Abstract

Hybrid elements containing optical power with both diffractive (holographic) and refractive components are shown to be useful for obtaining arbitrary or, in special cases, achromatic dispersive characteristics. In one configuration a volume holographic element is coated on the surface of a crown glass lens, and by varying the power distributions among the refractive and holographic components while maintaining constant overall optical power the effective Abbe V numbers of the resultant hybrid element are shown to span all real numbers excepting a narrow interval around zero. In the achromat case (V number = ∞), both refractive and diffractive components are of the same sign resulting in much smaller glass curvatures than in all-refractive achromat doublets or apochromat triplets. The large separation between holographic partial dispersions and available glass partial dispersions is shown to lead to hybrid three-color achromats with greatly reduced glass curvatures. Applications are expected to include broadband achromatic objectives and chromatic aberration corrector plates in high performance optical systems. Such corrector plates may have any net power (including zero) while exhibiting effective V numbers that are positive or negative and that span a wide range, e.g., ±1 or ±1000. Further advantages include reducing the need for choosing high dispersion glasses, which may be costly and difficult to grind or polish. High diffraction efficiency and broad spectral bandwidths (in excess of 3000 Å) are obtained in the holographic optical elements using single-element central-stop and cascaded element designs.

© 1988 Optical Society of America

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References

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  1. R. H. Katyl, “Compensating Optical Systems. Parts 1–3,” Appl. Opt. 11, 1241 (1972).
    [CrossRef] [PubMed]
  2. G. M. Morris, “Diffraction Theory for an Achromatic Fourier Transform,” Appl. Opt. 20, 2017 (1981).
    [CrossRef] [PubMed]
  3. N. George, G. M. Morris, “Optical Matched Filtering in Noncoherent Illumination,” invited paper in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, Eds. (Taylor and Francis, London, 1981).
  4. T. Stone, “Holographic Optical Elements,” Ph.D. Thesis, U. Rochester (1986).
  5. T. Stone, N. George, “Hybrid Singlet Arbitrarily Dispersive Element,” J. Opt. Soc. Am. A 4(13), P 77 (1987).
  6. R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 77–87.
  7. Schott Optical Glass Inc., 400 York Ave., Duryea, PA 18642. Catalogs 3050 and 3111e/USA IX/80.
  8. I. H. Malitson, “A Redetermination of Some Optical Properties of Calcium Fluoride,” Appl. Opt. 2, 1103 (1963).
    [CrossRef]
  9. A. E. Conrady, Applied Optics and Optical Design, Part 1 (Oxford U. P., New York, 1929; Dover, New York, 1957), pp. 142–166.
  10. Units of length are omitted in the calculations, as is customary in optical system design.
  11. N. v. d. W. Lessing, “Selection of Optical Glasses in Apochromats,” J. Opt. Soc. Am. 47, 955 (1957).
    [CrossRef]
  12. N. v. d. W. Lessing, “Further Considerations on the Selection of Optical Glasses in Apochromats,” J. Opt. Soc. Am. 47, 955 (1957).
    [CrossRef]
  13. R. E. Stephens, “Selection of Glasses for Three-Color Achromats,” J. Opt. Soc. Am. 49, 398 (1959).
    [CrossRef]
  14. M. Herzberger, “Colour Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
    [CrossRef]
  15. R. T. Ingwall, H. L. Fielding, “Hologram Recording with a New Photopolymer System,” Opt. Eng. 24, 808 (1985).
    [CrossRef]
  16. R. T. Ingwall, A. Stuck, W. T. Vetterling, “Diffraction Properties of Holograms Recorded in DMP-128,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 81 (1986).
  17. T. Stone, N. George, “Bandwidth of Holographic Optical Elements,” Opt. Lett. 7, 445 (1982).
    [CrossRef] [PubMed]
  18. T. Stone, N. George, “Wavelength Performance of Holographic Optical Elements,” Appl. Opt. 24, 3797 (1985).
    [CrossRef] [PubMed]
  19. J. N. Latta, “Analysis of Multiple Hologram Optical Elements with Low Dispersion and Low Aberrations,” Appl. Opt. 11, 1686 (1972).
    [CrossRef] [PubMed]
  20. B. J. Chang, “Doubly Modulated On-Axis Thick-Hologram Optical Elements,” J. Opt. Soc. Am. 67, 1435A (1977).
  21. D. H. Close, “Holographic Optical Elements,” Opt. Eng. 14, 408 (1975).

1987 (1)

T. Stone, N. George, “Hybrid Singlet Arbitrarily Dispersive Element,” J. Opt. Soc. Am. A 4(13), P 77 (1987).

1986 (1)

R. T. Ingwall, A. Stuck, W. T. Vetterling, “Diffraction Properties of Holograms Recorded in DMP-128,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 81 (1986).

1985 (2)

R. T. Ingwall, H. L. Fielding, “Hologram Recording with a New Photopolymer System,” Opt. Eng. 24, 808 (1985).
[CrossRef]

T. Stone, N. George, “Wavelength Performance of Holographic Optical Elements,” Appl. Opt. 24, 3797 (1985).
[CrossRef] [PubMed]

1982 (1)

1981 (1)

1977 (1)

B. J. Chang, “Doubly Modulated On-Axis Thick-Hologram Optical Elements,” J. Opt. Soc. Am. 67, 1435A (1977).

1975 (1)

D. H. Close, “Holographic Optical Elements,” Opt. Eng. 14, 408 (1975).

1972 (2)

1963 (1)

1959 (2)

M. Herzberger, “Colour Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
[CrossRef]

R. E. Stephens, “Selection of Glasses for Three-Color Achromats,” J. Opt. Soc. Am. 49, 398 (1959).
[CrossRef]

1957 (2)

Chang, B. J.

B. J. Chang, “Doubly Modulated On-Axis Thick-Hologram Optical Elements,” J. Opt. Soc. Am. 67, 1435A (1977).

Close, D. H.

D. H. Close, “Holographic Optical Elements,” Opt. Eng. 14, 408 (1975).

Conrady, A. E.

A. E. Conrady, Applied Optics and Optical Design, Part 1 (Oxford U. P., New York, 1929; Dover, New York, 1957), pp. 142–166.

Fielding, H. L.

R. T. Ingwall, H. L. Fielding, “Hologram Recording with a New Photopolymer System,” Opt. Eng. 24, 808 (1985).
[CrossRef]

George, N.

T. Stone, N. George, “Hybrid Singlet Arbitrarily Dispersive Element,” J. Opt. Soc. Am. A 4(13), P 77 (1987).

T. Stone, N. George, “Wavelength Performance of Holographic Optical Elements,” Appl. Opt. 24, 3797 (1985).
[CrossRef] [PubMed]

T. Stone, N. George, “Bandwidth of Holographic Optical Elements,” Opt. Lett. 7, 445 (1982).
[CrossRef] [PubMed]

N. George, G. M. Morris, “Optical Matched Filtering in Noncoherent Illumination,” invited paper in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, Eds. (Taylor and Francis, London, 1981).

Herzberger, M.

M. Herzberger, “Colour Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
[CrossRef]

Ingwall, R. T.

R. T. Ingwall, A. Stuck, W. T. Vetterling, “Diffraction Properties of Holograms Recorded in DMP-128,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 81 (1986).

R. T. Ingwall, H. L. Fielding, “Hologram Recording with a New Photopolymer System,” Opt. Eng. 24, 808 (1985).
[CrossRef]

Katyl, R. H.

Kingslake, R.

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 77–87.

Latta, J. N.

Lessing, N. v. d. W.

Malitson, I. H.

Morris, G. M.

G. M. Morris, “Diffraction Theory for an Achromatic Fourier Transform,” Appl. Opt. 20, 2017 (1981).
[CrossRef] [PubMed]

N. George, G. M. Morris, “Optical Matched Filtering in Noncoherent Illumination,” invited paper in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, Eds. (Taylor and Francis, London, 1981).

Stephens, R. E.

Stone, T.

T. Stone, N. George, “Hybrid Singlet Arbitrarily Dispersive Element,” J. Opt. Soc. Am. A 4(13), P 77 (1987).

T. Stone, N. George, “Wavelength Performance of Holographic Optical Elements,” Appl. Opt. 24, 3797 (1985).
[CrossRef] [PubMed]

T. Stone, N. George, “Bandwidth of Holographic Optical Elements,” Opt. Lett. 7, 445 (1982).
[CrossRef] [PubMed]

T. Stone, “Holographic Optical Elements,” Ph.D. Thesis, U. Rochester (1986).

Stuck, A.

R. T. Ingwall, A. Stuck, W. T. Vetterling, “Diffraction Properties of Holograms Recorded in DMP-128,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 81 (1986).

Vetterling, W. T.

R. T. Ingwall, A. Stuck, W. T. Vetterling, “Diffraction Properties of Holograms Recorded in DMP-128,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 81 (1986).

Appl. Opt. (5)

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (1)

T. Stone, N. George, “Hybrid Singlet Arbitrarily Dispersive Element,” J. Opt. Soc. Am. A 4(13), P 77 (1987).

Opt. Acta (1)

M. Herzberger, “Colour Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959).
[CrossRef]

Opt. Eng. (2)

R. T. Ingwall, H. L. Fielding, “Hologram Recording with a New Photopolymer System,” Opt. Eng. 24, 808 (1985).
[CrossRef]

D. H. Close, “Holographic Optical Elements,” Opt. Eng. 14, 408 (1975).

Opt. Lett. (1)

Proc. Soc. Photo-Opt. Instrum. Eng. (1)

R. T. Ingwall, A. Stuck, W. T. Vetterling, “Diffraction Properties of Holograms Recorded in DMP-128,” Proc. Soc. Photo-Opt. Instrum. Eng. 615, 81 (1986).

Other (6)

N. George, G. M. Morris, “Optical Matched Filtering in Noncoherent Illumination,” invited paper in Current Trends in Optics, F. T. Arecchi, F. R. Aussenegg, Eds. (Taylor and Francis, London, 1981).

T. Stone, “Holographic Optical Elements,” Ph.D. Thesis, U. Rochester (1986).

R. Kingslake, Lens Design Fundamentals (Academic, New York, 1978), pp. 77–87.

Schott Optical Glass Inc., 400 York Ave., Duryea, PA 18642. Catalogs 3050 and 3111e/USA IX/80.

A. E. Conrady, Applied Optics and Optical Design, Part 1 (Oxford U. P., New York, 1929; Dover, New York, 1957), pp. 142–166.

Units of length are omitted in the calculations, as is customary in optical system design.

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Figures (15)

Fig. 1
Fig. 1

Simple hybrid doublet. Schematic representation of a hybrid doublet optical element. In this case a holographic lens is fabricated on the flat surface of a plano-convex refractive lens.

Fig. 2
Fig. 2

Glass dispersions. The refractive indices of fluorite and six optical glasses which coarsely sample those available in the Schott optical glass catalog are plotted vs wavelength. The corresponding Abbe V numbers for each material are also shown.

Fig. 3
Fig. 3

Single-element dispersions. The focal lengths (arbitrary units) of thin lenses are plotted vs wavelength for refractive lenses fabricated from the materials of Fig. 2 and also for a diffractive holographic lens. Each lens was constrained to have a focal length of 10 at λd = 0.5876 μm.

Fig. 4
Fig. 4

Hybrid doublet achromat. The focal lengths (arbitrary units) of three lenses are plotted vs wavelength for cases (a) single element of BK7 glass; (b) BK7/SF10 all-glass achromat; (c) BK7/hologram hybrid doublet. The required curvature of the crown glass element has been greatly reduced in the hybrid case permitting much larger achromat apertures. Each lens was constrained to have a focal length of 10 at λd = 0.5876 μm.

Fig. 5
Fig. 5

Secondary spectrum. The focal lengths (arbitrary units) are plotted vs wavelength for two all-glass and three hybrid achromat lenses. Each lens was constrained to have a focal length of 10.0 at λd = 0.5876 μm and also has equal focal lengths at λC and λF. The secondary spectra of hybrid achromats are slightly larger than all-glass achromats due to the large diffractive dispersion.

Fig. 6
Fig. 6

Infrared hybrid achromat. The focal lengths (arbitrary units) of four lenses are plotted vs wavelength throughout the 3–5-μm band for single-element lenses of (a) germanium and (b) silicon and achromat cases (c) silicon/germanium and (d) hybrid silicon/hologram. In the hybrid case the need for germanium is eliminated, and the quantity of silicon required is reduced.

Fig. 7
Fig. 7

Relative partial dispersions. The relative partial dispersion in the blue Pge (defined in the text) is plotted vs the inverse dispersion Ve for fluorite and the span of optical glasses. The effective location of a diffractive (holographic) lens is plotted on the same scale.

Fig. 8
Fig. 8

Hybrid apochromat. The paraxial focal lengths of three-color achromats (apochromat predesigns) are plotted across the visible spectrum for the cases of (a) all-glass and (b) hybrid refractive/diffractive lenses. The required component powers are drastically reduced in the hybrid case while maintaining the desired focal length to 1 part in 104.

Fig. 9
Fig. 9

Infrared hybrid achromat. Tertiary spectra are plotted for three-color achromats in the 3–5-μm spectral band. The all-refractive case (a) consists of silicon, germanium, and zinc sulfide components. In the hybrid refractive/diffractive cases (b) and (c) a holographic element has been substituted for the zinc sulfide and germanium elements, respectively.

Fig. 10
Fig. 10

Hybrid singlet dispersions. The focal length is plotted vs wavelength for various distributions between refractive and diffractive optical power in a BK7/hologram hybrid singlet in which the net focal length is a constant 10.0 (arbitrary units) at λd = 0.5876 μm. As the power distribution is varied, the hybrid lens simulates the dispersion of a single element of arbitrary V number.

Fig. 11
Fig. 11

Hybrid singlet span in V. The effective V number of a hybrid singlet lens is shown as a function of the percentage of the total power that is contributed by the hologram. This total optical power is the sum of diffractive and refractive contributions and is fixed at 0.1 (a focal length of 10.0) at λd = 0.5876 μm. The singularity near 5% corresponds to the achromatic case in which the V number is infinite.

Fig. 12
Fig. 12

Hybrid singlet glass choice. The effective V number is plotted vs diffractive/refractive power distribution, as in the previous figure, for hybrid singlets composed of a holographic element and varied refractive materials. Since the span in V number is the same for the varied hybrid singlets, exotic or difficult to work refractive materials are not required

Fig. 13
Fig. 13

Low scatter holographic elements. Scattered intensity is plotted as a function of angle in the forward half space perpendicular to the grating modulation for normally illuminated samples: a, 99% efficient DMP-128 grating; b, 1.27 cm (½ in.). Thick float glass slab, a 99% efficient DMP-128 grating; b, 1.27-cm (½ in.) thick float glass slab.

Fig. 14
Fig. 14

Holographic lens configurations. Four configurations of holographic lenses are illustrated including the axial zone lens, off-axis zone lens, close cascade, and triangle configurations. For weak holographic lenses the close cascade configuration is particularly useful.

Fig. 15
Fig. 15

Centrally obscured axial holographic lens. The axial zone lens exhibits a region of low diffraction efficiency surrounding the optical axis. After blocking this region, this holographic lens configuration is again useful, particularly for strong holographic lenses where the dimension of the central obscuration becomes very small.

Tables (2)

Tables Icon

Table I Relative Partial Dispersions of Holographic Optical Elements Compared with Those for Varied Refractive Optical Materials

Tables Icon

Table II Deviations of Relative Partial Dispersions from the Normal Line for Holographic Optical Elements and Varied Refractive Optical Materials

Equations (31)

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V d = n d - 1 n F - n C ,
Φ ( λ ) = 1 f ( λ ) = [ n ( λ ) - 1 ] C 0 ,
t ( x , y ) = exp [ i π λ 0 f 0 ( x 2 + y 2 ) ] ,
v ( x , y , 0 ; t ) = exp [ i π λ f ( λ ) ( x 2 + y 2 ) + i 2 π ν t ] ,
f ( λ ) = ( λ 0 λ ) f 0 .
f C = f d ( λ d λ C ) and f F = f d ( λ d λ F ) .
1 f z = ( n z eff - 1 ) C 0 ,
n z eff = 1 + 1 C 0 f z = 1 + λ z C 0 f d λ d .
V d H = λ d λ F - λ C = - 3.452.
Φ hyb ( λ ) = Φ ref ( λ ) + Φ dif ( λ ) ,
f dif = F ( V dif - V ref V dif ) and f ref = F ( V ref - V dif V ref ) .
P λ 1 λ 2 = n λ 1 - n λ 2 n F - n C .
P λ 1 λ 2 / λ 3 λ 4 = n λ 1 - n λ 2 n λ 3 - n λ 4 ,
n λ 1 eff = 1 + 1 C 0 f λ 1 ,
n λ 2 eff = 1 + 1 C 0 f λ 2 = 1 + λ 2 C 0 f λ 1 λ 1 ,
n λ 3 eff = 1 + 1 C 0 f λ 3 = 1 + λ 3 C 0 f λ 1 λ 1 ,
n λ 4 eff = 1 + 1 C 0 f λ 4 = 1 + λ 4 C 0 f λ 1 λ 1 .
P λ 1 λ 2 / λ 3 λ 4 H = λ 1 - λ 2 λ 3 - λ 4 .
P g F H = λ g - λ F λ F - λ C = 0.2956.
Δ l λ F = - F ( P λ F a - P λ F b V d a - V d b ) ,
f a = F E ( V a - V c ) ( P b - P c ) V a ,
f b = F E ( V a - V c ) ( P c - P a ) V b ,
f c = F E ( V a - V c ) ( P a - P b ) V c ,
E = V a ( P b - P c ) + V b ( P c - P a ) + V c ( P a - P b ) ( V a - V c ) .
V e = n e - 1 n g - n C
V e H = λ e λ g - λ C = - 2.477.
P g e / g C = n λ g - n λ e n λ g - n λ C ,
P g e / g C H = λ g - λ e λ g - λ C = 0.500.
V 4.0 = n 4.0 - 1 n 3.5 - n 4.5
Φ hyb ( λ d ) = 0.1 = Φ ref ( λ d ) + Φ diff ( λ d ) ,
β = L Λ · L Λ ,

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