Abstract

The use of a large apex-angle axicon for common-path interferometric wavefront sensing is proposed. The approach is a variant of point-diffraction interferometry bearing similarities to pyramidal wavefront sensing. A theoretical basis for wavefront sensing with an axicon is developed, and the outcomes of numerical simulations are compared to experimental results obtained with spherical and cylindrical ophthalmic trial lenses. It is confirmed that the axicon can be used for wavefront sensing, although its refraction may ultimately complicate and limit its operational range.

© 2011 Optical Society of America

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References

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2010 (1)

2008 (1)

2006 (1)

2002 (2)

I. Iglesias, R. Ragazzoni, Y. Julien, and P. Artal, Opt. Express 10, 419 (2002).
[PubMed]

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

1997 (1)

D. P. S. O’Brart, C. S. Stephenson, K. Oliver, and J. Marshall, Ophthalmology 104, 1959 (1997).
[PubMed]

1996 (2)

1993 (1)

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401(1993).
[CrossRef] [PubMed]

1992 (1)

1975 (1)

R. N. Smartt and W. H. Steel, Jpn. J. Appl. Phys. 14, 351(1975).

1954 (1)

Acosta, E.

Artal, P.

Bará, S.

Bartels, R. A.

Blendowske, R.

Bokor, J.

Chamadoira, S.

Dainty, C.

Daly, E. M.

Dholakia, K.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Garcés-Chávez, V.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Goldberg, K. A.

Herminghaus, S.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401(1993).
[CrossRef] [PubMed]

Iglesias, I.

Jaroszewicz, Z.

Julien, Y.

Kolodziejczyk, A.

Kupta, D.

Marshall, J.

D. P. S. O’Brart, C. S. Stephenson, K. Oliver, and J. Marshall, Ophthalmology 104, 1959 (1997).
[PubMed]

McGloin, D.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

McLeod, J. H.

Medecki, H.

Melville, H.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

O’Brart, D. P. S.

D. P. S. O’Brart, C. S. Stephenson, K. Oliver, and J. Marshall, Ophthalmology 104, 1959 (1997).
[PubMed]

Oliver, K.

D. P. S. O’Brart, C. S. Stephenson, K. Oliver, and J. Marshall, Ophthalmology 104, 1959 (1997).
[PubMed]

Ragazzoni, R.

Schlup, P.

Sibbett, W.

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Smartt, R. N.

R. N. Smartt and W. H. Steel, Jpn. J. Appl. Phys. 14, 351(1975).

Sochacki, J.

Steel, W. H.

R. N. Smartt and W. H. Steel, Jpn. J. Appl. Phys. 14, 351(1975).

Stephenson, C. S.

D. P. S. O’Brart, C. S. Stephenson, K. Oliver, and J. Marshall, Ophthalmology 104, 1959 (1997).
[PubMed]

Tejnil, E.

Wulle, T.

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401(1993).
[CrossRef] [PubMed]

Appl. Opt. (3)

J. Mod. Opt. (1)

R. Ragazzoni, J. Mod. Opt. 43, 289 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Jpn. J. Appl. Phys. (1)

R. N. Smartt and W. H. Steel, Jpn. J. Appl. Phys. 14, 351(1975).

Nature (1)

V. Garcés-Chávez, D. McGloin, H. Melville, W. Sibbett, and K. Dholakia, Nature 419, 145 (2002).
[CrossRef] [PubMed]

Ophthalmology (1)

D. P. S. O’Brart, C. S. Stephenson, K. Oliver, and J. Marshall, Ophthalmology 104, 1959 (1997).
[PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. Lett. (1)

T. Wulle and S. Herminghaus, Phys. Rev. Lett. 70, 1401(1993).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Schematic drawing (top) of the 4-f arrangement with two f 25 mm achromatic lenses and an axicon inserted to facilitate wavefront sensing in a plane conjugate with the iris where trial lenses are inserted. Calculated intensity images (bottom) at the CCD for different amounts of defocus (with corresponding image cross sections) and cylinder expressed in diopters at the entrance pupil as obtained for a perfectly sharp 175 ° axicon apex.

Fig. 2
Fig. 2

Interferometric images of wavefront aberrations recorded with different amounts of defocus (top) and corresponding simulations (bottom) with a blunt axicon apex generating a suitable interferometric reference wave.

Fig. 3
Fig. 3

Interferometric images of wavefront aberrations recorded with different amounts of cylindrical defocus (top) and corresponding numerical simulations (bottom) with a blunt axicon apex generating a suitable interferometric reference wave.

Fig. 4
Fig. 4

Interferometric images of wavefront aberrations recorded with ± 0.50 D of sphere and cylinder of + 0.25 D and + 1.00 D (top) and corresponding numerical simulations (bottom) with a blunt axicon apex generating a suitable interferometric reference wave.

Fig. 5
Fig. 5

Measurements of increased spherical defocus + 3 , + 5 , and + 10 D , and (right) one example of crossed + 3 D / 3 D cylinder.

Equations (2)

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ψ i = ψ ¯ p exp ( i Φ ¯ WA ) * F { exp ( i Φ axicon ) } ,
F { exp ( i Φ axicon ) } = 2 π r exp ( i Φ axicon ) J 0 ( 2 π r ρ ) d r

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