRef] [PubMed]

2001 (1)

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with non-spherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

1999 (1)

1991 (1)

A. Fimia, A. Beléndez, I. Pascual, “Silver halide (sensitized) gelatin in Agfa-Gevaert plates: the optimized procedure,” J. Mod. Opt. 38, 2043–2051 (1991).
[CrossRef]

1990 (1)

M. Quintanilla, I. Arias, “Holographic imaging lenses. Composite lens with high efficiency,” J. Opt. 21, 67–72 (1990).
[CrossRef]

1987 (1)

M. Quintanilla, A. M. de Frutos, “Holographic lenses aberration balancing by angular selectivity,” Opt. Pura Apl. 20, 21–26 (1987).

1985 (1)

R. R. A. Syms, “Vector effects in holographical optical elements,” Opt. Acta 32, 1413–1425 (1985).
[CrossRef]

1984 (1)

1983 (2)

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[CrossRef]

R. R. A. Syms, L. Solymar, “The effect of angular selectivity on the monochromatic imaging performance of volume holographic lenses,” Opt. Acta 30, 1303–1318 (1983).
[CrossRef]

1982 (2)

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

R. R. A. Syms, L. Solymar, “Analysis of volume holographical cylindrical lenses,” J. Opt. Soc. Am. 72, 179–86 (1982).
[CrossRef]

1975 (1)

1971 (1)

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1967 (2)

Arias, I.

J. Atencia, I. Arias, M. Quintanilla, A. García, A. M. López, “Field improvement in a uniaxial centered lens composed of two stacked-volume holographic elements,” Appl. Opt. 38, 4011–4018 (1999).
[CrossRef]

M. Quintanilla, I. Arias, “Holographic imaging lenses. Composite lens with high efficiency,” J. Opt. 21, 67–72 (1990).
[CrossRef]

A. M. López, J. Atencia, I. Arias, M. Quintanilla, “Field improvement in optical uniaxial centered systems composed of holographic elements,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 177–186 (2000).
[CrossRef]

Atencia, J.

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with non-spherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

J. Atencia, I. Arias, M. Quintanilla, A. García, A. M. López, “Field improvement in a uniaxial centered lens composed of two stacked-volume holographic elements,” Appl. Opt. 38, 4011–4018 (1999).
[CrossRef]

A. M. López, J. Atencia, I. Arias, M. Quintanilla, “Field improvement in optical uniaxial centered systems composed of holographic elements,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 177–186 (2000).
[CrossRef]

Beléndez, A.

A. Fimia, A. Beléndez, I. Pascual, “Silver halide (sensitized) gelatin in Agfa-Gevaert plates: the optimized procedure,” J. Mod. Opt. 38, 2043–2051 (1991).
[CrossRef]

Case, S. K.

Champagne, E. B.

de Frutos, A. M.

M. Quintanilla, A. M. de Frutos, “Holographic lenses aberration balancing by angular selectivity,” Opt. Pura Apl. 20, 21–26 (1987).

Ferrante, R. A.

Fimia, A.

A. Fimia, A. Beléndez, I. Pascual, “Silver halide (sensitized) gelatin in Agfa-Gevaert plates: the optimized procedure,” J. Mod. Opt. 38, 2043–2051 (1991).
[CrossRef]

García, A.

Gaylord, T. K.

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[CrossRef]

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, Oxford, UK, 1950).

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Latta, J. N.

Leith, E. N.

López, A. M.

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with non-spherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

J. Atencia, I. Arias, M. Quintanilla, A. García, A. M. López, “Field improvement in a uniaxial centered lens composed of two stacked-volume holographic elements,” Appl. Opt. 38, 4011–4018 (1999).
[CrossRef]

A. M. López, J. Atencia, I. Arias, M. Quintanilla, “Field improvement in optical uniaxial centered systems composed of holographic elements,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 177–186 (2000).
[CrossRef]

Moharam, M. G.

M. G. Moharam, T. K. Gaylord, “Three-dimensional vector coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 73, 1105–1112 (1983).
[CrossRef]

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

Pascual, I.

A. Fimia, A. Beléndez, I. Pascual, “Silver halide (sensitized) gelatin in Agfa-Gevaert plates: the optimized procedure,” J. Mod. Opt. 38, 2043–2051 (1991).
[CrossRef]

Quintanilla, M.

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with non-spherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

J. Atencia, I. Arias, M. Quintanilla, A. García, A. M. López, “Field improvement in a uniaxial centered lens composed of two stacked-volume holographic elements,” Appl. Opt. 38, 4011–4018 (1999).
[CrossRef]

M. Quintanilla, I. Arias, “Holographic imaging lenses. Composite lens with high efficiency,” J. Opt. 21, 67–72 (1990).
[CrossRef]

M. Quintanilla, A. M. de Frutos, “Holographic lenses aberration balancing by angular selectivity,” Opt. Pura Apl. 20, 21–26 (1987).

A. M. López, J. Atencia, I. Arias, M. Quintanilla, “Field improvement in optical uniaxial centered systems composed of holographic elements,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 177–186 (2000).
[CrossRef]

Solymar, L.

R. R. A. Syms, L. Solymar, “The effect of angular selectivity on the monochromatic imaging performance of volume holographic lenses,” Opt. Acta 30, 1303–1318 (1983).
[CrossRef]

R. R. A. Syms, L. Solymar, “Analysis of volume holographical cylindrical lenses,” J. Opt. Soc. Am. 72, 179–86 (1982).
[CrossRef]

Syms, R. R. A.

R. R. A. Syms, “Vector effects in holographical optical elements,” Opt. Acta 32, 1413–1425 (1985).
[CrossRef]

R. R. A. Syms, L. Solymar, “The effect of angular selectivity on the monochromatic imaging performance of volume holographic lenses,” Opt. Acta 30, 1303–1318 (1983).
[CrossRef]

R. R. A. Syms, L. Solymar, “Analysis of volume holographical cylindrical lenses,” J. Opt. Soc. Am. 72, 179–86 (1982).
[CrossRef]

Upatnieks, J.

Appl. Opt. (3)

Appl. Phys. B (1)

T. K. Gaylord, M. G. Moharam, “Planar dielectric grating diffraction theories,” Appl. Phys. B 28, 1–14 (1982).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Mod. Opt. (1)

A. Fimia, A. Beléndez, I. Pascual, “Silver halide (sensitized) gelatin in Agfa-Gevaert plates: the optimized procedure,” J. Mod. Opt. 38, 2043–2051 (1991).
[CrossRef]

J. Opt. (1)

M. Quintanilla, I. Arias, “Holographic imaging lenses. Composite lens with high efficiency,” J. Opt. 21, 67–72 (1990).
[CrossRef]

J. Opt. A (1)

J. Atencia, A. M. López, M. Quintanilla, “HOE recording with non-spherical waves,” J. Opt. A 3, 53–60 (2001).
[CrossRef]

J. Opt. Soc. Am. (5)

Opt. Acta (2)

R. R. A. Syms, “Vector effects in holographical optical elements,” Opt. Acta 32, 1413–1425 (1985).
[CrossRef]

R. R. A. Syms, L. Solymar, “The effect of angular selectivity on the monochromatic imaging performance of volume holographic lenses,” Opt. Acta 30, 1303–1318 (1983).
[CrossRef]

Opt. Pura Apl. (1)

M. Quintanilla, A. M. de Frutos, “Holographic lenses aberration balancing by angular selectivity,” Opt. Pura Apl. 20, 21–26 (1987).

Other (2)

A. M. López, J. Atencia, I. Arias, M. Quintanilla, “Field improvement in optical uniaxial centered systems composed of holographic elements,” in Holography 2000, T. H. Jeong, W. K. Sobotka, eds., Proc. SPIE4149, 177–186 (2000).
[CrossRef]

H. H. Hopkins, Wave Theory of Aberrations (Oxford University, Oxford, UK, 1950).

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Figures (17)

Fig. 1
Fig. 1

Construction and reconstruction parameters for a biaxial holographic optical element.

Fig. 2
Fig. 2

Recording and reconstruction geometry for the uniaxial compound system.

Fig. 3
Fig. 3

Image fields that result from (a) a compound uniaxial holographic lens limited by angular selectivity and from (b) the partitioned-field holographic lens.

Fig. 4
Fig. 4

Dependence of light intensity on the η coordinate at the image plane of a partitioned-field lens.

Fig. 5
Fig. 5

Uniaxial lens at a meridianal plane.

Fig. 6
Fig. 6

(a) Schematic of the limited image field of the compound uniaxial system of Fig. 2. As the average construction-beams plane of the system is the ηζ plane, the intensity is limited for the y coordinate of the object. (b) Proposed partitioned-field lens with two multiplexed uniaxial elements, which produces an extension of the field in the y direction.

Fig. 7
Fig. 7

Efficiencies of the image formed by two compound systems, α = -4.41° and α* = 4.41°. The independent addition of these two efficiency curves is also shown.

Fig. 8
Fig. 8

Construction beams of the two lenses that are recorded on a single element of the compound system.

Fig. 9
Fig. 9

Diffraction efficiencies of the beams generated by the first plate where two gratings have been recorded. The curves are plotted as a function of the η coordinate of the object plane, with ξ = 0. The distance of incidence is equal to the focal distance of the system.

Fig. 10
Fig. 10

(a) Theoretical efficiency of the image produced by the compound system upon which the gratings defined in Fig. 8 have been superposed, as a function of the object plane coordinates. The system acts with unity magnification. (b) The same calculation for action of grating 1 only.

Fig. 11
Fig. 11

Experimental setup for studying real-image formation by a holographic lens.

Fig. 12
Fig. 12

Image of a periodic diffusing object formed by the compound system working with unity magnification.

Fig. 13
Fig. 13

Ratio of energy of the image and total incident energetic flux. Comparison of theoretical and experimental results.

Fig. 14
Fig. 14

Spot diagrams at the paraxial image plane for unity magnification obtained from one of the uniaxial lenses.

Fig. 15
Fig. 15

Spot diagram for unity magnification at the paraxial image plane and at image planes with different focal shifts.

Fig. 16
Fig. 16

Image of the 1951 U.S. Air Force resolution test, placed at the center of the object plane. The compound system works with unity magnification.

Fig. 17
Fig. 17

Spot diagrams at the paraxial image plane for an object at infinity obtained from one of the uniaxial lenses.

Equations (29)

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1ri=1ro-μ1r1-1r2,
xiri=xoro,
yi cos α2ri=yo cos α1ro-μ-1sin α1-sin α2
yiri=yoro-μ-1sin α1-sin α2.
yiri=yoro,
r1α=r10/cos α,
r2α=r20/cos α
roα=ro0/cos α,
riα=ri0/cos α.
Ψi=Φo-Φ1-Φ2.
W=Φo-Φ1-Φ2-Φi.
W=-2πλScρ4 spherical-½Cξcρ3 sin φ-½Cηcρ3 cos φ coma+½Aξcρ2 sin2 φ+½Aηcρ2 cos2 φ+Aξηcρ2 sin φ cos φ astigmatism+¼Fcρ2 curvature-½Dξcρ sin φ-½Dηcρ cos φ, distortion,
εr=εo+Δε1 cosK1r · r+Δε2 cosK2r · r.
K1r=ρ1r-σ1r,
K2r=ρ2r-σ2r,
ρ,
σ1=ρ-K1,
σ2=ρ-K2.
Er=Rzexp-iρ · r+S1z-iσ1 · r+S2z-iσ2 · r,
Hr=εo/μUzexp-iρ · r+T1z-iσ1 · r+T2z-iσ2 · r,
×E=-iωμoH,
×H=-iωεoεrE
εr=εo+Δε1 cosK1r · r+Δε2 cosK2r · r,
Kixξ, η=-Kix-ξ, η,
Kiyξ, η=Kiy-ξ, η,
Kizξ, η=-Kiz-ξ, η.
ρ-K1-K1,
ρ-K2-K2.
Sc=ρm41ro3-1ri3-μ1r13-1r23,Cξc=ρm3xoro3-xiri3,Cηc=ρm3yo+ro sin α1ro3-yi+ri sin α2ri3-μsin α1r12-sin α2r22,Aξc=ρm2xo2ro3-xi2ri3,Aηc=ρm2yo+ro sin α12ro3-yi+ri sin α22ri3-μsin2 α1r1-sin2 α2r2,Aξc=ρm2xoyo+ro sin α1ro3-xiyi+ri sin α2ri3,Fc=ρm2xo2+yo2+2yoro sin α1ro3-xi2+yi2+2yiri sin α2ri3,Dξc=ρmxoxo2+yo2+2yoro sin α1ro3-xixi2+yi2+2yiri sin α2ri3,Dηc=ρmyo+ro sin α1xo2+yo2+2yoro sin α1ro3-yi+ri sin α2xi2+yi2+2yiri sin α2ri3.

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