Abstract

To get physical insight into the 3D transfer characteristics of interference microscopy at high numerical apertures we study reflecting rectangular grating structures. In general, the height obtained from phase information seems to be reduced, whereas height values resulting from coherence scanning sometimes seem to be systematically overestimated. Increasing the numerical aperture of an interference microscope broadens the spectra of the resulting interference signals, thus offering a broad variety of wavelength contributions to be analyzed. If phase analysis of a measured far-field interference wavefront is performed at very short wavelengths the periodical profiles obtained from coherence scanning and phase shifting analysis differ only by the measured amplitude. However, at longer wavelength there is a 180° phase shift of the measured profiles obtained from phase analysis compared to coherence peak analysis. Increasing the evaluation wavelength improves the lateral resolution since the long wavelength contributions are related to electromagnetic waves of high angles of incidence. This behavior is to the best of our knowledge not documented in literature so far. It was first observed experimentally and could be confirmed by simulation results obtained from either Kirchhoff diffraction theory or an extended Richards-Wolf model developed in our group. Compared to original input profiles used for the simulation the profiles obtained from phase evaluation correspond quite well at longer wavelength, whereas the results obtained from coherence peak analysis are typically inverted with respect to height.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (4)

2016 (4)

P. Lehmann, S. Tereschenko, and W. Xie, “Fundamental aspects of resolution and precision in vertical scanning white-light interferometry,” Surf. Top.: Metrol. Prop. 4(0214004), 1–10 (2016).

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

W. Xie, P. Lehmann, J. Niehues, and S. Tereschenko, “Signal modeling in low coherence interference microscopy on example of rectangular grating,” Opt. Express 24(13), 14283–14300 (2016).
[Crossref] [PubMed]

2015 (2)

R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
[Crossref]

P. Lehmann and W. Xie, “Signal formation in depth-scanning 3D interference microscopy at high numerical apertures,” Proc. SPIE 9660, 966015 (2015).
[Crossref]

2014 (2)

R. Mandal, J. Coupland, R. Leach, and D. Mansfield, “Coherence scanning interferometry: measurement and correction of three-dimensional transfer and point-spread characteristics,” Appl. Opt. 53(8), 1554–1563 (2014).
[Crossref] [PubMed]

P. Lehmann, J. Niehues, and S. Tereschenko, “3-D optical interference microscopy at the lateral resolution limit,” Int. J. Optomechatronics 8(4), 231–241 (2014).
[Crossref]

2012 (5)

2009 (1)

2004 (2)

P. de Groot and X. C. de Lega, “Signal modeling for low-coherence height-scanning interference microscopy,” Appl. Opt. 43(25), 4821–4830 (2004).
[Crossref] [PubMed]

X. Colonna de Lega, D. Grigg, and P. de Groot, “Surface profiling using a reference-scanning Mirau interference microscope,” Proc. SPIE 5531, 106–116 (2004).
[Crossref]

2000 (3)

1995 (2)

C. J. R. Sheppard and K. G. Larkin, “Effect of numerical aperture on interference fringe spacing,” Appl. Opt. 34(22), 4731–4734 (1995).
[Crossref] [PubMed]

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42(9), 1785–1794 (1995).
[Crossref]

1990 (1)

1989 (2)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

1956 (1)

F. R. Tolmon and J. G. Wood, “Fringe spacing in interference microscopes,” J. Sci. Instrum. 33(6), 236–238 (1956).
[Crossref]

1909 (1)

P. Debye, “Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie,” Ann. Phys. 335(14), 755–776 (1909).
[Crossref]

1873 (1)

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für mikroskopische Anatomie 9(1), 413–418 (1873).
[Crossref]

Aakhte, M.

Abbasian, V.

Abbe, E.

E. Abbe, “Beiträge zur Theorie des Mikroskops und der mikroskopischen Wahrnehmung,” Archiv für mikroskopische Anatomie 9(1), 413–418 (1873).
[Crossref]

Abdulhalim, I.

I. Abdulhalim, “Spatial and temporal coherence effects in interference microscopy and full-field optical coherence tomography,” Ann. Phys. 524(12), 787–804 (2012).
[Crossref]

Aguilar, J. F.

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42(9), 1785–1794 (1995).
[Crossref]

Akhlaghi, E. A.

Anand, A.

Biegen, J. F.

Chang, B. J.

Chang, Y. C.

Chiang, S. Y.

Chim, S. S. C.

Chou, L. J.

Colonna de Lega, X.

X. Colonna de Lega, D. Grigg, and P. de Groot, “Surface profiling using a reference-scanning Mirau interference microscope,” Proc. SPIE 5531, 106–116 (2004).
[Crossref]

Coupland, J.

Creath, K.

de Groot, P.

X. Colonna de Lega, D. Grigg, and P. de Groot, “Surface profiling using a reference-scanning Mirau interference microscope,” Proc. SPIE 5531, 106–116 (2004).
[Crossref]

P. de Groot and X. C. de Lega, “Signal modeling for low-coherence height-scanning interference microscopy,” Appl. Opt. 43(25), 4821–4830 (2004).
[Crossref] [PubMed]

de Lega, X. C.

Debye, P.

P. Debye, “Das Verhalten von Lichtwellen in der Nähe eines Brennpunktes oder einer Brennlinie,” Ann. Phys. 335(14), 755–776 (1909).
[Crossref]

Evans, C.

R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
[Crossref]

Fleischer, M.

Giusca, C. L.

R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
[Crossref]

Grigg, D.

X. Colonna de Lega, D. Grigg, and P. de Groot, “Surface profiling using a reference-scanning Mirau interference microscope,” Proc. SPIE 5531, 106–116 (2004).
[Crossref]

Gronle, M.

Gustafsson, M. G. L.

M. G. L. Gustafsson, “Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy,” J. Microsc. 198(2), 82–87 (2000).
[Crossref] [PubMed]

Hæggström, E.

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
[Crossref] [PubMed]

S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
[Crossref] [PubMed]

Hagemeier, S.

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

Haitjema, H.

R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
[Crossref]

Harasaki, A.

Hillmer, H.

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

Javidi, B.

Jiang, X.

R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
[Crossref]

Kassamakov, I.

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
[Crossref] [PubMed]

S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
[Crossref] [PubMed]

Kino, G. S.

Larkin, K. G.

Leach, R.

Leach, R. K.

R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
[Crossref]

Lecler, S.

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
[Crossref] [PubMed]

S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
[Crossref] [PubMed]

Lehmann, P.

W. Xie, P. Lehmann, J. Niehues, and S. Tereschenko, “Signal modeling in low coherence interference microscopy on example of rectangular grating,” Opt. Express 24(13), 14283–14300 (2016).
[Crossref] [PubMed]

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

P. Lehmann, S. Tereschenko, and W. Xie, “Fundamental aspects of resolution and precision in vertical scanning white-light interferometry,” Surf. Top.: Metrol. Prop. 4(0214004), 1–10 (2016).

P. Lehmann and W. Xie, “Signal formation in depth-scanning 3D interference microscopy at high numerical apertures,” Proc. SPIE 9660, 966015 (2015).
[Crossref]

P. Lehmann, J. Niehues, and S. Tereschenko, “3-D optical interference microscopy at the lateral resolution limit,” Int. J. Optomechatronics 8(4), 231–241 (2014).
[Crossref]

P. Lehmann, J. Niehues, W. Xie, and J. Riebeling, “Measurement of rectangular edge and grating structures using extended low-coherence interferometry,” Proc. SPIE 8430, 84300U (2012).
[Crossref]

P. Lehmann, W. Xie, and J. Niehues, “Transfer characteristics of rectangular phase gratings in interference microscopy,” Opt. Lett. 37(4), 758–760 (2012).
[Crossref] [PubMed]

W. Xie, P. Lehmann, and J. Niehues, “Lateral resolution and transfer characteristics of vertical scanning white-light interferometers,” Appl. Opt. 51(11), 1795–1803 (2012).
[Crossref] [PubMed]

Leong-Hoï, A.

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
[Crossref] [PubMed]

S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
[Crossref] [PubMed]

Li, W. J.

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

Liu, L.

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

Liu, Z.

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

Lyda, W.

Mandal, R.

Mansfield, D.

Mauch, F.

Mendez, E. R.

J. F. Aguilar and E. R. Mendez, “On the limitations of the confocal scanning optical microscope as a profilometer,” J. Mod. Opt. 42(9), 1785–1794 (1995).
[Crossref]

Montgomery, P.

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
[Crossref] [PubMed]

S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
[Crossref] [PubMed]

Moradi, A.-R.

Niehues, J.

Nolvi, A.

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
[Crossref] [PubMed]

S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
[Crossref] [PubMed]

Osten, W.

Perrin, S.

Pfeiffer, P.

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Riebeling, J.

P. Lehmann, J. Niehues, W. Xie, and J. Riebeling, “Measurement of rectangular edge and grating structures using extended low-coherence interferometry,” Proc. SPIE 8430, 84300U (2012).
[Crossref]

Sheppard, C. J. R.

Su, R.

Tereschenko, S.

W. Xie, P. Lehmann, J. Niehues, and S. Tereschenko, “Signal modeling in low coherence interference microscopy on example of rectangular grating,” Opt. Express 24(13), 14283–14300 (2016).
[Crossref] [PubMed]

P. Lehmann, S. Tereschenko, and W. Xie, “Fundamental aspects of resolution and precision in vertical scanning white-light interferometry,” Surf. Top.: Metrol. Prop. 4(0214004), 1–10 (2016).

P. Lehmann, J. Niehues, and S. Tereschenko, “3-D optical interference microscopy at the lateral resolution limit,” Int. J. Optomechatronics 8(4), 231–241 (2014).
[Crossref]

Tiziani, H. J.

Tolmon, F. R.

F. R. Tolmon and J. G. Wood, “Fringe spacing in interference microscopes,” J. Sci. Instrum. 33(6), 236–238 (1956).
[Crossref]

Wang, F.

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

Wang, Y.

R. Su, Y. Wang, J. Coupland, and R. Leach, “On tilt and curvature dependent errors and the calibration of coherence scanning interferometry,” Opt. Express 25(4), 3297–3310 (2017).
[Crossref] [PubMed]

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

Windecker, R.

Woidt, C.

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems, II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci. 253(1274), 358–379 (1959).
[Crossref]

Wood, J. G.

F. R. Tolmon and J. G. Wood, “Fringe spacing in interference microscopes,” J. Sci. Instrum. 33(6), 236–238 (1956).
[Crossref]

Wyant, J. C.

Xie, W.

P. Lehmann, S. Tereschenko, and W. Xie, “Fundamental aspects of resolution and precision in vertical scanning white-light interferometry,” Surf. Top.: Metrol. Prop. 4(0214004), 1–10 (2016).

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

W. Xie, P. Lehmann, J. Niehues, and S. Tereschenko, “Signal modeling in low coherence interference microscopy on example of rectangular grating,” Opt. Express 24(13), 14283–14300 (2016).
[Crossref] [PubMed]

P. Lehmann and W. Xie, “Signal formation in depth-scanning 3D interference microscopy at high numerical apertures,” Proc. SPIE 9660, 966015 (2015).
[Crossref]

W. Xie, P. Lehmann, and J. Niehues, “Lateral resolution and transfer characteristics of vertical scanning white-light interferometers,” Appl. Opt. 51(11), 1795–1803 (2012).
[Crossref] [PubMed]

P. Lehmann, W. Xie, and J. Niehues, “Transfer characteristics of rectangular phase gratings in interference microscopy,” Opt. Lett. 37(4), 758–760 (2012).
[Crossref] [PubMed]

P. Lehmann, J. Niehues, W. Xie, and J. Riebeling, “Measurement of rectangular edge and grating structures using extended low-coherence interferometry,” Proc. SPIE 8430, 84300U (2012).
[Crossref]

Yu, H.

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

Yu, P.

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
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P. de Groot and X. C. de Lega, “Signal modeling for low-coherence height-scanning interference microscopy,” Appl. Opt. 43(25), 4821–4830 (2004).
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W. Xie, P. Lehmann, and J. Niehues, “Lateral resolution and transfer characteristics of vertical scanning white-light interferometers,” Appl. Opt. 51(11), 1795–1803 (2012).
[Crossref] [PubMed]

M. Aakhte, V. Abbasian, E. A. Akhlaghi, A.-R. Moradi, A. Anand, and B. Javidi, “Microsphere-assisted super-resolved Mirau digital holographic microscopy for cell identification,” Appl. Opt. 56(9), D8–D13 (2017).
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S. Perrin, A. Leong-Hoï, S. Lecler, P. Pfeiffer, I. Kassamakov, A. Nolvi, E. Hæggström, and P. Montgomery, “Microsphere-assisted phase-shifting profilometry,” Appl. Opt. 56(25), 7249–7255 (2017).
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R. K. Leach, C. L. Giusca, H. Haitjema, C. Evans, and X. Jiang, “Calibration and verification of areal surface texture measuring instruments,” CIRP Ann. 64(2), 797–813 (2015).
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P. Lehmann, J. Niehues, and S. Tereschenko, “3-D optical interference microscopy at the lateral resolution limit,” Int. J. Optomechatronics 8(4), 231–241 (2014).
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Opt. Express (4)

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Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

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Proc. SPIE (4)

W. Xie, S. Hagemeier, C. Woidt, H. Hillmer, and P. Lehmann, “Influences of edges and steep slopes in 3D interference and confocal microscopy,” Proc. SPIE 9890, 98900X (2016).
[Crossref]

P. Lehmann, J. Niehues, W. Xie, and J. Riebeling, “Measurement of rectangular edge and grating structures using extended low-coherence interferometry,” Proc. SPIE 8430, 84300U (2012).
[Crossref]

P. Lehmann and W. Xie, “Signal formation in depth-scanning 3D interference microscopy at high numerical apertures,” Proc. SPIE 9660, 966015 (2015).
[Crossref]

X. Colonna de Lega, D. Grigg, and P. de Groot, “Surface profiling using a reference-scanning Mirau interference microscope,” Proc. SPIE 5531, 106–116 (2004).
[Crossref]

Sci. Rep. (2)

F. Wang, L. Liu, P. Yu, Z. Liu, H. Yu, Y. Wang, and W. J. Li, “Three-dimensional super-resolution morphology by near-field assisted white-light interferometry,” Sci. Rep. 6(1), 24703 (2016).
[Crossref] [PubMed]

I. Kassamakov, S. Lecler, A. Nolvi, A. Leong-Hoï, P. Montgomery, and E. Hæggström, “3D super-resolution optical profiling using microsphere enhanced Mirau interferometry,” Sci. Rep. 7(1), 3683 (2017).
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Surf. Top.: Metrol. Prop. (1)

P. Lehmann, S. Tereschenko, and W. Xie, “Fundamental aspects of resolution and precision in vertical scanning white-light interferometry,” Surf. Top.: Metrol. Prop. 4(0214004), 1–10 (2016).

Other (8)

W. Xie, “Transfer Characteristics of White Light Interferometers and Confocal Microscopes,” Dissertation Universität Kassel (2017).

P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, 1963).

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R. Leach, ed., Optical measurement of surface topography (Springer, 2011).

P. de Groot and X. C. de Lega, “Interpreting interferometric height measurements using the instrument transfer function,” Fringe 2005 (Springer, 2005), pp. 30–37.

ISO standard 25178–604 “Geometrical product specifications (GPS) — Surface texture: Areal — Part 604: Nominal characteristics of non-contact (coherence scanning interferometry) instruments,” (2013).

A. Lipson, S. G. Lipson, and H. Lipson, Optical Physics, 4th ed. (Cambridge University, 2011).

E. R. Meinders, A. V. Mijiritskii, L. van Pieterson, and M. Wuttig, Optical Data Storage (Springer, 2006).

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Figures (11)

Fig. 1
Fig. 1 (a) Simulated CSI signal based on the Richards-Wolf model (see sect. 3.3) and (b) measured CSI signal using blue LED illumination; (c), (d) the corresponding spectra compared to the nominal spectrum of the LED (blue peaks).
Fig. 2
Fig. 2 Measured surface profiles of a rectangular grating (Simetrics RS-N) of 300 nm period obtained with a high- resolution Linnik interferometer (NA = 0.9) using blue LED illumination. The profiles either result from the coherence peak or from phase analysis at different evaluation wavelengths λeval.
Fig. 3
Fig. 3 Surface profiles of the rectangular grating (Simetrics RS-N) of 300 nm period and an additional edge and plateau structure obtained with the high-resolution Linnik interferometer. The profiles either result from the coherence peak or from phase analysis at different evaluation wavelengths λeval.
Fig. 4
Fig. 4 Surface topographies obtained from a Blu-ray disc structure: (a) coherence topography, (b) phase topography using the center wavelength of 570 nm for phase analysis, (c) phase topography using a wavelength of 900 nm for phase analysis.
Fig. 5
Fig. 5 Diffraction from a one-dimensional phase grating depending on the angle of incidence a) pupil plane coordinate kx and diffraction pattern coordinate qx assuming θ s = θ r for zero order diffraction, b) diffraction pattern in the pupil plane at perpendicular incidence with zero order diffraction component at k x = k y =0, c) diffraction pattern in the pupil plane with zero order diffraction component at θ e = θ max , k x =ksin θ max , k y =0.
Fig. 6
Fig. 6 Profiles obtained from Kirchhoff simulations assuming a rectangular input profile of 140 nm PV amplitude (a) and 20 nm PV amplitude (b) and either coherence peak or phase analysis at different evaluation wavelengths.
Fig. 7
Fig. 7 Schematic illustration of the Richards-Wolf model applied to an interferometric system.
Fig. 8
Fig. 8 Local and global coordinate systems used for the Richards-Wolf model.
Fig. 9
Fig. 9 Simulation results based on Richards-Wolf modeling for profiles measured by CSI assuming different grating periods Λ and illumination with blue LED and NA = 0.9, black: original rectangular profiles with PV-amplitude of 140 nm, blue: coherence profiles, red: phase profiles for λeval = 600 nm (with fringe order determination based on coherence peak position).
Fig. 10
Fig. 10 Simulation based on Richards-Wolf modeling for a rectangular grating of period Λ = 0.3 µm (bottom profile), black: coherence profile obtained from the coherence peak position, color: phase profiles obtained for different evaluation wavelengths ( λ eval = 400 nm, 500 nm, 550nm, 650 nm and 900 nm).
Fig. 11
Fig. 11 Comparison of Kirchhoff and Richards-Wolf modeling for a rectangular grating of period Λ = 0.3 µm and 140 nm PV-amplitude, showing coherence profiles and phase profiles obtained for an evaluation wavelength of 900 nm.

Equations (16)

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r(x)=exp{ i q z h(x) }exp{ iarctan( 4 π tan( q z h 0 )cos( ω x x ) ) }.
q z =k( cos θ e +cos θ s )= 2π λ ( cos θ e +cos θ s ) 4π λ cos θ e = 4π λ eff ,
h(x) arctan( 4 π tan( q z h 0 )cos( ω x x ) ) q z .
4π λ eff h 0 > π 2 λ eff /4 <Δh=2 h 0 .
U s;k, θ e ( θ s )= i U 0 e ikr 4πr S R s ( k, θ e ) e i( k e k s ) r ( k e k s ) n ^ dS,
k e k s = q =( k( sin θ e sin θ s ) 0 k( cos θ e +cos θ s ) ), r =( x 0 h(x) ), n ^ =( 0 0 1 ).
q x =k( sin θ s sin θ e )=0.
k x 2 k 2 sin 2 θ max = k 2 (NA) 2 .
U s;k, θ e ( θ s )=P( θ e , θ s ) R s ( k, θ e ) q z exp( i q z h(x) )exp( i q x x )dx
U r;k, θ e ( θ s )=P( θ e , θ s ) R s ( k, θ e ) q z exp( i q x x )dx ,
h(x)= h 0 rect( ω x x )= h 0 cos( ω x x )/ | cos( ω x x ) |
r(x)=cos( q z h 0 )+ n=1 { α n exp( in ω x x )+ α n exp( in ω x x ) } , α n ={ 0forevenn 2i (1) (n+1)/2 sin( q z h 0 )/ (n π)foroddn }
φ(mΔz)=exp( ik(cos θ e +cos θ s )mΔz )
I(x,Δz; x c )= k min k max 0 arcsinNA P ( θ e )cos θ e sin 2 θ e J 0 2 (ksin θ e | x c |)| E int | 2 d θ e S( k )dk
P( θ e )= P 1 2 ( θ e ) P 2 2 ( θ e ) and E int = R s ( k, θ e )Γ( x, x c ;k, θ e )exp{ i2k[ mΔz+h( x, x c ) ]cos θ e }+ R r ( k, θ e ).
I(x,Δz)= δ x δ x I(x,Δz; x c )d x c .

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