Abstract

The harmonic diffractive lens is a diffractive imaging lens for which the optical path-length transition between adjacent facets is an integer multiple m of the design wavelength λ0. The total lens thickness in air is mλ0/(n − 1), which is m times thicker than the so-called modulo 2π diffractive lens. Lenses constructed in this way have hybrid properties of both refractive and diffractive lenses. Such a lens will have a diffraction-limited, common focus for a number of discrete wavelengths across the visible spectrum. A 34.75-diopter, 6-mm-diameter lens is diamond turned in aluminum and replicated in optical materials. The sag of the lens is 23 μm. Modulation transfer function measurements in both monochromatic and white light verify the performance of the lens. The lens approaches the diffraction limit for 10 discrete wavelengths across the visible spectrum.

© 1995 Optical Society of America

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References

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  1. D. W. Sweeney, G. Sommargren, “Single element achromatic lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.
  2. G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.
  3. M. W. Farn, J. W. Goodman, “Diffractive doublets corrected at two wavelengths,” J. Opt. Soc. Am. 8, 860–867; see also, M. W. Farn, “Design and fabrication of binary diffractive optics,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1990).
  4. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” DARPA Tech. Rep. 854 (Defense Advanced Research Projects Agency, Washington, D.C., 1989).
  5. D. A. Buralli, G. M. Morris, “Design of a wide field diffractive landscape lens,” Appl. Opt. 28, 3950–3959 (1989).
    [CrossRef] [PubMed]
  6. S. J. Bennett, “Achromatic combinations of hologram optical elements,” Appl. Opt. 15, 542–545 (1976).
    [CrossRef] [PubMed]
  7. W. C. Sweatt, “Achromatic triplet using holographic optical elements,” Appl. Opt. 16, 1390–1391 (1977).
    [CrossRef] [PubMed]
  8. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  9. D. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
    [CrossRef] [PubMed]
  10. Finish 2001 Car Polish, distributed by Turtle Wax Inc., Chicago, Ill., 60638-6211.

1992 (1)

1989 (1)

1977 (1)

1976 (1)

Bennett, S. J.

Buralli, D.

Buralli, D. A.

Faklis, D.

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Farn, M. W.

M. W. Farn, J. W. Goodman, “Diffractive doublets corrected at two wavelengths,” J. Opt. Soc. Am. 8, 860–867; see also, M. W. Farn, “Design and fabrication of binary diffractive optics,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1990).

Goodman, J. W.

M. W. Farn, J. W. Goodman, “Diffractive doublets corrected at two wavelengths,” J. Opt. Soc. Am. 8, 860–867; see also, M. W. Farn, “Design and fabrication of binary diffractive optics,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1990).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Morris, G. M.

D. Buralli, G. M. Morris, “Effects of diffraction efficiency on the modulation transfer function of diffractive lenses,” Appl. Opt. 31, 4389–4396 (1992).
[CrossRef] [PubMed]

D. A. Buralli, G. M. Morris, “Design of a wide field diffractive landscape lens,” Appl. Opt. 28, 3950–3959 (1989).
[CrossRef] [PubMed]

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

Sommargren, G.

D. W. Sweeney, G. Sommargren, “Single element achromatic lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” DARPA Tech. Rep. 854 (Defense Advanced Research Projects Agency, Washington, D.C., 1989).

Sweatt, W. C.

Sweeney, D. W.

D. W. Sweeney, G. Sommargren, “Single element achromatic lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.

Appl. Opt. (4)

J. Opt. Soc. Am. (1)

M. W. Farn, J. W. Goodman, “Diffractive doublets corrected at two wavelengths,” J. Opt. Soc. Am. 8, 860–867; see also, M. W. Farn, “Design and fabrication of binary diffractive optics,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1990).

Other (5)

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” DARPA Tech. Rep. 854 (Defense Advanced Research Projects Agency, Washington, D.C., 1989).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Finish 2001 Car Polish, distributed by Turtle Wax Inc., Chicago, Ill., 60638-6211.

D. W. Sweeney, G. Sommargren, “Single element achromatic lens,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 26–29.

G. M. Morris, D. Faklis, “Achromatic and apochromatic diffractive singlets,” in Diffractive Optics, Vol. 11 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 53–56.

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Figures (13)

Fig. 1
Fig. 1

Blazed diffractive lenses. The lens on the left is the thin-limit case and is referred to here as a simple diffractive lens or modulo 2π diffractive lens. The lens on the right is a harmonic diffractive lens; it is a generalization of the modulo 2π diffractive lens.

Fig. 2
Fig. 2

Top panel shows the optical power of the diffracted orders from a harmonic diffractive lens as a function of wavelength; the bottom panel shows the diffraction efficiency as a function of wavelength for each order. An example of diffracted order (shown in bold) diffracts only significant light in the spectral region shown.

Fig. 3
Fig. 3

Distribution of energy for the m = 15 harmonic diffractive lens. Diffracted orders 12 to 21 (i.e., k values) contribute to the focus across the visible. For a simple diffractive lens, the diffracted energy would be (to first order) distributed along the dashed line labeled m = 1.

Fig. 4
Fig. 4

Diffractive element on the left can be decomposed into the difference between the two elements on the right.

Fig. 5
Fig. 5

Phase factor introduced by the echelon structure shown in Fig. 4 for various wavelengths. t e is the echelon thickness shown in Fig. 4.

Fig. 6
Fig. 6

Coordinate system used in the simulation.

Fig. 7
Fig. 7

Numerical simulation of the energy distribution for a 34.75-diopter, 6-mm-diameter lens between 500 and 640 nm. Diffracted orders 18–23 are labeled. The circles represent experimental measurements of focal length.

Fig. 8
Fig. 8

(a) Impulse response, (b) associated MTF for the 34.75-diopter lens as a function of wavelength. The radial coordinate in (a) is normalized by the Rayleigh resolution; for this particular example it corresponds to 0.44 μm.

Fig. 9
Fig. 9

Diamond-turned, aluminum harmonic diffractive lens master. The lens is 6 mm in diameter, and it has 14 zones and a total modulation depth of 23 μm.

Fig. 10
Fig. 10

View of the injection-molded acrylic lens held over a U.S. one-dollar note.

Fig. 11
Fig. 11

Measured MTF of the replicated harmonic diffractive lens at several discrete wavelengths and with white light. The curves at 511.9, 537.1, 563.3, 593.5, and 626.8 nm are all at resonant wavelengths. Although the curves are labeled only at increments of 25 cycles/mm, the resolution in the frequency plane is 3 cycles/mm.

Fig. 12
Fig. 12

Monochrome reproduction of an outdoor scene originally recorded on color film.

Fig. 13
Fig. 13

Polychromatic encircled energy plot for various f/4.8 lenses with 6-mm diameter. The radial coordinate is normalized by the Rayleigh resolution at 550 nm. The spectral band is from 450 to 700 nm. The four curves are (a) a dispersion-free refractive lens, (b) a refractive lens made of acrylic with V d = 57, (c) a harmonic diffractive lens with m = 30, and (d) a simple diffractive lens (i.e., m = 1). The lenses are free of all third-and higher-order aberrations.

Equations (10)

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P 1 f = k λ r 1 2 so that Δ P P = Δ λ λ ,
t ( r , λ 0 ) = ( 1 Δ n ) MOD m λ 0 ( r 2 2 f ) , m = 1 , 2 , 3 , 4 , , Δ n ( n 1 ) ,
η = sinc 2 ( m λ 0 λ k ) .
P = k ( λ eff / k ) r 1 2 = λ eff r 1 2 .
Δ P P = Δ λ λ = λ 0 m λ 0 ( m + 1 ) λ 0 1 m and Δ t max = m λ 0 Δ n .
t ( r , λ 0 ) = ( 1 Δ n ) r 2 2 f ( 1 Δ n ) FLOOR m λ 0 | r 2 2 f | , m = 1 , 2 , 3 , ,
FLOOR b ( a ) b INTEGER ( a b ) ,
U ( P 0 , λ i ) = i λ i U ( P 1 , λ i ) exp ( i k s ) s r d r d Ө ,
s z + r ρ z cos ( θ φ ) + r 2 2 z ,
ζ = r 2 , d ζ = 2 r d r ,

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