Abstract

In this paper a new high NA shape measurement technique working with an arbitrary spherical wave illumination is presented. The main contribution of this work are formulas, derived from exact reflection and refraction laws for both the reflection and the transmission configurations, which enable accurate shape calculations in systems with an arbitrary location of the illuminating point source. The proposed algorithms permit measurement of multiple samples of arbitrary shapes using a single hologram. An accuracy of this method is confirmed with numerical simulations, which show superiority of this approach over a standard procedure utilizing paraxial approximation. The method is validated experimentally using a reflective measurement of a microlens topography, whose NA in reflection is 0.7. Furthermore, a new measurement configuration is presented that extends the capabilities of transmission systems for characterization of high gradient shapes.

© 2014 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
  5. F. Charrière, J. Kühn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45(5), 829–835 (2006).
    [Crossref] [PubMed]
  6. T. Colomb, N. Pavillon, J. Kühn, E. Cuche, Ch. Depeursinge, and Y. Emery, “Extended depth-of-focus by digital holographic microscopy,” Opt. Lett. 35(11), 1840–1842 (2010).
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2013 (3)

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

T. Kozacki, K. Liżewski, and J. Kostencka, “Holographic method for topography measurement of highly tilted and high numerical aperture micro structures,” Opt. Laser Technol. 49, 38–46 (2013).
[Crossref]

K. Liżewski, T. Kozacki, and J. Kostencka, “Digital holographic microscope for measurement of high gradient deep topography object based on superresolution concept,” Opt. Lett. 38(11), 1878–1880 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (2)

2010 (3)

2009 (1)

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

2007 (1)

T. Miyashita, “Standardization for microlenses and microlens arrays,” Jpn. J. Appl. Phys. 46(8B), 5391–5396 (2007).
[Crossref]

2006 (2)

F. Charrière, J. Kühn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, “Characterization of microlenses by digital holographic microscopy,” Appl. Opt. 45(5), 829–835 (2006).
[Crossref] [PubMed]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

2005 (1)

2001 (1)

P. Nussbaum and H. Herzig, “Low numerical aperture refractive microlenses in fused silica,” Opt. Eng. 40(7), 1412–1414 (2001).
[Crossref]

1998 (1)

1997 (1)

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

1995 (1)

J. Schwider and O. Falkenstoerfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34(10), 2972–2975 (1995).
[Crossref]

1994 (1)

H. Sickinger, O. Falkenstoerfer, N. Lindlein, and J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33(8), 2680–2686 (1994).
[Crossref]

1987 (1)

1948 (1)

E. Wolf, “On the Designing of Aspheric Surfaces,” Proc. Phys. Soc. 61(6), 494–503 (1948).
[Crossref]

Asundi, A.

Bergner, B.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Charrière, F.

Chen, Y.-L.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Choo, C. O.

Colomb, T.

Cox, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Cuche, E.

Davies, A.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Depeursinge, C.

Depeursinge, Ch.

Doblas, A.

Eiju, T.

Eisner, M.

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

Emery, Y.

Falaggis, K.

Falkenstoerfer, O.

J. Schwider and O. Falkenstoerfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34(10), 2972–2975 (1995).
[Crossref]

H. Sickinger, O. Falkenstoerfer, N. Lindlein, and J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33(8), 2680–2686 (1994).
[Crossref]

Ferraro, P.

Gao, W.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Gardner, N.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Ghim, Y.-S.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Gomez, V.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Hariharan, P.

Haselbeck, S.

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

Herzig, H.

P. Nussbaum and H. Herzig, “Low numerical aperture refractive microlenses in fused silica,” Opt. Eng. 40(7), 1412–1414 (2001).
[Crossref]

Herzig, H. P.

M.-S. Kim, T. Scharf, and H. P. Herzig, “Small-size microlens characterization by multiwavelength high-resolution interference microscopy,” Opt. Express 18(14), 14319–14329 (2010).
[Crossref] [PubMed]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

Ito, S.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Jia, Z.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Józwik, M.

Kim, M.-S.

Kostencka, J.

T. Kozacki, K. Liżewski, and J. Kostencka, “Holographic method for topography measurement of highly tilted and high numerical aperture micro structures,” Opt. Laser Technol. 49, 38–46 (2013).
[Crossref]

K. Liżewski, T. Kozacki, and J. Kostencka, “Digital holographic microscope for measurement of high gradient deep topography object based on superresolution concept,” Opt. Lett. 38(11), 1878–1880 (2013).
[Crossref] [PubMed]

Kozacki, T.

Kühn, J.

Kujawinska, M.

Li, X.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Lindlein, N.

H. Sickinger, O. Falkenstoerfer, N. Lindlein, and J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33(8), 2680–2686 (1994).
[Crossref]

Lizewski, K.

Marquet, P.

Martínez-Corral, M.

Medicus, K.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Miyashita, T.

T. Miyashita, “Standardization for microlenses and microlens arrays,” Jpn. J. Appl. Phys. 46(8B), 5391–5396 (2007).
[Crossref]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Montfort, F.

Naessens, K.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Nussbaum, P.

P. Nussbaum and H. Herzig, “Low numerical aperture refractive microlenses in fused silica,” Opt. Eng. 40(7), 1412–1414 (2001).
[Crossref]

Nussbaum, Ph.

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

Oreb, B. F.

Ottevaere, H.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Pavillon, N.

Reichelt, S.

Rohrbach, A.

Saavedra, G.

Sánchez-Ortiga, E.

Scharf, T.

Schwider, J.

J. Schwider and O. Falkenstoerfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34(10), 2972–2975 (1995).
[Crossref]

H. Sickinger, O. Falkenstoerfer, N. Lindlein, and J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33(8), 2680–2686 (1994).
[Crossref]

Shimizu, Y.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Sickinger, H.

H. Sickinger, O. Falkenstoerfer, N. Lindlein, and J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33(8), 2680–2686 (1994).
[Crossref]

Singer, W.

Taghizadeh, M.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Thienpont, H.

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Völkel, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

Weible, K.

Weijuan, Q.

Wolf, E.

E. Wolf, “On the Designing of Aspheric Surfaces,” Proc. Phys. Soc. 61(6), 494–503 (1948).
[Crossref]

Woo, H. J.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

Xu, B.

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Yingjie, Y.

Zappe, H.

Appl. Opt. (5)

J. Opt. A, Pure Appl. Opt. (1)

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, “Comparing glass and plastic refractive microlenses fabricated with different technologies,” J. Opt. A, Pure Appl. Opt. 8(7), S407–S429 (2006).
[Crossref]

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

Jpn. J. Appl. Phys. (1)

T. Miyashita, “Standardization for microlenses and microlens arrays,” Jpn. J. Appl. Phys. 46(8B), 5391–5396 (2007).
[Crossref]

Meas. Sci. Technol. (1)

V. Gomez, Y.-S. Ghim, H. Ottevaere, N. Gardner, B. Bergner, K. Medicus, A. Davies, and H. Thienpont, “Micro-optic reflection and transmission interferometer for complete microlens characterization,” Meas. Sci. Technol. 20(2), 025901 (2009).
[Crossref]

Opt. Eng. (3)

H. Sickinger, O. Falkenstoerfer, N. Lindlein, and J. Schwider, “Characterization of microlenses using a phase-shifting shearing interferometer,” Opt. Eng. 33(8), 2680–2686 (1994).
[Crossref]

J. Schwider and O. Falkenstoerfer, “Twyman-Green interferometer for testing microspheres,” Opt. Eng. 34(10), 2972–2975 (1995).
[Crossref]

P. Nussbaum and H. Herzig, “Low numerical aperture refractive microlenses in fused silica,” Opt. Eng. 40(7), 1412–1414 (2001).
[Crossref]

Opt. Express (1)

Opt. Laser Technol. (1)

T. Kozacki, K. Liżewski, and J. Kostencka, “Holographic method for topography measurement of highly tilted and high numerical aperture micro structures,” Opt. Laser Technol. 49, 38–46 (2013).
[Crossref]

Opt. Lett. (3)

Proc. Phys. Soc. (1)

E. Wolf, “On the Designing of Aspheric Surfaces,” Proc. Phys. Soc. 61(6), 494–503 (1948).
[Crossref]

Proc. SPIE (1)

B. Xu, Z. Jia, X. Li, Y.-L. Chen, Y. Shimizu, S. Ito, and W. Gao, “Surface form metrology of micro-optics,” Proc. SPIE 8769, 876902 (2013).
[Crossref]

Pure Appl. Opt. (1)

Ph. Nussbaum, R. Völkel, H. P. Herzig, M. Eisner, and S. Haselbeck, “Design, fabrication and testing of microlens arrays for sensors and microsystems,” Pure Appl. Opt. 6(6), 617–636 (1997).
[Crossref]

Other (2)

W. Osten, Optical inspection of micro systems (CRC, Taylor and Francis, 2007).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).

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Figures (12)

Fig. 1
Fig. 1 The DH microscope setup in reflection measurement configuration.
Fig. 2
Fig. 2 Measurement settings for reflection (a-c) and transmission (d-f) configurations for various object illumination and imaging schemes: (a,d) PWC–plane wave configuration, (b,e) FC–focal configuration, (c,f) IC–imaging configuration.
Fig. 3
Fig. 3 The object beam generation for the reflection configuration.
Fig. 4
Fig. 4 Simulation of measurement of a microlens (ROC = 0.3mm, ϕ = 0.2mm) in reflection mode for FC with IRP at vertex (a-c) and substrate (d-f) and for various sample shapes: (a,d) paraboloid, (b,e) sphere, (c,f) hyperboloid; green line – wavefront given at IRP; black line – error of topography reconstruction ΔZREC using Eq. (6), red dotted line – ΔZREC for TEA.
Fig. 5
Fig. 5 Simulation of measurement of a microlens (ROC = 0.2mm, ϕ = 0.2mm) in reflection mode for IC with IRP at vertex (a-c) and substrate (d-f) and for various sample shapes: (a,d) paraboloid, (b,e) sphere, (c,f) hyperboloid; green line – aberration given at IRP; black line – error of topography reconstruction ΔZREC using Eq. (6), red dotted line – ΔZREC for TEA.
Fig. 6
Fig. 6 The object beam generation for the transmission configuration.
Fig. 7
Fig. 7 Simulation of measurement of the microlens (ROC = 0.2mm, ϕ = 0.2mm) in transmission mode for FC with IRP at vertex (a-c) and substrate (d-f) and for various sample shapes: (a,d) paraboloid, (b,e) sphere, (c,f) hyperboloid; green line – aberration given at IRP; black line – error of topography reconstruction ΔZREC using Eq. (12), red dotted line – ΔZREC for TEA.
Fig. 8
Fig. 8 Simulation of measurement of the microlens (ROC = 0.2mm, ϕ = 0.2mm) in transmission mode for IC with IRP at vertex (a-c) and substrate (d-f) and for various sample shapes: (a,d) paraboloid, (b,e) sphere, (c,f) hyperboloid; green line – aberration given at IRP; black line – error of topography reconstruction ΔZREC using Eq. (12), red dotted line – ΔZREC for TEA.
Fig. 9
Fig. 9 (a,c) Interferograms and (b,d) wrapped phases for the measured microlens (NA = 0.19) in DH setup with IRP at substrate plane for (a,b) IC and (c,d) PWC.
Fig. 10
Fig. 10 Contour map of the reconstructed shape for (a) IC and (b) PWC, (c) cross–section through the center of microlens shape in (a) and (b).
Fig. 11
Fig. 11 The differences between topographies obtained for IC and PWC of reflection DH microscope setup (Fig. 1); (a) contour map, (b) central cross–section.
Fig. 12
Fig. 12 The differences between topographies obtained for IC of reflection DH setup (Fig. 1) and for PWC of transmission DH; (a) contour map, (b) central cross–section.

Equations (15)

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sin α T = n sin u 1 + sin u 2 ( 1 + n 2 2 n cos ( u 1 + u 2 ) ) 1 / 2 ,
[ Q M ] = [ Q S ] .
[ QS ] = R [ OQ ] = R ( z O Z ) 2 + ( x x O + Z tan u ) 2 ,
[ QM ] = Z sec u + [ NM ] ,
[ NM ] = P N sin u d x .
Z ( x + x s ) = C B 1 ,
B = 2 z O + 2 ( x x O ) tan u + 2 sec u ' ( R n + [ NM ] ) ,
C = z O 2 + ( x x O ) 2 ( R + [ NM ] ) 2 ,
n 1 [ QS ] = n 2 [ QM ] .
[ QS ] = R [ OQ ] = R ( z O Z ) 2 + ( x x O + Z tan u ) 2 ,
[ QM ] = Z sec u + [ NM ] ,
Z ( x + x s ) = B ± ( B 2 4 A C ) 1 / 2 2 A ,
A = ( n 1 2 n 2 2 ) s e c 2 u ' ,
B = 2 n 1 2 z O + 2 n 1 2 ( x x O ) tan u 2 sec u ' ( R n 1 n 2 n 2 2 [ NM ] ) ,
C = n 1 2 z O 2 + n 1 2 ( x x O ) 2 ( n 1 R n 2 [ NM ] ) 2 ,

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