Abstract

A method is proposed for separating light reflected from turbid media with a rough surface into a bulk and a surface component. Dye is added to the sample, thereby increasing absorption and canceling bulk scattering. The remaining reflected light is surface reflectance, which can be subtracted from the total reflectance of an undyed sample to obtain the bulk component. The method is applied to paper where the addition of dye is accomplished by inkjet printing. The results show that the bulk scattered light is efficiently canceled, and that both the spectrally neutral surface reflectance and the surface topography of the undyed paper is maintained. The proposed method is particularly suitable for characterization of dielectric, highly randomized materials with significant bulk reflectance and rough surfaces, which are difficult to analyze with existing methods. A reliable separation method opens up for new ways of analyzing, e.g., biological tissues and optical coatings, and is also a valuable tool in the development of more comprehensive reflectance models.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  32. J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
    [CrossRef]

2011

2010

2009

2008

P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” Inverse Probl. Sci. Eng. 16, 927–951 (2008).
[CrossRef]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, “Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis,” Opt. Commun. 281, 1739–1744 (2008).
[CrossRef]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces and bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

2006

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 06603 (2006).
[CrossRef]

2005

2004

2002

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

1999

T. Germer and C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

1997

1995

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227–251 (1995).
[CrossRef]

S. Krishnan, “Mueller-matrix ellipsometry on electroformed rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
[CrossRef]

1994

1991

X. D. He, K. E. Torrance, F. Sillion, and D. Greenberg, “A comprehensive physical model for light-reflection,” Comput. Graph. 25, 175–186 (1991).
[CrossRef]

1981

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

1970

R. M. Leekley, C. W. Denzer, and R. F. Tyler, “Measurement of surface reflection from paper and prints,” Tappi J. 53, 615–621 (1970).

Allen, G.

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Amra, C.

Apostol, A.

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 06603 (2006).
[CrossRef]

Arnaud, L.

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
[CrossRef]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, “Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis,” Opt. Commun. 281, 1739–1744 (2008).
[CrossRef]

Ashikhmin, M.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in Proceedings of SIGGRAPH 2000 (ACM, 2000), pp. 65–74.

Asmail, C.

T. Germer and C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

Castiglione, P.

Conrath, J.

G. Latour, G. Georges, L. S. Lamoine, C. Deumié, and J. Conrath, “Light scattering from human corneal grafts: bulk and surface contribution,” J. Appl. Phys. 108, 053104 (2010).
[CrossRef]

Cook, R. L.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

Dalton, J.

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Denzer, C. W.

R. M. Leekley, C. W. Denzer, and R. F. Tyler, “Measurement of surface reflection from paper and prints,” Tappi J. 53, 615–621 (1970).

Deumie, C.

Deumié, C.

G. Latour, G. Georges, L. S. Lamoine, C. Deumié, and J. Conrath, “Light scattering from human corneal grafts: bulk and surface contribution,” J. Appl. Phys. 108, 053104 (2010).
[CrossRef]

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
[CrossRef]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces and bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, “Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis,” Opt. Commun. 281, 1739–1744 (2008).
[CrossRef]

O. Gilbert, C. Deumié, and C. Amra, “Angle-resolved ellipsometry of scattering patterns from arbitrary surfaces and bulks,” Opt. Express 13, 2403–2418 (2005).
[CrossRef]

Dogariu, A.

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 06603 (2006).
[CrossRef]

Edström, P.

M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. I. Theory,” J. Opt. Soc. Am. A 27, 1032–1039 (2010).
[CrossRef]

M. Neuman and P. Edström, “Anisotropic reflectance from turbid media. II. Measurements,” J. Opt. Soc. Am. A 27, 1040–1045 (2010).
[CrossRef]

P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” Inverse Probl. Sci. Eng. 16, 927–951 (2008).
[CrossRef]

P. Edström, “A fast and stable solution method for the radiative transfer problem,” SIAM Rev. 47, 447–468 (2005).
[CrossRef]

Elias, G.

Elias, M.

Elton, N.

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Foo, S.-C.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in Proceedings of SIGGRAPH 1997 (ACM, 1997), pp. 117–126.

Georges, G.

G. Latour, G. Georges, L. S. Lamoine, C. Deumié, and J. Conrath, “Light scattering from human corneal grafts: bulk and surface contribution,” J. Appl. Phys. 108, 053104 (2010).
[CrossRef]

L. Arnaud, G. Georges, J. Sorrentini, M. Zerrad, C. Deumié, and C. Amra, “An enhanced contrast to detect bulk objects under arbitrary rough surfaces,” Opt. Express 17, 5758–5773 (2009).
[CrossRef]

C. Amra, M. Zerrad, L. Siozade, G. Georges, and C. Deumié, “Partial polarization of light induced by random defects at surfaces and bulks,” Opt. Express 16, 10372–10383 (2008).
[CrossRef]

L. Arnaud, G. Georges, C. Deumié, and C. Amra, “Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis,” Opt. Commun. 281, 1739–1744 (2008).
[CrossRef]

Germer, T.

T. Germer and C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

T. Germer, “Angular dependence and polarization of out-of-plane optical scattering from particulate contamination, subsurface defects, and surface microroughness,” Appl. Opt. 36, 8798–8805 (1997).
[CrossRef]

Gilbert, O.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS monograph 160 (National Bureau of Standards, 1977).

Greenberg, D.

X. D. He, K. E. Torrance, F. Sillion, and D. Greenberg, “A comprehensive physical model for light-reflection,” Comput. Graph. 25, 175–186 (1991).
[CrossRef]

Greenberg, D. P.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in Proceedings of SIGGRAPH 1997 (ACM, 1997), pp. 117–126.

Haefner, D.

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 06603 (2006).
[CrossRef]

Hanrahan, P.

P. Hanrahan and W. Krueger, “Reflection from layered surfaces due to subsurface scattering,” in Proceedings of SIGGRAPH 1993 (ACM, 1993), pp. 165–174.

He, X. D.

X. D. He, K. E. Torrance, F. Sillion, and D. Greenberg, “A comprehensive physical model for light-reflection,” Comput. Graph. 25, 175–186 (1991).
[CrossRef]

Heard, P.

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS monograph 160 (National Bureau of Standards, 1977).

Husband, J.

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Krishnan, S.

S. Krishnan, “Mueller-matrix ellipsometry on electroformed rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
[CrossRef]

Krueger, W.

P. Hanrahan and W. Krueger, “Reflection from layered surfaces due to subsurface scattering,” in Proceedings of SIGGRAPH 1993 (ACM, 1993), pp. 165–174.

Lacoste, D.

Lafortune, E. P. F.

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in Proceedings of SIGGRAPH 1997 (ACM, 1997), pp. 117–126.

Lamoine, L. S.

G. Latour, G. Georges, L. S. Lamoine, C. Deumié, and J. Conrath, “Light scattering from human corneal grafts: bulk and surface contribution,” J. Appl. Phys. 108, 053104 (2010).
[CrossRef]

Latour, G.

G. Latour, G. Georges, L. S. Lamoine, C. Deumié, and J. Conrath, “Light scattering from human corneal grafts: bulk and surface contribution,” J. Appl. Phys. 108, 053104 (2010).
[CrossRef]

Leekley, R. M.

R. M. Leekley, C. W. Denzer, and R. F. Tyler, “Measurement of surface reflection from paper and prints,” Tappi J. 53, 615–621 (1970).

Lenke, R.

Li, H.

S. H. Westin, H. Li, and K. E. Torrance, “A comparision of four BRDF models,” Tech. Rep.  (Cornell University, 2004).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS monograph 160 (National Bureau of Standards, 1977).

Mattson, L.

L. Mattson and R. Usbeck, “Technique for analysis of surface and bulk scattering of paper sheets,” in Proceedings of TAPPI 1996 International Printing & Graphics Art Conference (TAPPI, 1996).

Nayar, S. K.

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227–251 (1995).
[CrossRef]

Neuman, M.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS monograph 160 (National Bureau of Standards, 1977).

Oren, M.

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227–251 (1995).
[CrossRef]

Premoze, S.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in Proceedings of SIGGRAPH 2000 (ACM, 2000), pp. 65–74.

Preston, J.

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS monograph 160 (National Bureau of Standards, 1977).

Rojas-Ochoa, L. F.

Scheffold, F.

Schurtenberger, P.

Shirley, P.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in Proceedings of SIGGRAPH 2000 (ACM, 2000), pp. 65–74.

Sillion, F.

X. D. He, K. E. Torrance, F. Sillion, and D. Greenberg, “A comprehensive physical model for light-reflection,” Comput. Graph. 25, 175–186 (1991).
[CrossRef]

Simonot, L.

Siozade, L.

Soriano, G.

Sorrentini, J.

Stover, J. C.

J. C. Stover, Optical Scattering, 2nd ed. (SPIE, 1995).

Torrance, K. E.

X. D. He, K. E. Torrance, F. Sillion, and D. Greenberg, “A comprehensive physical model for light-reflection,” Comput. Graph. 25, 175–186 (1991).
[CrossRef]

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in Proceedings of SIGGRAPH 1997 (ACM, 1997), pp. 117–126.

S. H. Westin, H. Li, and K. E. Torrance, “A comparision of four BRDF models,” Tech. Rep.  (Cornell University, 2004).

Tyler, R. F.

R. M. Leekley, C. W. Denzer, and R. F. Tyler, “Measurement of surface reflection from paper and prints,” Tappi J. 53, 615–621 (1970).

Usbeck, R.

L. Mattson and R. Usbeck, “Technique for analysis of surface and bulk scattering of paper sheets,” in Proceedings of TAPPI 1996 International Printing & Graphics Art Conference (TAPPI, 1996).

Westin, S. H.

S. H. Westin, H. Li, and K. E. Torrance, “A comparision of four BRDF models,” Tech. Rep.  (Cornell University, 2004).

Wolff, L. B.

Zerrad, M.

Appl. Opt.

Colloids Surf. A

J. Preston, N. Elton, J. Husband, J. Dalton, P. Heard, and G. Allen, “Investigation into the distribution of ink components on printed coated paper Part 1: optical and roughness considerations,” Colloids Surf. A, 205, 183–198 (2002).
[CrossRef]

Comput. Graph.

R. L. Cook and K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

X. D. He, K. E. Torrance, F. Sillion, and D. Greenberg, “A comprehensive physical model for light-reflection,” Comput. Graph. 25, 175–186 (1991).
[CrossRef]

Int. J. Comput. Vis.

M. Oren and S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Comput. Vis. 14, 227–251 (1995).
[CrossRef]

Inverse Probl. Sci. Eng.

P. Edström, “A two-phase parameter estimation method for radiative transfer problems in paper industry applications,” Inverse Probl. Sci. Eng. 16, 927–951 (2008).
[CrossRef]

J. Appl. Phys.

G. Latour, G. Georges, L. S. Lamoine, C. Deumié, and J. Conrath, “Light scattering from human corneal grafts: bulk and surface contribution,” J. Appl. Phys. 108, 053104 (2010).
[CrossRef]

J. Mod. Opt.

S. Krishnan, “Mueller-matrix ellipsometry on electroformed rough surfaces,” J. Mod. Opt. 42, 1695–1706 (1995).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

L. Arnaud, G. Georges, C. Deumié, and C. Amra, “Discrimination of surface and bulk scattering of arbitrary level based on angle-resolved ellipsometry: theoretical analysis,” Opt. Commun. 281, 1739–1744 (2008).
[CrossRef]

Opt. Express

Phys. Rev. E

A. Apostol, D. Haefner, and A. Dogariu, “Near-field characterization of effective optical interfaces,” Phys. Rev. E 74, 06603 (2006).
[CrossRef]

Rev. Sci. Instrum.

T. Germer and C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688–3695 (1999).
[CrossRef]

SIAM Rev.

P. Edström, “A fast and stable solution method for the radiative transfer problem,” SIAM Rev. 47, 447–468 (2005).
[CrossRef]

Tappi J.

R. M. Leekley, C. W. Denzer, and R. F. Tyler, “Measurement of surface reflection from paper and prints,” Tappi J. 53, 615–621 (1970).

Other

L. Mattson and R. Usbeck, “Technique for analysis of surface and bulk scattering of paper sheets,” in Proceedings of TAPPI 1996 International Printing & Graphics Art Conference (TAPPI, 1996).

J. C. Stover, Optical Scattering, 2nd ed. (SPIE, 1995).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Geometrical Considerations and Nomenclature for Reflectance, NBS monograph 160 (National Bureau of Standards, 1977).

P. Hanrahan and W. Krueger, “Reflection from layered surfaces due to subsurface scattering,” in Proceedings of SIGGRAPH 1993 (ACM, 1993), pp. 165–174.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in Proceedings of SIGGRAPH 2000 (ACM, 2000), pp. 65–74.

S. H. Westin, H. Li, and K. E. Torrance, “A comparision of four BRDF models,” Tech. Rep.  (Cornell University, 2004).

E. P. F. Lafortune, S.-C. Foo, K. E. Torrance, and D. P. Greenberg, “Non-linear approximation of reflectance functions,” in Proceedings of SIGGRAPH 1997 (ACM, 1997), pp. 117–126.

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Figures (7)

Fig. 1.
Fig. 1.

(a) Reflected light, Φr, consists of both surface reflectance Φs and bulk reflectance Φb when the sample is unprinted. By printing the sample with (b) cyan and (c) magenta ink, the bulk component can be canceled for wavelengths within the absorption band of the dyes, centered around λc640nm and λm550nm. The reflected light is then due to surface reflection, and subtracting this from the total reflectance of the unprinted sample gives the bulk reflectance.

Fig. 2.
Fig. 2.

Light microscopy images of matte photo paper. The image to the left shows an unprinted sample and the image to the right a sample printed with four layers of cyan ink. The size of each sample is 3.4mm×2.3mm.

Fig. 3.
Fig. 3.

Defining angles and measurement geometry when using the ARTA goniophotometer accessory for goniophotometric measurement.

Fig. 4.
Fig. 4.

Radiance factor of a sample printed with one to four layers of magenta ink measured in a 45°/45° geometry, together with corresponding measurement on the unprinted sample and on a black diffuse reflectance standard with a nominal 8/d-reflectance factor of 0.02. The radiance factor reaches a minimum already at one layer of ink, which is evident from the bottom image where the absorption band of the magenta ink is shown in greater detail.

Fig. 5.
Fig. 5.

Separation of reflected radiance from an unprinted sample into its surface and bulk components using measurements at 640 nm and light incident at an angle of θi=45°. The bulk contribution is obtained by subtracting the surface component, estimated from C4, from the total reflectance of the unprinted sample.

Fig. 6.
Fig. 6.

Surface component of the reflected radiance factor, estimated at wavelengths 640 and 550 nm by measurements on two samples printed with four overlapping layers of cyan and magenta ink, respectively. The angle of incidence is θi=45°. No spectral dependence of the surface component is observed since the two curves coincide.

Fig. 7.
Fig. 7.

Power spectral density spectra of topography measurement, averaged over wavelength bins 1/8 of an octave wide. No significant difference can be observed between the printed (C4) and unprinted (U) samples.

Equations (1)

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β(λ)=Φr(λ)Φi(λ)·πωrcosθr,

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