Abstract

A diffractive Alvarez lens is demonstrated that consists of two separate phase plates, each having complementary 16-level surface-relief profiles that contain cubic phase delays. Translation of these two components in the plane of the phase plates is shown to produce a variable astigmatic focus. Both spherical and cylindrical phase profiles are demonstrated with good accuracy, and the discrete surface-relief features are shown to cause less than λ/10 wave-front aberration in the transmitted wave front over a 40 mm×80 mm region.

© 2000 Optical Society of America

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References

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  1. L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent3,305,294 (February21, 1967).
  2. L. W. Alvarez and W. E. Humphrey, “Variable-power lens and system,” U.S. patent3,507,565 (April21, 1970).
  3. L. W. Alvarez, J. Am. Optom. Assoc. 49, 24 (1978).
    [PubMed]
  4. N. López-Gil, H. C. Howland, B. Howland, N. Charman, and R. Applegate, J. Opt. Soc. Am. A 15, 2563 (1998).
    [Crossref]
  5. M. Oka, N. Eguchi, and H. Suganuma, “Apparatus and method for compensating coma aberration,” U.S. patent5,726,436 (March10, 1998).
  6. I. A. Palusinski, J. M. Sasian, and J. E. Greivenkamp, Proc. SPIE 3482, 96 (1998).
    [Crossref]
  7. See, for example, H.-P. Herzig, ed., Micro-Optics: Elements, Systems, and Applications (Taylor & Francis, London, 1997).

1998 (2)

1978 (1)

L. W. Alvarez, J. Am. Optom. Assoc. 49, 24 (1978).
[PubMed]

Alvarez, L. W.

L. W. Alvarez, J. Am. Optom. Assoc. 49, 24 (1978).
[PubMed]

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent3,305,294 (February21, 1967).

L. W. Alvarez and W. E. Humphrey, “Variable-power lens and system,” U.S. patent3,507,565 (April21, 1970).

Applegate, R.

Charman, N.

Eguchi, N.

M. Oka, N. Eguchi, and H. Suganuma, “Apparatus and method for compensating coma aberration,” U.S. patent5,726,436 (March10, 1998).

Greivenkamp, J. E.

I. A. Palusinski, J. M. Sasian, and J. E. Greivenkamp, Proc. SPIE 3482, 96 (1998).
[Crossref]

Howland, B.

Howland, H. C.

Humphrey, W. E.

L. W. Alvarez and W. E. Humphrey, “Variable-power lens and system,” U.S. patent3,507,565 (April21, 1970).

López-Gil, N.

Oka, M.

M. Oka, N. Eguchi, and H. Suganuma, “Apparatus and method for compensating coma aberration,” U.S. patent5,726,436 (March10, 1998).

Palusinski, I. A.

I. A. Palusinski, J. M. Sasian, and J. E. Greivenkamp, Proc. SPIE 3482, 96 (1998).
[Crossref]

Sasian, J. M.

I. A. Palusinski, J. M. Sasian, and J. E. Greivenkamp, Proc. SPIE 3482, 96 (1998).
[Crossref]

Suganuma, H.

M. Oka, N. Eguchi, and H. Suganuma, “Apparatus and method for compensating coma aberration,” U.S. patent5,726,436 (March10, 1998).

J. Am. Optom. Assoc. (1)

L. W. Alvarez, J. Am. Optom. Assoc. 49, 24 (1978).
[PubMed]

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

Proc. SPIE (1)

I. A. Palusinski, J. M. Sasian, and J. E. Greivenkamp, Proc. SPIE 3482, 96 (1998).
[Crossref]

Other (4)

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

M. Oka, N. Eguchi, and H. Suganuma, “Apparatus and method for compensating coma aberration,” U.S. patent5,726,436 (March10, 1998).

L. W. Alvarez, “Two-element variable-power spherical lens,” U.S. patent3,305,294 (February21, 1967).

L. W. Alvarez and W. E. Humphrey, “Variable-power lens and system,” U.S. patent3,507,565 (April21, 1970).

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Figures (5)

Fig. 1
Fig. 1

Schematic showing the operation of the Alvarez lens. Translation of the two complementary cubic phase plates with respect to each other along the x axis y axis generates focus (defocus) in that axis. A variable astigmatic lens is formed by control of the relative displacement in both directions.

Fig. 2
Fig. 2

Comparison of the measured depth of each phase level with the expected value for each component of the Alvarez lens (A and B). The deviation of the measured depths from the theoretical values is <15 mm.

Fig. 3
Fig. 3

Transmission wave front of a 40 mm×80 mm region of the Alvarez lens when the two components are displaced along the y axis by 20 mm and registered in the x axis. The resulting phase profile is a cylindrical lens with some small fine-scale structure as a result of quantization and fabrication errors in the diffractive elements and of the test wavelength’s being different from the design wavelength.

Fig. 4
Fig. 4

Transmission wave front of a 40 mm×80 mm region of the Alvarez lens when the two components are displaced in each axis by 20 mm. The resulting phase profile corresponds to an astigmatic lens with a 1:4 power ratio.

Fig. 5
Fig. 5

Performance of the diffractive Alvarez lens as a function of the relative translation (shear) of the two components in the y axis is detailed. The measured peak-to-valley (P-V) wave-front excursion is compared with that predicted from theory over a 50-mm translation range. The residual rms wave-front error is also shown.

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