Journal of the European Optical Society - Rapid publications, Vol 2 (2007)

Strehl ratio and optimum focus of high-numerical-aperture beams

A.J.E.M. Janssen, S. van Haver, J.J.M. Braat, P. Dirksen


We analytically calculate the focus setting for a beam with a high numerical aperture (NA) that optimizes its Strehl ratio in the case of small aberrations up to the ’just’ diffraction-limited value (Strehl ratio ≥0.80). The optimum focus setting deviates from the one that follows from a minimization of the wavefront aberration with the aid of the Zernike aberration coefficients. This deviation stems largely from the fact that the
common quadratic approximation of the focus term becomes inadequate in the high-NA case. Fundamental high-NA amplitude nonuniformity in the exit pupil of an optical system in the case of a linearly polarized incident beam also nfluences the optimum focus setting. Results for spherical aberration and astigmatism are presented for an NA-value
of 0.95.

© The Authors. All rights reserved. [DOI: 10.2971/jeos.2007.07008]

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N. Bobroff and A.E. Rosenbluth, Appl. Opt. 31, 1523-1536 (1992).

V. N. Mahajan, J. Opt. Soc. Am. 72, 1258-1266 (1982).

M. Born and E. Wolf, Principles of Optics (4th rev. ed., Pergamon Press, New York, 1970).

W. Welford, Aberrations of optical systems (Adam Hilger, Bristol, 1986).

B. Richards and E. Wolf, P. Roy. Soc. A:Math Phy 253, 358-379 (1959).

S.M. Mansfield and G.S. Kino, Appl. Phys. Lett. 57, 2615-2616 (1990).

K. Svoboda and S.M. Block, Annu. Rev. Bioph. Biom. 23, 247-285 (1994).

P. Trk, P. Varga, Z. Laczik and G.R. Booker, J. Opt. Soc. Am. A 12, 325-332 (1995).

I. Ichimura, S. Hayashi and G.S. Kino, Appl. Opt. 36, 4339-4348 (1997).

S. Quabis, R. Dorn, M. Eberler, O. Glockl and G. Leuchs, Opt. Commun. 179, 1-6 (2000).

J. J. M. Braat, P. Dirksen, A. J. E. M. Janssen, and A.S. van de Nes, J. Opt. Soc. Am. A 20, 2281-2292 (2003).

B.J. Lin, J. Microlith. Microfab. 1, 7-12 (2002).

S. Stallinga, Appl. Opt. 44, 849-858 (2005).