Abstract

Ellipsometry by specular reflection has been reworked as a precise surface normal vector detection method for the geometrical shape study of a glossy object. When the object is illuminated by circularly polarized light, the surface normal vector defines the shape of the reflection polarization ellipse; the azimuth and ellipticity are determined by the angle of the incident plane and the angle of incidence, respectively. The tilt-ellipsometry principle of tilt detection is demonstrated experimentally with a metallic polygon and a cube sample.

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  15. W. A. P. Smith and E. R. Hancock, “Recovering facial shape using a statistical model of surface normal direction,” IEEE Trans. Pattern Anal. Mach. Intell.28(12), 1914–1930 (2006).
    [CrossRef] [PubMed]

2006

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process.15(6), 1653–1664 (2006).
[CrossRef] [PubMed]

W. A. P. Smith and E. R. Hancock, “Recovering facial shape using a statistical model of surface normal direction,” IEEE Trans. Pattern Anal. Mach. Intell.28(12), 1914–1930 (2006).
[CrossRef] [PubMed]

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt.45(17), 4062–4068 (2006).
[CrossRef] [PubMed]

J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt.45(22), 5453–5469 (2006).
[CrossRef] [PubMed]

2005

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

2002

1999

1996

R. Klette and K. Schlüns, “Height data from gradient fields,” Proc. SPIE2908, 204–215 (1996).
[CrossRef]

1995

L. B. Wolff and A. G. Andreou, “Polarization camera sensors,” Image Vis. Comput.13(6), 497–510 (1995).
[CrossRef]

1988

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell.10(4), 439–451 (1988).
[CrossRef]

1987

K. Koshikawa and Y. Shirai, “A model-based recognition of glossy objects using their polarimetrical properties,” Adv. Robot.2(2), 137–147 (1987).
[CrossRef]

Andreou, A. G.

L. B. Wolff and A. G. Andreou, “Polarization camera sensors,” Image Vis. Comput.13(6), 497–510 (1995).
[CrossRef]

Atkinson, G. A.

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process.15(6), 1653–1664 (2006).
[CrossRef] [PubMed]

Bensrhair, A.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Chellappa, R.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell.10(4), 439–451 (1988).
[CrossRef]

Chenault, D. B.

Frankot, R. T.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell.10(4), 439–451 (1988).
[CrossRef]

Goldstein, D. L.

Gorria, P.

Hancock, E. R.

W. A. P. Smith and E. R. Hancock, “Recovering facial shape using a statistical model of surface normal direction,” IEEE Trans. Pattern Anal. Mach. Intell.28(12), 1914–1930 (2006).
[CrossRef] [PubMed]

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process.15(6), 1653–1664 (2006).
[CrossRef] [PubMed]

Ikeuchi, K.

Kashiwagi, H.

Klette, R.

R. Klette and K. Schlüns, “Height data from gradient fields,” Proc. SPIE2908, 204–215 (1996).
[CrossRef]

Koshikawa, K.

K. Koshikawa and Y. Shirai, “A model-based recognition of glossy objects using their polarimetrical properties,” Adv. Robot.2(2), 137–147 (1987).
[CrossRef]

K. Koshikawa, “A polarimetric approach to shape understanding of glossy objects,” in Proceedings of International Joint Conference on Artificial Intelligence (Tokyo, Japan, 1979), pp. 493–495.

Lebrun, D.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Meriaudeau, F.

Miché, P.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Miyazaki, D.

Morel, O.

Saito, M.

Sato, Y.

Schlüns, K.

R. Klette and K. Schlüns, “Height data from gradient fields,” Proc. SPIE2908, 204–215 (1996).
[CrossRef]

Shaw, J. A.

Shirai, Y.

K. Koshikawa and Y. Shirai, “A model-based recognition of glossy objects using their polarimetrical properties,” Adv. Robot.2(2), 137–147 (1987).
[CrossRef]

Smith, W. A. P.

W. A. P. Smith and E. R. Hancock, “Recovering facial shape using a statistical model of surface normal direction,” IEEE Trans. Pattern Anal. Mach. Intell.28(12), 1914–1930 (2006).
[CrossRef] [PubMed]

Stolz, C.

Tyo, J. S.

Wolff, L. B.

L. B. Wolff and A. G. Andreou, “Polarization camera sensors,” Image Vis. Comput.13(6), 497–510 (1995).
[CrossRef]

Adv. Robot.

K. Koshikawa and Y. Shirai, “A model-based recognition of glossy objects using their polarimetrical properties,” Adv. Robot.2(2), 137–147 (1987).
[CrossRef]

Appl. Opt.

IEEE Trans. Image Process.

G. A. Atkinson and E. R. Hancock, “Recovery of surface orientation from diffuse polarization,” IEEE Trans. Image Process.15(6), 1653–1664 (2006).
[CrossRef] [PubMed]

IEEE Trans. Pattern Anal. Mach. Intell.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell.10(4), 439–451 (1988).
[CrossRef]

W. A. P. Smith and E. R. Hancock, “Recovering facial shape using a statistical model of surface normal direction,” IEEE Trans. Pattern Anal. Mach. Intell.28(12), 1914–1930 (2006).
[CrossRef] [PubMed]

Image Vis. Comput.

L. B. Wolff and A. G. Andreou, “Polarization camera sensors,” Image Vis. Comput.13(6), 497–510 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Eng.

P. Miché, A. Bensrhair, and D. Lebrun, “Passive 3-D shape recovery of unknown objects using cooperative polarimetric and radiometric stereo vision processes,” Opt. Eng.44(2), 027005 (2005).
[CrossRef]

Proc. SPIE

R. Klette and K. Schlüns, “Height data from gradient fields,” Proc. SPIE2908, 204–215 (1996).
[CrossRef]

Other

P. Kovesi, “Shaplets correlated with surface normals produce surface,” in Proceedings of 10th IEEE International Conference on Computer Vision (Institute of Electrical and Electronics Engineers, Beijing, 2005), pp. 994–1001.
[CrossRef]

K. Koshikawa, “A polarimetric approach to shape understanding of glossy objects,” in Proceedings of International Joint Conference on Artificial Intelligence (Tokyo, Japan, 1979), pp. 493–495.

T. Kawashima, Y. Sasaki, Y. Inoue, Y. Honma, T. Sato, S. Ohta, and S. Kawakami, “Polarization imaging camera and its application by utilizing a photonic crystal,” presented at the 32th Optical Symposium, Japan, 5–6, Jul. 2007.

R. M. A. Azzam and N. M. Bashara, Ellipsometry and polarized light (North-Holland, Amsterdam, 1988).

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Figures (9)

Fig. 1
Fig. 1

Coordinate systems of (a) reflection ellipse and (b) surface normal vector used in this manuscript. θ and ε indicate azimuth and ellipticity angles of reflection polarization, respectively. α and β show azimuth and slope angles of surface normal vector, respectively. Right circular polarization light is illuminated at incident angle ϕi and the polarized light is reflected at the reflection angle ϕr.

Fig. 2
Fig. 2

Tilt-ellipsometry concept of specular reflection shown by a spherical object observed from the z-direction. ϕn and α indicate incident angles at point n and the azimuthal angle of the incident plane, respectively.

Fig. 3
Fig. 3

Angle of incidence variations of relative complex amplitude reflectance under right circular polarization illumination plotted in a complex plane. Complex refractive indices n-ik of 1.5, 2.90-3.07i, 1.36-7.59i, and 0.385-3.41i were used for the calculation assuming glass, Fe, Al, and Au surfaces for a wavelength of 632.8 nm.

Fig. 4
Fig. 4

Angle of incidence variations of ellipticity angle ε under right circular polarization for glass, water, Fe, Al, Au, and Si surfaces for a wavelength of 632.8 nm.

Fig. 5
Fig. 5

Reflection polarization map (observed from z-direction) of expected specular surface reflection of a metallic sphere under right circular polarization illumination. Shading in the middle shows the region of left-handed polarization.

Fig. 6
Fig. 6

Experimental setup for proof-of-concept experiments. Circular polarization illumination was made by a commercially available circular polarizing film rolled and inserted in the dome-type illuminator. A rotating analyzer method was used for reflection polarization measurements with a Polaroid sheet. An interference filter for a wavelength of 632.8 nm was used.

Fig. 7
Fig. 7

Photographs of Au-coated polygon and stainless steel cube for tilt-ellipsometry measurements.

Fig. 8
Fig. 8

(a) and (b) Measured polarization maps of azimuth of Au-coated polygon and stainless steel cube, respectively; (c) and (d) Ellipticity angle of Au-coated polygon and stainless steel cube, respectively. Imperfections in the right circular polarization illumination in the left middle area in (a) and (c) were caused by the connection of the rolled polarizing film shown in Fig. 5.

Fig. 9
Fig. 9

(a) 3D shapes of a polygon and (b) cube reconstructed using the measured reflection ellipse shown in Fig. 8.

Equations (5)

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

E out =T(α)ST(α) E in .
T(α)=( 1 0 0 0 0 cos2α sin2α 0 0 sin2α cos2α 0 0 0 0 1 ),
S=( 1 cos2Ψ 0 0 cos2Ψ 1 0 0 0 0 sin2ΨcosΔ sin2ΨsinΔ 0 0 sin2ΨsinΔ sin2ΨcosΔ ),
E out =( 1 cos2αcos2Ψ+sin2αsin2ΨsinΔ sin2αcos2Ψ+cos2αsin2ΨsinΔ sin2ΨcosΔ ).
E out =( 1 cos2αcos2Ψ sin2αcos2Ψ 0 ).

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