Abstract

The reduction of wavefront aberrations is essential in a number of fields, including astronomy, microscopy, photography, vision science, lithography, and lasers. Aberrations may be determined either directly with wavefront sensors or indirectly with signal- or image-based optimization algorithms. Here, we introduce a novel wavefront-sensing methodology that employs intensity differences across a beam of light to encode local wavefront slopes via attenuated total internal reflection following surface-plasmon excitation at the surface of a thin gold film. This method excels due to the dense spatial sampling of the wavefront and the fact that the wavefront itself can be determined by straightforward integration of two sets of images captured in orthogonal directions without time-consuming optimization, deconvolution, or spot centroiding.

© 2015 Optical Society of America

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References

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A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

2013 (1)

2011 (1)

S. Roh, T. Chung, and B. Lee, Sensors 11, 1565 (2011).
[Crossref]

2010 (1)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

2009 (1)

B. Ashall, B. Vohnsen, M. Berndt, and D. Zerulla, Phys. Rev. B 80, 245413 (2009).
[Crossref]

1998 (1)

1996 (2)

1995 (1)

S. I. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, and A. V. Zayats, Opt. Commun. 117, 417 (1995).
[Crossref]

1994 (1)

1990 (1)

1951 (1)

F. P. Bowden and W. R. Throssell, Proc. R. Soc. A 209, 297 (1951).
[Crossref]

Akondi, V.

Ashall, B.

B. Ashall, B. Vohnsen, M. Berndt, and D. Zerulla, Phys. Rev. B 80, 245413 (2009).
[Crossref]

Bernardin, T.

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

Berndt, M.

B. Ashall, B. Vohnsen, M. Berndt, and D. Zerulla, Phys. Rev. B 80, 245413 (2009).
[Crossref]

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Bokor, J.

Bowden, F. P.

F. P. Bowden and W. R. Throssell, Proc. R. Soc. A 209, 297 (1951).
[Crossref]

Bozhevolnyi, S. I.

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

S. I. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, and A. V. Zayats, Opt. Commun. 117, 417 (1995).
[Crossref]

Castillo, S.

Chung, T.

S. Roh, T. Chung, and B. Lee, Sensors 11, 1565 (2011).
[Crossref]

Djurišic, A. B.

Elazar, J. M.

Falldorf, C.

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N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

Goelz, S.

Goldberg, K. A.

Grimm, B.

Hentschel, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

Lee, B.

S. Roh, T. Chung, and B. Lee, Sensors 11, 1565 (2011).
[Crossref]

Liang, J.

Liu, N.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

Majewski, M. L.

Marcos, S.

Medecki, H.

Mesch, M.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

Nielsen, M. G.

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

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A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1988).

Ragazzoni, R.

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

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Roh, S.

S. Roh, T. Chung, and B. Lee, Sensors 11, 1565 (2011).
[Crossref]

Smolyaninov, I. I.

S. I. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, and A. V. Zayats, Opt. Commun. 117, 417 (1995).
[Crossref]

Tejnil, E.

Throssell, W. R.

F. P. Bowden and W. R. Throssell, Proc. R. Soc. A 209, 297 (1951).
[Crossref]

Tyson, R. K.

R. K. Tyson, Principles of Adaptive Optics (CRC Press, 2011).

Valente, D.

Vohnsen, B.

D. Valente, D. Rativa, and B. Vohnsen, Opt. Express 23, 13005 (2015).
[Crossref]

V. Akondi, C. Falldorf, S. Marcos, and B. Vohnsen, Opt. Express 23, 25425 (2015).
[Crossref]

V. Akondi, S. Castillo, and B. Vohnsen, Opt. Express 21, 18261 (2013).
[Crossref]

B. Ashall, B. Vohnsen, M. Berndt, and D. Zerulla, Phys. Rev. B 80, 245413 (2009).
[Crossref]

S. I. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, and A. V. Zayats, Opt. Commun. 117, 417 (1995).
[Crossref]

Weeber, J.-C.

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

Weiss, T.

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

Zayats, A. V.

S. I. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, and A. V. Zayats, Opt. Commun. 117, 417 (1995).
[Crossref]

Zerulla, D.

B. Ashall, B. Vohnsen, M. Berndt, and D. Zerulla, Phys. Rev. B 80, 245413 (2009).
[Crossref]

Appl. Opt. (2)

J. Mod. Opt. (1)

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

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

Light (1)

A. Pors, M. G. Nielsen, T. Bernardin, J.-C. Weeber, and S. I. Bozhevolnyi, Light 3, e197 (2014).
[Crossref]

Nano Lett. (1)

N. Liu, M. Mesch, T. Weiss, M. Hentschel, and H. Giessen, Nano Lett. 10, 2342 (2010).
[Crossref]

Opt. Commun. (1)

S. I. Bozhevolnyi, B. Vohnsen, I. I. Smolyaninov, and A. V. Zayats, Opt. Commun. 117, 417 (1995).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (1)

B. Ashall, B. Vohnsen, M. Berndt, and D. Zerulla, Phys. Rev. B 80, 245413 (2009).
[Crossref]

Proc. R. Soc. A (1)

F. P. Bowden and W. R. Throssell, Proc. R. Soc. A 209, 297 (1951).
[Crossref]

Sensors (1)

S. Roh, T. Chung, and B. Lee, Sensors 11, 1565 (2011).
[Crossref]

Other (2)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer Verlag, 1988).

R. K. Tyson, Principles of Adaptive Optics (CRC Press, 2011).

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Figures (9)

Fig. 1.
Fig. 1.

ATIR angular spectrum for SPP excitation in the Kretschmann configuration with an incident collimated p-polarized light beam at 632.8 nm wavelength for a 50 nm Au film coated onto BK7 glass with a 2 nm Ti binding layer. Comparison between experiment (dots) and theory (solid line). A bias offset at either side of the resonance angle (highlighted here as configurations I and II, respectively) allows for determination of wavefront slopes.

Fig. 2.
Fig. 2.

Schematic of the experimental setup used to measure wavefront derivatives. SPP excitation transforms WA set by the AO subsystem to ATIR changes captured by the CCD camera across a 2.8 mm pupil. For the configuration shown, only x derivatives can be determined. Rotation of the prism-CCD branch by 90° out of the plane and polarization rotation with a half-wave plate allows for characterization of wavefront derivatives in the y direction. The insets show captured gray-scale images of the ATIR light for configuration I with a plane wave Iref and for defocus I4 with c4=+1μm, respectively.

Fig. 3.
Fig. 3.

Circular Zernike polynomials (top) and their corresponding Cartesian derivatives along the x and y coordinates shown both with a positive and negative scaling factor of cn=±1μm.

Fig. 4.
Fig. 4.

Intensity measurements across the ATIR beam showing difference images ΔIn=IWAIref. Results for configuration I (below the SPP resonance angle) are shown at the top and beneath it for configuration II (above the SPP resonance angle). In both cases, measurements have been made for individual Zernike polynomials applied with the AO subsystem and scaled by cn=±1μm.

Fig. 5.
Fig. 5.

Intensity measurements across the ATIR beam showing difference images ΔIn=IWAIref. Results for configuration I (below the SPP resonance angle) are shown at the top and beneath it for configuration II (above the SPP resonance angle). In both cases, measurements have been made for individual Zernike polynomials applied with the AO subsystem and scaled by cn=±1μm.

Fig. 6.
Fig. 6.

Linearity analysis of the SPP-WFS for the x derivative of Z2 measured in the range from 1μm to +1μm. For clarity, the negative ATIR slope for configuration I has not been corrected.

Fig. 7.
Fig. 7.

Reconstructed aberrations by inversion of the intensity gradients from Figs. 4 and 5. The reconstructed Zernike aberrations are shown for separate measurement series with scaling factors of cn=±1μm for both configurations I and II.

Fig. 8.
Fig. 8.

Sensing of wavefront derivatives when introducing a linear combination of Zernike terms from Z2 to Z11 with the AO subsystem where cn=0.2μm for all odd and cn=+0.2μm for all even indices n. The wavefront slopes have been integrated for a quick estimate and the least-square estimate of the WA has been determined, showing improved reconstruction for both configurations I and II.

Fig. 9.
Fig. 9.

Diagram showing the applied Zernike coefficients Cn (blue) and the reconstructed Zernike coefficients based on the least-square estimates for configurations I (Cn_I, red) and II (Cn_II, green) for a linear combination of Z2 to Z11 as shown in Fig. 8. The Zernike coefficients for both reconstructions have been uniformly scaled to match the 0.63 μm RMS of the applied WA. The percentage values show the ratio of the sensed terms with respect to the AO-applied WA.

Equations (1)

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cest=[ATA]1ATbmeas,

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