Abstract

Optical absorbance within a liquid is used as a photometric probe to measure the topography of optical surfaces relative to a reference. The liquid fills the gap between the reference surface and the measuring surface. By comparing two transmission images at different wavelengths we can profile the height distribution in a simple and reliable way. The presented method handles steep surface slopes (<90°) without difficulty. It adapts well to any field of view and height range (peak to valley). A height resolution in the order of the nanometer may be achieved and the height range can be tailored by adapting the concentration of water soluble dyes. It is especially appropriate for 3D profiling of transparent complex optical surfaces, like those found in micro-optic arrays and for Fresnel, aspheric or free-form lenses, which are very difficult to measure by other optical methods. We show some experimental results to validate its capabilities as a metrological tool and handling of steep surface slopes.

© 2012 OSA

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References

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2012

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News23(6), 30–35 (2012).
[CrossRef]

2011

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. SPIE8169, 816910-8 (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

2008

M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc.231(1), 156–167 (2008).
[CrossRef] [PubMed]

2007

2006

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE6024, 602401, 602401-11 (2006).
[CrossRef]

2004

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–243 (2004).
[CrossRef]

2002

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002).
[CrossRef]

C. H. Lee, H. Y. Mong, and W. C. Lin, “Noninterferometric wide-field optical profilometry with nanometer depth resolution,” Opt. Lett.27(20), 1773–1775 (2002).
[CrossRef] [PubMed]

2001

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001).
[CrossRef]

2000

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

1997

1994

1955

G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res.9(3), 428–433 (1955).
[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. SPIE8169, 816910-8 (2011).
[CrossRef]

Blais, F.

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–243 (2004).
[CrossRef]

Blank, J. L.

M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc.231(1), 156–167 (2008).
[CrossRef] [PubMed]

Bor, Z.

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Csete, M.

Davies, A.

de Groot, P.

Deck, L.

Farahi, F.

Glover, P.

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002).
[CrossRef]

Glover, P. W. J.

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001).
[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. SPIE8169, 816910-8 (2011).
[CrossRef]

Harris, T.

Hsu, I. J.

Isakov, E.

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002).
[CrossRef]

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001).
[CrossRef]

Johnson, J.

Khitrin, A. K.

M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc.231(1), 156–167 (2008).
[CrossRef] [PubMed]

Lai, C. C.

Lee, C. H.

Lin, W. C.

Liu, J.

Liu, T.

Martínez Antón, J. C.

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. SPIE8169, 816910-8 (2011).
[CrossRef]

Model, M. A.

M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc.231(1), 156–167 (2008).
[CrossRef] [PubMed]

Mong, H. Y.

Ogilvie, S.

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002).
[CrossRef]

Ogilvie, S. R.

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001).
[CrossRef]

Ottevaere, H.

Purcell, D.

Quiroga, 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. SPIE8169, 816910-8 (2011).
[CrossRef]

Rolland, J. P.

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News23(6), 30–35 (2012).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Suratkar, A.

Svensson, G.

G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res.9(3), 428–433 (1955).
[CrossRef] [PubMed]

Tan, J.

Tang, J.

Taylor, C.

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002).
[CrossRef]

Taylor, C. W.

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001).
[CrossRef]

Thienpont, H.

Thompson, K. P.

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News23(6), 30–35 (2012).
[CrossRef]

Wyant, J. C.

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE6024, 602401, 602401-11 (2006).
[CrossRef]

Zhao, C.

Appl. Opt.

Earth Planet. Sci. Lett.

E. Isakov, S. R. Ogilvie, C. W. Taylor, and P. W. J. Glover, “Fluid flow through rough fractures in rocks 1: high resolution aperture determinations,” Earth Planet. Sci. Lett.191(3-4), 267–282 (2001).
[CrossRef]

Exp. Cell Res.

G. Svensson, “A method for measurement of the absorption in extremely high-absorbing solutions,” Exp. Cell Res.9(3), 428–433 (1955).
[CrossRef] [PubMed]

Image Anal. Stereol.

S. Ogilvie, E. Isakov, C. Taylor, and P. Glover, “A new high resolution optical method for obtaining the topography of fracture surfaces in rocks,” Image Anal. Stereol.21(1), 61–66 (2002).
[CrossRef]

J. Electron. Imaging

F. Blais, “Review of 20 years of range sensor development,” J. Electron. Imaging13(1), 231–243 (2004).
[CrossRef]

J. Microsc.

M. A. Model, A. K. Khitrin, and J. L. Blank, “Measurement of the absorption of concentrated dyes and their use for quantitative imaging of surface topography,” J. Microsc.231(1), 156–167 (2008).
[CrossRef] [PubMed]

Opt. Eng.

F. Chen, G. M. Brown, and M. Song, “Overview of three-dimensional shape measurement using optical methods,” Opt. Eng.39(1), 10–22 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Opt. Photon. News

K. P. Thompson and J. P. Rolland, “A revolution in imaging optical design,” Opt. Photon. News23(6), 30–35 (2012).
[CrossRef]

Proc. SPIE

J. C. Wyant, “Advances in interferometric surface measurement,” Proc. SPIE6024, 602401, 602401-11 (2006).
[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. SPIE8169, 816910-8 (2011).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Basic configuration for the sample to be measured.

Fig. 2
Fig. 2

Absorption spectra of methyl violet dye in water (blue line) and the laser lines used for reference (red) and for sampling (green) in the measurements.

Fig. 3
Fig. 3

(a) Image of a thin wedge between flats and partially filled with absorbing fluid. Interference fringes are observed at the air gap. (b) Signal profile along the line drawn in (a). Notice the exponential decay in the absorption region and the fringe contrast in the air gap side. (c) Topographic image of the wedge of by processing the image of (a) applying Eq. (4). (d) Height profile along the line drawn in (c), ordinate axis is in microns.

Fig. 4
Fig. 4

Residuals of a regression fit to a plane for the image of Fig. 4. Regression is only computed within the red polygon drawn.

Fig. 5
Fig. 5

Images of the synthetic transmittance M of a plano-convex lens: (a) measurement in day 1 and (b) after 5 days and rotating and displacing the lens to test reproducibility.

Fig. 6
Fig. 6

Results on the spherical surface of a spherical lens (R = 5151mm). (a) Regression fit residuals of the processed measurements of Fig. 5(a). (b) the same as (a) but for Fig. 5(b). (b) and (d) are linear profiles of fit residuals along the lines drawn in (a) and (c) respectively.

Fig. 7
Fig. 7

Topography of a cylindrical lens array. (a) 3D rendering of a profilometric measurement. (b) Partial linear profile along a line perpendicular to the array axis.

Fig. 8
Fig. 8

Prismatic array. (a) image ratio M, (b) partial height profile perpendicular to prism edges (c) 3D representation of the full field of view.

Fig. 9
Fig. 9

Linear array of prisms (apex of 60°). (a) 3D rendering of processed image ratio M, (b) height profile along a line perpendicular to prism wedges. Notice the horizontal and vertical scales are the same in both representations.

Equations (5)

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L= L 0 Texp( αt ),
M= L 0A T A exp( α A t ) L 0R T R exp( α R t ) =Cexp[ ( α A α R )t ],
M=exp[ α S (t t 0 ) ],
t= t 0 ln( M ) t S ,
Δt=( ΔM /M ) t S ,

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