Abstract

The conventional signal model of confocal sensors is well established and has proven to be exceptionally robust especially when measuring rough surfaces. Its physical derivation however is explicitly based on plane surfaces or point like objects, respectively. Here we show experimental results of a confocal point sensor measurement of a surface standard. The results illustrate the rise of severe artifacts when measuring curved surfaces. On this basis, we present a systematic extension of the conventional signal model that is proven to be capable of qualitatively explaining these artifacts.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef]
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2012 (1)

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

2011 (1)

J. Bischoff, E. Manske, and H. Baitinger, “Modeling of profilometry with laser focus sensors,” Proc. SPIE8083, 80830C, 80830C-12 (2011).
[CrossRef]

2010 (1)

D. Fleischle, W. Lyda, F. Mauch, and W. Osten, “Optical metrology for process control: modeling and simulation of sensors for a comparison of different measurement principles,” Proc. SPIE7718, 77181D, 77181D-12 (2010).
[CrossRef]

2009 (1)

2008 (1)

2007 (1)

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess.74(11), 572–576 (2007).
[CrossRef]

2006 (1)

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

2003 (1)

2002 (1)

2000 (1)

H. J. Tiziani, M. Wegner, and D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng.39(1), 32 (2000).
[CrossRef]

1996 (1)

1995 (1)

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]

1994 (3)

1993 (1)

1992 (1)

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal Surface Profiling Utilizing Chromatic Aberration,” Scanning14(3), 145–153 (1992).
[CrossRef]

1984 (1)

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun.49(4), 229–233 (1984).
[CrossRef]

1978 (1)

A. Atalar, “An angularspectrum approach to contrast in reflection acoustic microscopy,” J. Appl. Phys.49(10), 5130–5139 (1978).
[CrossRef]

1968 (1)

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]

J. F. Aguilar and E. R. Mendez, “Imaging optically thick objects in scanning microscopy: perfectly conducting surfaces,” J. Opt. Soc. Am. A11(1), 155–167 (1994).
[CrossRef]

Akinyemi, O.

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal Surface Profiling Utilizing Chromatic Aberration,” Scanning14(3), 145–153 (1992).
[CrossRef]

Atalar, A.

A. Atalar, “An angularspectrum approach to contrast in reflection acoustic microscopy,” J. Appl. Phys.49(10), 5130–5139 (1978).
[CrossRef]

Baitinger, H.

J. Bischoff, E. Manske, and H. Baitinger, “Modeling of profilometry with laser focus sensors,” Proc. SPIE8083, 80830C, 80830C-12 (2011).
[CrossRef]

Bakucz, P.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess.74(11), 572–576 (2007).
[CrossRef]

Bin, H.

Bischoff, J.

J. Bischoff, E. Manske, and H. Baitinger, “Modeling of profilometry with laser focus sensors,” Proc. SPIE8083, 80830C, 80830C-12 (2011).
[CrossRef]

Booth, M. J.

Boseck, S.

Botcherby, E. J.

Boyd, A.

A. Boyd, “Bibliography on confocal microscopy and its applications,” Scanning16, 33–56 (1994).

Boyde, A.

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal Surface Profiling Utilizing Chromatic Aberration,” Scanning14(3), 145–153 (1992).
[CrossRef]

Briggs, A.

Browne, M. A.

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal Surface Profiling Utilizing Chromatic Aberration,” Scanning14(3), 145–153 (1992).
[CrossRef]

Egger, M.

Fleischle, D.

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

D. Fleischle, W. Lyda, F. Mauch, and W. Osten, “Optical metrology for process control: modeling and simulation of sensors for a comparison of different measurement principles,” Proc. SPIE7718, 77181D, 77181D-12 (2010).
[CrossRef]

Galambos, R.

Gronle, M.

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

Hadravský, M.

Jung, L.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess.74(11), 572–576 (2007).
[CrossRef]

Juskaitis, R.

Krüger-Sehm, R.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess.74(11), 572–576 (2007).
[CrossRef]

Lajunen, H.

Li, P.

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

Liu, J.

Liu, Z.

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

Lyda, W.

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

D. Fleischle, W. Lyda, F. Mauch, and W. Osten, “Optical metrology for process control: modeling and simulation of sensors for a comparison of different measurement principles,” Proc. SPIE7718, 77181D, 77181D-12 (2010).
[CrossRef]

Manske, E.

J. Bischoff, E. Manske, and H. Baitinger, “Modeling of profilometry with laser focus sensors,” Proc. SPIE8083, 80830C, 80830C-12 (2011).
[CrossRef]

Mauch, F.

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

D. Fleischle, W. Lyda, F. Mauch, and W. Osten, “Optical metrology for process control: modeling and simulation of sensors for a comparison of different measurement principles,” Proc. SPIE7718, 77181D, 77181D-12 (2010).
[CrossRef]

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]

J. F. Aguilar and E. R. Mendez, “Imaging optically thick objects in scanning microscopy: perfectly conducting surfaces,” J. Opt. Soc. Am. A11(1), 155–167 (1994).
[CrossRef]

Molesini, G.

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun.49(4), 229–233 (1984).
[CrossRef]

Nam, S.

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

Osten, W.

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

D. Fleischle, W. Lyda, F. Mauch, and W. Osten, “Optical metrology for process control: modeling and simulation of sensors for a comparison of different measurement principles,” Proc. SPIE7718, 77181D, 77181D-12 (2010).
[CrossRef]

Pedrini, G.

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun.49(4), 229–233 (1984).
[CrossRef]

Petrán, M.

Poggi, P.

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun.49(4), 229–233 (1984).
[CrossRef]

Quercioli, F.

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun.49(4), 229–233 (1984).
[CrossRef]

Ricka, J.

Ruprecht, A. K.

Shi, K.

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

Steudle, D.

H. J. Tiziani, M. Wegner, and D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng.39(1), 32 (2000).
[CrossRef]

Tan, J.

Tervo, J.

Tiziani, H. J.

Turunen, J.

Uhde, H.-M.

Vallius, T.

Wang, Y.

Wegner, M.

H. J. Tiziani, M. Wegner, and D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng.39(1), 32 (2000).
[CrossRef]

Weise, W.

Wiesendanger, T. F.

Wilhelms, H.

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess.74(11), 572–576 (2007).
[CrossRef]

Wilson, T.

Wyrowski, F.

Yin, S.

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

Zinin, P.

Appl. Opt. (5)

J. Appl. Phys. (1)

A. Atalar, “An angularspectrum approach to contrast in reflection acoustic microscopy,” J. Appl. Phys.49(10), 5130–5139 (1978).
[CrossRef]

J. Mod. Opt. (1)

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]

J. Opt. Soc. Am. (1)

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

Meas. Sci. Technol. (1)

W. Lyda, M. Gronle, D. Fleischle, F. Mauch, and W. Osten, “Advantages of chromatic-confocal spectral interferometry in comparison to chromatic confocal microscopy,” Meas. Sci. Technol.23(5), 054009 (2012).
[CrossRef]

Opt. Commun. (2)

K. Shi, S. Nam, P. Li, S. Yin, and Z. Liu, “Wavelength division multiplexed confocal microscopy using supercontinuum,” Opt. Commun.263(2), 156–162 (2006).
[CrossRef]

G. Molesini, G. Pedrini, P. Poggi, and F. Quercioli, “Focus-wavelength encoded optical profilometer,” Opt. Commun.49(4), 229–233 (1984).
[CrossRef]

Opt. Eng. (1)

H. J. Tiziani, M. Wegner, and D. Steudle, “Confocal principle for macro- and microscopic surface and defect analysis,” Opt. Eng.39(1), 32 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Proc. SPIE (2)

J. Bischoff, E. Manske, and H. Baitinger, “Modeling of profilometry with laser focus sensors,” Proc. SPIE8083, 80830C, 80830C-12 (2011).
[CrossRef]

D. Fleischle, W. Lyda, F. Mauch, and W. Osten, “Optical metrology for process control: modeling and simulation of sensors for a comparison of different measurement principles,” Proc. SPIE7718, 77181D, 77181D-12 (2010).
[CrossRef]

Scanning (2)

M. A. Browne, O. Akinyemi, and A. Boyde, “Confocal Surface Profiling Utilizing Chromatic Aberration,” Scanning14(3), 145–153 (1992).
[CrossRef]

A. Boyd, “Bibliography on confocal microscopy and its applications,” Scanning16, 33–56 (1994).

Tech. Mess. (1)

R. Krüger-Sehm, P. Bakucz, L. Jung, and H. Wilhelms, “Chirp calibration standards for surface measuring instruments,” Tech. Mess.74(11), 572–576 (2007).
[CrossRef]

Other (7)

M. Born and E. Wolf, Principles of Optics, 6th edition (Pergamon Press, 1980).

VDI/VDE-Gesellschaft, “Optical measurement of microtopography – Calibration of confocal microscopes and depth setting standards for roughness measurement,” 2655 Blatt 1.2, Beuth Verlag, (2010).

T. R. Corle and G. S. Kino, Confocal Scanning Optical Microscopy and Related Imaging Systems (Academic Press, 1996).

E. Neumann, Single-Mode Fibers (Springer-Verlag, 1988).

J. W. Goodman, Introduction to Fourier Optics, 3rd edition (Roberts & Company Publishers, 2005).

A. Schuldt, “Seeing the wood for the trees,” in Nature Milestones in Light Microscopy 12–13 (Macmillan Publishers Limited, 2009).

T. Wilson and C. J. R. Sheppard, Theory and practice of scanning optical microscopy (Academic Press 1984).

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Figures (8)

Fig. 1
Fig. 1

Schematic of a confocal system illustrating the signal model.

Fig. 2
Fig. 2

Schematic of unfolded system

Fig. 3
Fig. 3

Reference measurement of the chirp calibration standard surface profile conducted by the PTB with a 2 µm stylus apparatus [26]. The dashed circles mark the areas of the surface that will be examined in more detail in Fig. 4. Note however that the absolute values of the horizontal axis differ to Fig. 4 since the measurement of Fig. 4 was done with a different sensor in a different coordinate system.

Fig. 4
Fig. 4

Detailed view of a measurement of the chirp calibration standard with a custom build chromatic confocal sensor with an Olympus LMPlan FI objective lens with 50x magnification and 0.5 NA at a centre wavelength of 830nm. The measured surface profile and the corresponding ideal data are shown for the cosine intercept with a) 91µm wavelength, b) 39 µm wavelength and c) 24 µm wavelength.

Fig. 5
Fig. 5

Schematic illustrating the signal model with improved modeling of light object interaction

Fig. 6
Fig. 6

Illustration of the improved signal model. In case of a plane surface the wavefront in the focus of the illumination field shows the maximum overlap with the surface profile. In case of a locally curved surface, a defocused wavefront may exhibit a bigger overlap with the surface profile than the focused wavefront, thereby producing artifacts with the common signal processing.

Fig. 7
Fig. 7

Simulation result for a measurement of the chirp calibration standard with an ideal confocal point sensor of 0.5NA at 830nm illumination wavelength. The simulation result and the corresponding ideal data is shown for the cosine intercept with a) with 91µm wavelength, b) 39 µm wavelength and c) 24 µm wavelength.

Fig. 8
Fig. 8

Simulation result for a measurement of the chirp calibration standard with an ideal confocal point sensor of 0.5NA at 830nm illumination wavelength. A spherical aberration of λ/10 following the definition of Zernike fringe polynomials has been introduced into the pupil field. As before, simulation result, the real measurement data as well as the corresponding ideal data is shown for the cosine intercept with a) 91 µm, b) 39 µm and c) 24 µm wavelength.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

I= | dxdy u i * ( x,y ) u s ( x,y ) | 2
I( Δz )= | dxdy u i * ( x,y ) P ^ ( x O , y O ,x,y,Δz ){ O ^ ( x O , y O ){ P ^ ( x,y, x O , y O ,Δz ){ u i ( x,y ) } } } | 2
P ^ ( x,y, x 0 , y 0 ){ u i ( x,y ) }= F ^ { F ^ { u i ( x,y ) }L( x p , y p ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 }.
P ^ ( x O , y O ,x,y,Δz ){ u ˜ S ( x O , y O ) }= F ^ { F ^ { u ˜ S ( x O , y O ) }L( x p , y p ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 }
I( Δz )=| dxdy u i * ( x,y ) F ^ { F ^ { O ^ { F ^ { F ^ { u i ( x,y ) }L( x p , y p ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 } } } L( x p , y p ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 } | 2
I( Δz )= | dxdy[ u i * ( x,y ) F ^ { F ^ { u i ( x,y ) }L( x p , y p )L( x p , y p ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 } ] | 2
F ^ { g( x ) }= dxg( x ) e i2π f X x
I( Δz )= | dxdyδ( x,y )( d x p d y p L( x p , y p )L( x p , y p ) e ik2Δz 1 x p 2 / f 2 2 y p 2 / f 2 2 e ik( x p f 2 x+ y p f 2 y ) ) | 2 = | d x p d y p L( x p , y p )L( x p , y p ) e ik2Δz 1 x p 2 / f 2 2 y p 2 / f 2 2 | 2
I( Δz )= | 0 R drr e ikΔz r 2 / f 2 2 | 2 = | R 2 2 e ik π R 2 λ f 2 2 Δz sin( π R 2 λ f 2 Δz ) π R 2 λ f 2 Δz | 2 .
I( u )= ( sin( u/2 ) u/2 ) 2 .
C= ΔzI( Δz ) I( Δz ) .
I( Δz )=| dxdy u i * ( x,y ) d x p d y p ( d x O d y O u ˜ s ( x O , y O ) e ik( x p f 2 x O + y p f 2 y O ) . L( x P , y P ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 e ik( x p f 1 x+ y p f 1 y ) ) | 2
I( Δz )=| d x O d y O u ˜ s ( x O , y O ) d x P d y p ( dxdy u i ( x,y ) e ik( x p f 1 x+ y p f 1 y ) . L( x P , y P ) e ikΔz 1 x p 2 / f 2 2 y p 2 / f 2 2 e ik( x p f 2 x O + y p f 2 y O ) ) | 2
I( Δz )= | d x O d y O O ^ { u ˜ i ( x O , y O ) } u ˜ ( x O , y O ) | 2
O ^ { u i ( x O , y O ) } e ik2h( x O , y O ) ,
I( Δz )= | dxdy u ˜ i ( x O , y O ,Δz ) u ˜ i ( x O , y O ,Δz ) e ik2h( x O , y O ) | 2
I( Δz )= | dxdy | u ˜ i ( x O , y O ,Δz ) | 2 e i2 φ i ( x O , y O ,Δz ) e ik2h( x O , y O ) | 2

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