Abstract

A method for designing achromatic hybrid refractive-diffractive elements that can produce beams with long focal depths while they preserve the entire aperture for capture of light and high transverse resolution is presented. Its working principle is based on the combination of a diffractive optical element that generates a long range of pseudonondiffractive rays and a refractive lens of opposite dispersion to form an achromatic hybrid lens. A hybrid lens with a fast f-number (f/1) that works in the entire visible wave band (400–700 nm) was designed and fabricated. Simulation results demonstrate a factor-of-10 improvement in depth of focus compared with that of a conventional f/1 lens, with matching 1-μm lateral resolution. Experimental results confirm the effectiveness of the proposed method through demonstration of an achromatic hybrid lens with better than a factor-of-7 improvement in depth of focus and 1-μm transverse resolution.

© 2004 Optical Society of America

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    [CrossRef]

2002 (1)

2001 (1)

M. R. Wang, C. Yu, A. J. Varela, “Efficient pseudo-nondiffracting beam shaping using a quasicontinuous-phase diffractive element,” Opt. Eng. 40, 517–524 (2001).
[CrossRef]

1998 (5)

1997 (1)

H. Haidner, G. M. Morris, “Wavefront quality of optimized diffractive lenses,” Pure Appl. Opt. 6, 191–202 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

1993 (3)

1992 (2)

1991 (1)

1989 (1)

1981 (1)

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

1974 (1)

1973 (1)

1972 (2)

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

R. Gerchberg, W. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

1960 (1)

Bara, S.

Bryngdahl, O.

Cathey, W. T.

Chen, N.

Clark, P.

Cong, W.

Davidson, N.

Dong, B.

R. Liu, B. Dong, B. Gu, “Implementation of pseudo-nondiffracting beams by use of diffractive phase element,” Appl. Opt. 37, 8219–8223 (1998).
[CrossRef]

R. Liu, B. Dong, G. Yang, B. Gu, “Generation of pseudo-nondiffracting beams with use of diffractive phase elements designed by the conjugate-gradient method,” J. Opt. Soc. A 15, 144–151 (1998).
[CrossRef]

Dowski, E. R.

Feldman, M. R.

Fienup, J.

Friberg, A.

Friesem, A. A.

Gan, F.

Gerchberg, R.

R. Gerchberg, W. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), p. 65.

Gu, B.

R. Liu, B. Dong, B. Gu, “Implementation of pseudo-nondiffracting beams by use of diffractive phase element,” Appl. Opt. 37, 8219–8223 (1998).
[CrossRef]

W. Cong, N. Chen, B. Gu, “Generation of nondiffracting beams by diffractive phase elements,” J. Opt. Soc. Am. A 15, 2362–2364 (1998).
[CrossRef]

R. Liu, B. Dong, G. Yang, B. Gu, “Generation of pseudo-nondiffracting beams with use of diffractive phase elements designed by the conjugate-gradient method,” J. Opt. Soc. A 15, 144–151 (1998).
[CrossRef]

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

Haidner, H.

H. Haidner, G. M. Morris, “Wavefront quality of optimized diffractive lenses,” Pure Appl. Opt. 6, 191–202 (1997).
[CrossRef]

Hasman, E.

Hausler, G.

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Hudson Welch, W.

Jaroszewic, Z.

Kolodzieiczykm, A.

Kress, B.

B. Kress, P. Meyrueis, Digital Diffractive Optics (Wiley, West Sussex, England, 2000).

Lit, J. W. Y.

Liu, R.

R. Liu, B. Dong, G. Yang, B. Gu, “Generation of pseudo-nondiffracting beams with use of diffractive phase elements designed by the conjugate-gradient method,” J. Opt. Soc. A 15, 144–151 (1998).
[CrossRef]

R. Liu, B. Dong, B. Gu, “Implementation of pseudo-nondiffracting beams by use of diffractive phase element,” Appl. Opt. 37, 8219–8223 (1998).
[CrossRef]

Londono, C.

Mcleod, J. H.

Meyrueis, P.

B. Kress, P. Meyrueis, Digital Diffractive Optics (Wiley, West Sussex, England, 2000).

Morris, G. M.

H. Haidner, G. M. Morris, “Wavefront quality of optimized diffractive lenses,” Pure Appl. Opt. 6, 191–202 (1997).
[CrossRef]

Morris, J. E.

Saxton, W.

R. Gerchberg, W. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Sochacki, J.

Su, H.

Tremblay, R.

Turunen, J.

Varela, A. J.

M. R. Wang, C. Yu, A. J. Varela, “Efficient pseudo-nondiffracting beam shaping using a quasicontinuous-phase diffractive element,” Opt. Eng. 40, 517–524 (2001).
[CrossRef]

Vasara, A.

Wach, H. B.

Wang, H.

Wang, M. R.

M. R. Wang, C. Yu, A. J. Varela, “Efficient pseudo-nondiffracting beam shaping using a quasicontinuous-phase diffractive element,” Opt. Eng. 40, 517–524 (2001).
[CrossRef]

M. R. Wang, H. Su, “Laser direct-write gray-level mask and one-step etching for diffractive microlens fabrication,” Appl. Opt. 37, 7568–7576 (1998).
[CrossRef]

Yang, G.

R. Liu, B. Dong, G. Yang, B. Gu, “Generation of pseudo-nondiffracting beams with use of diffractive phase elements designed by the conjugate-gradient method,” J. Opt. Soc. A 15, 144–151 (1998).
[CrossRef]

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

Yatagi, T.

Yoshikawa, N.

Yu, C.

M. R. Wang, C. Yu, A. J. Varela, “Efficient pseudo-nondiffracting beam shaping using a quasicontinuous-phase diffractive element,” Opt. Eng. 40, 517–524 (2001).
[CrossRef]

Acta Phys. Sin. (1)

G. Yang, B. Gu, “On the amplitude-phase retrieval problem in the optical system,” Acta Phys. Sin. 30, 410–413 (1981).

Appl. Opt. (10)

J. Fienup, “Phase-retrieval algorithms for a complicated optical system,” Appl. Opt. 32, 1737–1746 (1993).
[CrossRef] [PubMed]

N. Davidson, A. A. Friesem, E. Hasman, “Analytic design of hybrid diffractive-refractive achromats,” Appl. Opt. 32, 4770–4774 (1993).
[CrossRef] [PubMed]

C. Londono, P. Clark, “Modeling diffraction efficiency effects when designing hybrid diffractive lens systems,” Appl. Opt. 31, 2248–2252 (1992).
[CrossRef] [PubMed]

M. R. Wang, H. Su, “Laser direct-write gray-level mask and one-step etching for diffractive microlens fabrication,” Appl. Opt. 37, 7568–7576 (1998).
[CrossRef]

H. Wang, F. Gan, “Phase-shifting apodizers for increasing focal depth,” Appl. Opt. 41, 5263–5266 (2002).
[CrossRef] [PubMed]

E. R. Dowski, W. T. Cathey, “Extended depth of field through wave-front coding,” Appl. Opt. 34, 1859–1866 (1995).
[CrossRef] [PubMed]

H. B. Wach, E. R. Dowski, W. T. Cathey, “Control of chromatic focal shift through wave-front coding,” Appl. Opt. 37, 5359–5367 (1998).
[CrossRef]

R. Liu, B. Dong, B. Gu, “Implementation of pseudo-nondiffracting beams by use of diffractive phase element,” Appl. Opt. 37, 8219–8223 (1998).
[CrossRef]

J. Sochacki, A. Kolodzieiczykm, Z. Jaroszewic, S. Bara, “Nonparaxial design of design of generalized axicons,” Appl. Opt. 31, 5326–5330 (1992).
[CrossRef] [PubMed]

N. Yoshikawa, T. Yatagi, “Phase optimization of a kinoform by simulated annealing,” Appl. Opt. 33, 863–868 (1994).
[CrossRef] [PubMed]

J. Opt. Soc. A (1)

R. Liu, B. Dong, G. Yang, B. Gu, “Generation of pseudo-nondiffracting beams with use of diffractive phase elements designed by the conjugate-gradient method,” J. Opt. Soc. A 15, 144–151 (1998).
[CrossRef]

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (4)

Opt. Commun. (1)

G. Hausler, “A method to increase the depth of focus by two step image processing,” Opt. Commun. 6, 38–42 (1972).
[CrossRef]

Opt. Eng. (1)

M. R. Wang, C. Yu, A. J. Varela, “Efficient pseudo-nondiffracting beam shaping using a quasicontinuous-phase diffractive element,” Opt. Eng. 40, 517–524 (2001).
[CrossRef]

Opt. Lett. (1)

Optik (1)

R. Gerchberg, W. Saxton, “A practical algorithm for determination of phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Pure Appl. Opt. (1)

H. Haidner, G. M. Morris, “Wavefront quality of optimized diffractive lenses,” Pure Appl. Opt. 6, 191–202 (1997).
[CrossRef]

Other (4)

V. A. Soifer, ed., Methods for Computer Design of Diffractive Optical Elements (Wiley, New York, 2002).

B. Kress, P. Meyrueis, Digital Diffractive Optics (Wiley, West Sussex, England, 2000).

H. P. Herzig, ed., Micro-Optics: Elements, Systems, and Applications (Taylor Francis, London, 1997).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, San Francisco, Calif., 1968), p. 65.

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Figures (18)

Fig. 1
Fig. 1

(a) Extended DOF hybrid refractive-diffractive lens system and (b) conventional refractive lens system.

Fig. 2
Fig. 2

Rotationally symmetric optical system with DOE placed at input plane P1.

Fig. 3
Fig. 3

Chromatic aberration of (a) a refractive lens and (b) a diffractive lens.

Fig. 4
Fig. 4

(a) Simulated on-axis intensity distribution along the z axis of the designed DOE, (b) corresponding simulated phase profile of the designed DOE, and (c) simulation of the on-axis intensity distribution along the z axis of the combined refractive-diffractive hybrid f/1 lens (solid curve) and the conventional f/1 SF11 lens (dotted curve).

Fig. 5
Fig. 5

Experimental arrangement for measuring the focusing performance of a long-focal-depth DOE and both hybrid and conventional f/1 lenses.

Fig. 6
Fig. 6

Beam spot images observed at different planes from the DOE lens at (a) 24.6, (b) 25.0, (c) 25.4, and (d) 25.93 mm. A long DOF is demonstrated.

Fig. 7
Fig. 7

Transverse intensity distribution from the fabricated DOE at (a) 24.6, (b) 25.0, (c) 25.4, and (d) 25.93 mm from the lens. The beam remains in focus from 24.6 to 25.93 mm. Note that spot sizes have been obtained by use of a 60× objective magnification.

Fig. 8
Fig. 8

Simulated focused on-axis beam intensity distribution along the z axis for three arbitrary wavelengths: (a) before achromatization, (b) after achromatization, and (c) for a conventional f/1 SF11 lens.

Fig. 9
Fig. 9

Three-dimensional simulation plot demonstrating simultaneous factor-of-10 DOF improvement and 1-μm transverse resolution.

Fig. 10
Fig. 10

Variation in on-axis focus spot intensity of the fabricated hybrid refractive-diffractive lens, demonstrating the long DOF.

Fig. 11
Fig. 11

PSIs acquired experimentally at the focal plane by a conventional f/1 lens at (a) 2.999, (b) 3.000, (c) 3.001, and (d) 3.002 mm from the lens. The measured DOF is 2.6 μm.

Fig. 12
Fig. 12

PSIs acquired experimentally at the focal plane by our hybrid f/1 lens at (a) 2.990, (b) 2.997, (c) 3.005, and (d) 3.01 mm from the lens. The measured DOF is ∼20 μm.

Fig. 13
Fig. 13

Image of a portion of a U.S. Air Force resolution target taken with the fabricated hybrid f/1 lens. The target is illuminated with a white-light source and separated by color filters.

Fig. 14
Fig. 14

(a) Zemax simulation plot of the transverse resolution of an SF11 f/1 lens. Measured transverse resolution for (b) a conventional f/1 lens and (c) the hybrid f/1 lens. Note that spot sizes were obtained with a 60× objective magnification.

Fig. 15
Fig. 15

Diffraction-limited simulation results demonstrating a comparison of resolution between extended-DOF and conventional lenses. The small-aperture lens (dotted curve) is designed with the same depth of focus as the extended DOF lens (dashed curve).

Fig. 16
Fig. 16

Image of a portion of the U.S. Air Force resolution target taken with the conventional f/1 lens. The target is illuminated with a white-light source and separated by color filters.

Fig. 17
Fig. 17

Focus-free images of a 228-line pair/mm resolution target when the hybrid f/1 imaging lens was used. Clear images were formed from 5.72 to 5.85 mm.

Fig. 18
Fig. 18

Images of a 228-line pair/mm target pattern with a conventional f/1 lens.

Tables (1)

Tables Icon

Table 1 Required Refractive (SF11 Glass) and Diffractive f-Numbers Needed to Achieve Corresponding Hybrid Lenses

Equations (22)

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ΔX=k1λ/NA, ΔZ=k2λ/NA2,
u1r1=ρ1r1expiφ1r1,
u2r2, z=ρ2r2, zexpiφ2r2, z,
u2r2, z=r1 max Gr2, r1, zu1r1dr1,
Gr2, r1, z=2πr1jλzexpjkr01.
r01=z2+r12+r22-2r1r2 cosθ1-θ21/2,
r01z1+12r12z2-18r14z4+348r18z8,
Gr2, r1, z=2π expi2πz/λiλz×expiπλzr22+r12J02πr2r1λzr1,
u1,m=ρ1,m expiφ1,m, m=1, 2,, M,
u2,l,z=m=1M Gl,m,zu1,m, l=1, 2,, L,
E=q=1Nz Wql=1Lρ20l-m=1M G1,l,m,zρ1,m expiφ1,m2,
φ1k+1=φ1k+τkdk, k=0, 1, 2, 3,,
φ1=-1/2a lnd1+ar2+const.,
a=d2-d1/R12
tr=λφr2πn-1.
1fλ=nλ-11R1-1R2+t[nλ-1)R1R2,
1fλ=nλ-11R1.
Vr=nd-1nF-nc,
P=P1+P2,P1V1+P2V2=0,
Vd=λdλF-λc,
1Pnear_hyb=1P-δz2, 1Pfar_hyb=1P+δz2,
Pd_near=Pnear_hyb-Pr, Pd_far=Pfar_hyb-Pr, fd_near=1Pd_near, fd_far=1Pd_far.

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