Abstract

Optical aberrations of microscope lenses are known as a source of systematic errors in confocal surface metrology, which has become one of the most popular methods to measure the surface topography of microstructures. We demonstrate that these errors are not constant over the entire field of view but also depend on the local slope angle of the microstructure and lead to significant deviations between the measured and the actual surface. It is shown by means of a full vectorial high NA numerical model that a change in the slope angle alters the shape of the intensity depth response of the microscope and leads to a shift of the intensity peak of up to several hundred nanometers. Comparative experimental data are presented which support the theoretical results. Our studies allow for correction of optical aberrations and, thus, increase the accuracy in profilometric measurements.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  15. J. L. Beverage, R.V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002)
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  16. Y. Yasuno, T. Yatagai, T. F. Wiesendanger, A. K. Ruprecht, and H. J. Tiziani, “Aberration measurement from confocal axial intensity response using neuronal network,” Opt. Express 10(25), 1451–1457 (2002)
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  17. N.N., www.komeg.com , accessed December 28th (2014)

2012 (1)

2011 (1)

2010 (1)

2008 (1)

2002 (3)

2001 (1)

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik 112(9), 399–406 (2001)
[Crossref]

2000 (2)

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–414 (2000)
[Crossref]

C. J. R. Sheppard, “Validity of the debye approximation,” Opt. Lett. 25(22), 1660–1662 (2000)
[Crossref]

1995 (1)

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profiler,” J. Mod. Opt. 42, 1785–1794 (1995)
[Crossref]

1991 (1)

1989 (1)

T. Wilson and A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” Journal of Microscopy 154(3), 1365–2818 (1989)
[Crossref]

1986 (1)

Aguilar, J. F.

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profiler,” J. Mod. Opt. 42, 1785–1794 (1995)
[Crossref]

Backman, V.

Beverage, J. L.

J. L. Beverage, R.V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002)
[Crossref] [PubMed]

Born, M.

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

Çapoglu, I. R.

Carlini, A. R.

T. Wilson and A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” Journal of Microscopy 154(3), 1365–2818 (1989)
[Crossref]

Descour, M. R.

J. L. Beverage, R.V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002)
[Crossref] [PubMed]

Gronle, M.

Kothiyal, M. P.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–414 (2000)
[Crossref]

Kriezis, Em. E.

Lehmann, P.

Lyda, W.

Mansuripur, M.

Mauch, F.

Mendez, E. R.

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profiler,” J. Mod. Opt. 42, 1785–1794 (1995)
[Crossref]

Munro, P. R. T.

Osten, W.

Rogers, J. D.

Ruprecht, A. K.

Shack, R.V.

J. L. Beverage, R.V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002)
[Crossref] [PubMed]

Sheppard, C. J. R.

Singaperumal, M.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–414 (2000)
[Crossref]

Sirohi, R. S.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–414 (2000)
[Crossref]

Subramanian, H.

Taflove, A.

Tiziani, H. J.

Török, P.

Totzeck, M.

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik 112(9), 399–406 (2001)
[Crossref]

Udupa, G.

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–414 (2000)
[Crossref]

Visser, T. D.

White, C. A.

Wiersma, S. H.

Wiesendanger, T. F.

Wilson, T.

T. Wilson and A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” Journal of Microscopy 154(3), 1365–2818 (1989)
[Crossref]

Wolf, E.

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

Yasuno, Y.

Yatagai, T.

Appl. Opt. (1)

J. Microsc. (1)

J. L. Beverage, R.V. Shack, and M. R. Descour, “Measurement of the three-dimensional microscope point spread function using a Shack-Hartmann wavefront sensor,” J. Microsc. 205, 61–75 (2002)
[Crossref] [PubMed]

J. Mod. Opt. (1)

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profiler,” J. Mod. Opt. 42, 1785–1794 (1995)
[Crossref]

J. Opt. Soc. Am. A (2)

Journal of Microscopy (1)

T. Wilson and A. R. Carlini, “The effect of aberrations on the axial response of confocal imaging systems,” Journal of Microscopy 154(3), 1365–2818 (1989)
[Crossref]

Meas. Sci. Technol. (1)

G. Udupa, M. Singaperumal, R. S. Sirohi, and M. P. Kothiyal, “Characterization of surface topography by confocal microscopy: I. Principles and the measurement system,” Meas. Sci. Technol. 11(3), 305–414 (2000)
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Optik (1)

M. Totzeck, “Numerical simulation of high-NA quantitative polarization microscopy and corresponding near-fields,” Optik 112(9), 399–406 (2001)
[Crossref]

Other (3)

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

T. Wilson (ed.), Confocal Microscopy (Academix, 1990)

N.N., www.komeg.com , accessed December 28th (2014)

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Figures (7)

Fig. 1
Fig. 1 Beam path through a microscope objective with third order spherical aberration and phase distribution inside the entrance/exit pupil of the objective when illuminating and imaging a curved microstructure.
Fig. 2
Fig. 2 Numerical model of a reflection-type confocal microscope consisting of an illuminating (a) and an imaging optical path (b).
Fig. 3
Fig. 3 Three-dimensional model of a high-NA lens.
Fig. 4
Fig. 4 Simulated confocal intensity response for various tilt angels α: a) without aberrations; b) with spherical aberration (C40 = 0.1).
Fig. 5
Fig. 5 a) Measured and fitted theoretical intensity response; b) Measured and simulated systematic error Δz as a function of the inclination angle α (experimental results were obtained using a peak find based algorithm).
Fig. 6
Fig. 6 Simulated systematic error Δz as a function of the inclination angle α caused by various aberrations: distortion (C11), defocus (C20), astigmatism (C22), coma (C31), trefoil (C33), 3rd order spherical aberration (C40) and 5th order spherical aberration (C60); each aberration coefficient accounts for 0.05λ.
Fig. 7
Fig. 7 Simulated systematic error Δz as a function of various Zernike coefficients Cnm: distortion (C11), astigmatism (C22), coma (C31), trefoil (C33), 3rd order spherical aberration (C40) and 5th order spherical aberration (C60); the tilt angle is fixed to α = 25°.

Tables (1)

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Table 1 Effective NA and aberration coefficients obtained by least-square-fit.

Equations (6)

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E f ( k x , k y , z ) = k / k z R θ ( k x , k y ) E i n ( k x , k y ) exp [ i k z z i k W ( k x , k y ) ) ] ,
R θ = ( cos ( θ ) + ( 1 cos ( θ ) ) u 2 ( 1 cos ( θ ) ) u v sin ( θ ) v ( 1 cos ( θ ) ) u v cos ( α ) + ( 1 cos ( θ ) ) v 2 sin ( θ ) u sin ( θ ) v sin ( α ) u cos ( θ ) ) ,
cos ( θ ) = k z k = 1 ( k x k ) 2 ( k y k ) 2 ,
sin ( θ ) = k 1 k x 2 + k y 2 ,
Ω ( k x , k y ) = ( u v 0 ) = 1 k x 2 + k y 2 ( k y k x 0 ) .
W ( r k ) = n 1 N C n m R 2 n m = 0 ( r k ) ,

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