Abstract

In this Letter, we introduce an analytic procedure for designing diffractive lenses using the combination of wavefronts aberrated by Zernike polynomials. We show how to design amplitude-only, phase-only, continuous, and binary lenses providing equivalent results. As an example we apply it to the design of a multiple-axis, multifocal lens. The number of foci and their positions can be easily controlled. Theoretical predictions have been experimentally confirmed. The main advantage of this procedure is that, because it is simple and intuitive, it can be used successfully for the design of complex lenses.

© 2012 Optical Society of America

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References

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2008

2007

2004

M. A. Golub, Opt. Photon. News 15, 36 (2004).

2003

1999

1995

Anzai, Y.

Bará, S.

Ben David, M.

Blanchard, P. M.

Born, M.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Cagigal, M. P.

P. J. Valle, V. F. Canales, and M. P. Cagigal, Opt. Express 18, 7820 (2010).
[CrossRef]

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Commun. 272, 325 (2007).
[CrossRef]

Canales, V. F.

P. J. Valle, V. F. Canales, and M. P. Cagigal, Opt. Express 18, 7820 (2010).
[CrossRef]

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Commun. 272, 325 (2007).
[CrossRef]

Cohen, R.

Faklis, D.

Fengjie, X.

Gannot, G.

Gannot, I.

García, A.

Golub, M. A.

M. A. Golub, Opt. Photon. News 15, 36 (2004).

Gómez García, M.

Greenaway, A. H.

Huisken, J.

Ide, T.

Jaroszewicz, Z.

Javidi, B.

Kimura, S.

Kolodziejczyk, A.

Kurokawa, T.

Martínez-Corral, M.

Martínez-Cuenca, R.

Morris, G. M.

Navarro, H.

Oti, J. E.

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Commun. 272, 325 (2007).
[CrossRef]

Petelczyc, K.

Saavedra, G.

Shintani, T.

Sochen, N.

Stelzer, E. H. K.

Swoger, J.

Tatsu, E.

Valle, P. J.

P. J. Valle, V. F. Canales, and M. P. Cagigal, Opt. Express 18, 7820 (2010).
[CrossRef]

P. J. Valle, J. E. Oti, V. F. Canales, and M. P. Cagigal, Opt. Commun. 272, 325 (2007).
[CrossRef]

Watanabe, K.

Wolf, E.

M. Born and E. Wolf, Principles of Optics (Cambridge University, 1999).

Xiaojun, X.

Yifeng, G.

Zongfu, J.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Three focal points (a,b,c) placed along the x axis as a result of using the pupil function given by Eq. (2) for m=1 and φ1=0. (b) Three focal points (d,b,e) placed along the z axis as a result of using the pupil function given by Eq. (3) for m=1.

Fig. 2.
Fig. 2.

(a) Experimental setup used for checking the different foci and (b) that used for checking the diffractive lens capability of simultaneously imaging objects placed at different distances.

Fig. 3.
Fig. 3.

(a–c) Light intensity distribution at the focal planes a, b and c shown in Fig. 2(a). (d) Phase-only pupil function represented as a grey-level function.

Fig. 4.
Fig. 4.

Images obtained in the CCD when the object was placed at three different positions (a, b, and c).

Equations (6)

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U(v,ϕ,u)=02π01P(ρ,θ)exp[ivρcos(θϕ)+i2uρ2]ρdθdρ,
P(ρ,θ)=offset+mcmcos[αmρcos(θϕm)].
P(ρ,θ)=offset+mcmcos(βmρ2).
P(ρ,θ)=offset+mcmcos[αmρcos(θϕm)+βmρ2].
P(ρ,θ)=exp[imcmcos(αmρcos(θφm)+βmρ2)].
P(ρ,θ)=exp{icos[αρcos(θ)+βρ2]}.

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