Abstract

Optical profilometers based on light reflection may fail at surfaces presenting steep slopes and highly curved features. Missed light, interference and diffraction at steps, peaks and valleys are some of the reasons. Consequently, blind areas or profile artifacts may be observed when using common reflection micro-optical profilometers (confocal, scanning interferometers, etc…). The Topographic Optical Profilometry by Absorption in Fluids (TOPAF) essentially avoids these limitations. In this technique an absorbing fluid fills the gap between a reference surface and the surface to profile. By comparing transmission images at two different spectral bands we obtain a reliable topographic map of the surface. In this contribution we develop a model to obtain the profile under micro-optical observation, where high numerical aperture (NA) objectives are mandatory. We present several analytical and experimental results, validating the technique’s capabilities for profiling steep slopes and highly curved micro-optical surfaces with nanometric height resolution.

© 2015 Optical Society of America

Full Article  |  PDF Article
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References

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2014 (1)

2013 (6)

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]

J. Seewig, I. Raid, C. Wiehr, and B. A. George, “Robust evaluation of intensity curves measured by confocal microscopies,” Proc. SPIE 8788, 87880T (2013).
[Crossref]

F. Mauch, W. Lyda, and W. Osten, “Model-based assistance system for confocal measurements of rough surfaces,” Proc. SPIE 8788, 87880U (2013).
[Crossref]

P. Lehmann, W. Xie, P. Kühnhold, and J. Niehues, “Interferometric measurement of functional surfaces,” Proc. SPIE 8769, 876904 (2013).
[Crossref]

J. C. Martínez Antón, J. M. Plaza Ortega, and J. Alonso, “3D-form metrology of arbitrary optical surfaces by absorption in fluids,” Proc. SPIE 8884, 888413 (2013).
[Crossref]

M. A. Model and E. Schonbrun, “Optical determination of intracellular water in apoptotic cells,” J. Physiol. 591(23), 5843–5849 (2013).
[Crossref] [PubMed]

2012 (7)

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News 23, 31–35 (2012).

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Object depending artifacts in confocal measurements,” Proc. SPIE 8466, 846609 (2012).
[Crossref]

A. Ettemeyer, “New three-dimensional fiber probe for multisensory coordinate measurement,” Opt. Eng. 51(8), 081502 (2012).
[Crossref]

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

Y. Tan and H. Chen, “Diffraction of transmission light through triangular apertures in array of retro-reflective microprisms,” Appl. Opt. 51(16), 3403–3409 (2012).
[Crossref] [PubMed]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Improved signal model for confocal sensors accounting for object depending artifacts,” Opt. Express 20(18), 19936–19945 (2012).
[Crossref] [PubMed]

J. C. Antón, J. Alonso, J. A. Pedrero, and J. A. Quiroga, “Topographic optical profilometry by absorption in liquids,” Opt. Express 20(27), 28631–28640 (2012).
[Crossref] [PubMed]

2011 (3)

J. Niehues and P. Lehmann, “Improvement of lateral resolution and reduction of batwings in vertical scanning white-light interferometry,” Proc. SPIE 8082, 80820W (2011).
[Crossref]

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910 (2011).
[Crossref]

C. Zhao, J. Tan, J. Tang, T. Liu, and J. Liu, “Confocal simultaneous phase-shifting interferometry,” Appl. Opt. 50(5), 655–661 (2011).
[Crossref] [PubMed]

2010 (2)

J. M. Coupland and J. Lobera, “Measurement of Steep Surfaces Using White Light Interferometry,” Strain 46(1), 69–78 (2010).
[Crossref]

A. Ettemeyer, “Optical 3D testing of micro structures,” Proc. SPIE 7997, 79971S (2010).
[Crossref]

2007 (1)

2006 (1)

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401 (2006).
[Crossref]

2002 (1)

1994 (1)

Alonso, J.

J. C. Martínez Antón, J. M. Plaza Ortega, and J. Alonso, “3D-form metrology of arbitrary optical surfaces by absorption in fluids,” Proc. SPIE 8884, 888413 (2013).
[Crossref]

J. C. Antón, J. Alonso, J. A. Pedrero, and J. A. Quiroga, “Topographic optical profilometry by absorption in liquids,” Opt. Express 20(27), 28631–28640 (2012).
[Crossref] [PubMed]

Alonso Fernández, J.

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910 (2011).
[Crossref]

Antón, J. C.

Chen, H.

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]

Coupland, J.

Coupland, J. M.

J. M. Coupland and J. Lobera, “Measurement of Steep Surfaces Using White Light Interferometry,” Strain 46(1), 69–78 (2010).
[Crossref]

de Groot, P.

Deck, L.

Ettemeyer, A.

A. Ettemeyer, “New three-dimensional fiber probe for multisensory coordinate measurement,” Opt. Eng. 51(8), 081502 (2012).
[Crossref]

A. Ettemeyer, “Optical 3D testing of micro structures,” Proc. SPIE 7997, 79971S (2010).
[Crossref]

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]

George, B. A.

J. Seewig, I. Raid, C. Wiehr, and B. A. George, “Robust evaluation of intensity curves measured by confocal microscopies,” Proc. SPIE 8788, 87880T (2013).
[Crossref]

Gómez Pedrero, J. A.

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910 (2011).
[Crossref]

Gronle, M.

Hsu, I. J.

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]

Kühnhold, P.

P. Lehmann, W. Xie, P. Kühnhold, and J. Niehues, “Interferometric measurement of functional surfaces,” Proc. SPIE 8769, 876904 (2013).
[Crossref]

Lai, C. C.

Leach, R.

Lee, C. H.

Lehmann, P.

P. Lehmann, W. Xie, P. Kühnhold, and J. Niehues, “Interferometric measurement of functional surfaces,” Proc. SPIE 8769, 876904 (2013).
[Crossref]

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

J. Niehues and P. Lehmann, “Improvement of lateral resolution and reduction of batwings in vertical scanning white-light interferometry,” Proc. SPIE 8082, 80820W (2011).
[Crossref]

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]

Lin, W. C.

Liu, J.

Liu, T.

Lobera, J.

J. M. Coupland and J. Lobera, “Measurement of Steep Surfaces Using White Light Interferometry,” Strain 46(1), 69–78 (2010).
[Crossref]

Lyda, W.

F. Mauch, W. Lyda, and W. Osten, “Model-based assistance system for confocal measurements of rough surfaces,” Proc. SPIE 8788, 87880U (2013).
[Crossref]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Improved signal model for confocal sensors accounting for object depending artifacts,” Opt. Express 20(18), 19936–19945 (2012).
[Crossref] [PubMed]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Object depending artifacts in confocal measurements,” Proc. SPIE 8466, 846609 (2012).
[Crossref]

Mandal, R.

Mansfield, D.

Martínez Antón, J. C.

J. C. Martínez Antón, J. M. Plaza Ortega, and J. Alonso, “3D-form metrology of arbitrary optical surfaces by absorption in fluids,” Proc. SPIE 8884, 888413 (2013).
[Crossref]

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910 (2011).
[Crossref]

Mauch, F.

F. Mauch, W. Lyda, and W. Osten, “Model-based assistance system for confocal measurements of rough surfaces,” Proc. SPIE 8788, 87880U (2013).
[Crossref]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Object depending artifacts in confocal measurements,” Proc. SPIE 8466, 846609 (2012).
[Crossref]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Improved signal model for confocal sensors accounting for object depending artifacts,” Opt. Express 20(18), 19936–19945 (2012).
[Crossref] [PubMed]

Model, M. A.

M. A. Model and E. Schonbrun, “Optical determination of intracellular water in apoptotic cells,” J. Physiol. 591(23), 5843–5849 (2013).
[Crossref] [PubMed]

Mong, H. Y.

Niehues, J.

P. Lehmann, W. Xie, P. Kühnhold, and J. Niehues, “Interferometric measurement of functional surfaces,” Proc. SPIE 8769, 876904 (2013).
[Crossref]

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

J. Niehues and P. Lehmann, “Improvement of lateral resolution and reduction of batwings in vertical scanning white-light interferometry,” Proc. SPIE 8082, 80820W (2011).
[Crossref]

Osten, W.

F. Mauch, W. Lyda, and W. Osten, “Model-based assistance system for confocal measurements of rough surfaces,” Proc. SPIE 8788, 87880U (2013).
[Crossref]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Object depending artifacts in confocal measurements,” Proc. SPIE 8466, 846609 (2012).
[Crossref]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Improved signal model for confocal sensors accounting for object depending artifacts,” Opt. Express 20(18), 19936–19945 (2012).
[Crossref] [PubMed]

Pedrero, J. A.

Plaza Ortega, J. M.

J. C. Martínez Antón, J. M. Plaza Ortega, and J. Alonso, “3D-form metrology of arbitrary optical surfaces by absorption in fluids,” Proc. SPIE 8884, 888413 (2013).
[Crossref]

Quiroga, J. A.

J. C. Antón, J. Alonso, J. A. Pedrero, and J. A. Quiroga, “Topographic optical profilometry by absorption in liquids,” Opt. Express 20(27), 28631–28640 (2012).
[Crossref] [PubMed]

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910 (2011).
[Crossref]

Raid, I.

J. Seewig, I. Raid, C. Wiehr, and B. A. George, “Robust evaluation of intensity curves measured by confocal microscopies,” Proc. SPIE 8788, 87880T (2013).
[Crossref]

Riebeling, J.

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

Rolland, J. P.

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News 23, 31–35 (2012).

Schonbrun, E.

M. A. Model and E. Schonbrun, “Optical determination of intracellular water in apoptotic cells,” J. Physiol. 591(23), 5843–5849 (2013).
[Crossref] [PubMed]

Seewig, J.

J. Seewig, I. Raid, C. Wiehr, and B. A. George, “Robust evaluation of intensity curves measured by confocal microscopies,” Proc. SPIE 8788, 87880T (2013).
[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]

Tan, J.

Tan, Y.

Tang, J.

Thompson, K. P.

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News 23, 31–35 (2012).

Wiehr, C.

J. Seewig, I. Raid, C. Wiehr, and B. A. George, “Robust evaluation of intensity curves measured by confocal microscopies,” Proc. SPIE 8788, 87880T (2013).
[Crossref]

Wyant, J. C.

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401 (2006).
[Crossref]

Xie, W.

P. Lehmann, W. Xie, P. Kühnhold, and J. Niehues, “Interferometric measurement of functional surfaces,” Proc. SPIE 8769, 876904 (2013).
[Crossref]

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

Zhao, C.

Appl. Opt. (4)

J. Physiol. (1)

M. A. Model and E. Schonbrun, “Optical determination of intracellular water in apoptotic cells,” J. Physiol. 591(23), 5843–5849 (2013).
[Crossref] [PubMed]

Opt. Eng. (1)

A. Ettemeyer, “New three-dimensional fiber probe for multisensory coordinate measurement,” Opt. Eng. 51(8), 081502 (2012).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Opt. Photon. News (1)

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News 23, 31–35 (2012).

Proc. SPIE (11)

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]

A. Ettemeyer, “Optical 3D testing of micro structures,” Proc. SPIE 7997, 79971S (2010).
[Crossref]

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE 6024, 602401 (2006).
[Crossref]

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

J. Niehues and P. Lehmann, “Improvement of lateral resolution and reduction of batwings in vertical scanning white-light interferometry,” Proc. SPIE 8082, 80820W (2011).
[Crossref]

F. Mauch, W. Lyda, M. Gronle, and W. Osten, “Object depending artifacts in confocal measurements,” Proc. SPIE 8466, 846609 (2012).
[Crossref]

J. Seewig, I. Raid, C. Wiehr, and B. A. George, “Robust evaluation of intensity curves measured by confocal microscopies,” Proc. SPIE 8788, 87880T (2013).
[Crossref]

F. Mauch, W. Lyda, and W. Osten, “Model-based assistance system for confocal measurements of rough surfaces,” Proc. SPIE 8788, 87880U (2013).
[Crossref]

P. Lehmann, W. Xie, P. Kühnhold, and J. Niehues, “Interferometric measurement of functional surfaces,” Proc. SPIE 8769, 876904 (2013).
[Crossref]

J. C. Martínez Antón, J. M. Plaza Ortega, and J. Alonso, “3D-form metrology of arbitrary optical surfaces by absorption in fluids,” Proc. SPIE 8884, 888413 (2013).
[Crossref]

J. C. Martínez Antón, J. A. Gómez Pedrero, J. Alonso Fernández, and J. A. Quiroga, “Optical method for the surface topographic characterization of Fresnel lenses,” Proc. SPIE 8169, 816910 (2011).
[Crossref]

Strain (1)

J. M. Coupland and J. Lobera, “Measurement of Steep Surfaces Using White Light Interferometry,” Strain 46(1), 69–78 (2010).
[Crossref]

Other (6)

J. C. Martínez Antón, “Three-dimensional profilometer based on optical absorption in fluids,” patent application WO2013011172 (2011).

J. Schmit, K. Creath, and J. C. Wyant, “Surface profilers, multiple wavelength, and white light interferometry,” in: Optical Shop Testing. Malacara D., editor (John Wiley & Sons Inc., 2007), pp. 667–755.

D. Vázquez-Moliní, A. Álvarez Fernández-Balbuena, and B. García-Fernandez, “Natural lighting systems based on dielectric prismatic Film”, in Dielectric Material, Alexandru Silaghi M., Ed. (Intech, 2012), pp. 155–180.

M. Pluta, Advanced Light Microscopy (Elsevier, 1988), Vol.1, p.464.

I. T. Young, R. Zagers, L. J. van Vliet, J. Mullikin, F. Boddeke, and H. Netten, “Depth-of-focus in microscopy,” in Proceedings SCIA’93 (8th Scandinavian Conference on Image Analysis), Tromso, Norway, 1993, pp.493–498.

V. Borovytsky and A. Fesenko, “Diffraction depth of focus in optical microscope,” Proc. SPIE vol. 7786, 77860X (2010).
[Crossref]

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Figures (14)

Fig. 1
Fig. 1 (a) Optical scheme for TOPAF [22]. An absorbing water-soluble dye is sandwiched between two surfaces. A transmission image provides topographic data of the surface of interest with respect to a reference surface. In a simplified model the images are taken with very low numerical aperture (NA ~0). (b) Absorption (dash line) and radiance spectra (continuous lines) used in experiments: the absorbing fluid is a methyl violet dye in a glycerol-water solution and the light sources have peak wavelengths at λΑ = 594 nm and λR = 635 nm.
Fig. 2
Fig. 2 (a) Optical scheme for microscopic observation. High numerical aperture beams are typically involved. (b) Beam parametric description for the Eq. (3).
Fig. 3
Fig. 3 Logarithm of the bi-chromatic ratio M as a function of the normalized thickness t/tS according to Eq. (4) (see text).
Fig. 4
Fig. 4 Profile error Δt/tS (%) versus the normalized profile t/tS when using Eq. (9) for different numerical apertures: NA = 0.25 (left) and NA = 0.7 (right).
Fig. 5
Fig. 5 Same as Fig. 4 but expressed as a global map of contour lines.
Fig. 6
Fig. 6 Relation between the depth of field (DOF) and the numerical aperture NA (left) or the lateral resolution δ (right) and for the wavelengths λ = 0.7 μm (red) and λ = 0.4 μm (blue).
Fig. 7
Fig. 7 Graphical description of the combined effect of high NA beams, depth of field (DOF) and the surface height features. We assume index matching to simplify ray trajectories. Left: DOF concept, typically determined by the diffraction limit. Right: some focusing situations: numbers 1 and 4 represent focused images of the sample surface features within the DOF range. We may also have an observation out of focus (2) and/or out of DOF range (3).
Fig. 8
Fig. 8 Description of the smoothing effect of a high NA beam profiling a tall step. We assume index matching to simplify ray trajectories. The discontinuous line represents the observed profile (see text).
Fig. 9
Fig. 9 (a-b) Images of the exit port of an integrating sphere with an opal diffuser and a flat window on it. The integrating sphere is internally illuminated from a monochromator light source at λA and λR spectral bands. The signal level (~color) is proportional to the respective light radiances LA and LR. (c) Linear profiles along the drawn line of these radiances (blue and red lines respectively) and its ratio LA/LR (black line). Notice the high uniformity of the ratio ( ± 0.05%) compared with the less uniform original radiances.
Fig. 10
Fig. 10 (a-b) Topographic images of a micro-optical Fresnel lens measured at the central part. (c-d) Linear profiles along vertical and horizontal lines drawn up-left.
Fig. 11
Fig. 11 (a-c) Topographic images of a close-up area of a blazed DOE for laser pattern projection and (d) linear profile taken along an arbitrary location. Abrupt steps are captured within the lateral resolution (see text).
Fig. 12
Fig. 12 (a-b) Topographic images of a micro-prismatic array of cube-corners. (c) Slope map estimated from topographic data. (d) Detail of linear profile corresponding to an edge to flank trajectory with expected corner angle of 90°.
Fig. 13
Fig. 13 (a) Topographic image of a linear prismatic array (apex of 90°) used in TIR light conductive tubes. (b) Map of calculated absolute slope.
Fig. 14
Fig. 14 Topographic close-up images of the ridges (a) and valleys (b) of a prism array (see text). Notice the different scale for each axis.

Equations (11)

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t= t 0 ln( M ) t S ,
Δt=( ΔM /M ) t S ,
ϕ= A S 2π L 0 T 0 σ sin(θ)cos(θ)exp( αt / cos(θ) )dθ ,
M= L 0A T A L 0R T R I(σ, α A ,t) I(σ, α R ,t) .
0 σ sin(θ)cos(θ)exp( αt cos(θ) )dθ sin 2 (σ) 2 +αt( cos(σ)1 )+..,
M= L 0A T A L 0R T R 1+2 α A t cosσ1 sin 2 σ 1+2 α R t cosσ1 sin 2 σ = L 0A T A L 0R T R 1 α A t cos 2 (σ/2) 1 α R t cos 2 (σ/2) .
ln(M)= t 0 ( α A α R )t cos 2 (σ/2) ,
τ S = t S cos 2 (σ/2)= t S cos 2 (arcsin(NA/ n f )/2),
t= t 0 ln(M) τ S .
δ 0.61 NA λ.
DOF= λ 2 n f ( 1 1 ( NA / n f ) 2 ) λ n f N A 2 ,

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