Abstract

Since polarimetry has extended its use for the study of scattering from surfaces and tissues, Spectralon, a white reflectance standard, is acquiring the role of a polarimetric standard. Both the behavior of Spectralon as a Lambertian surface and its performance as a perfect depolarizer are analyzed in detail. The accuracy of our dynamic polarimeter, together with the polar decomposition to describe the Mueller matrix (MM) depolarizing action, combine to produce a powerful tool for the proper analysis of this scattering surface. Results allowed us to revisit, for confirmation or revision, the role of some MM elements, as described in the bibliography. The conditions under which it can be considered a good Lambertian surface are specified in terms of incidence and scattering angle and verified over a large wavelength range.

© 2013 Optical Society of America

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References

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    [CrossRef]
  34. A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
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    [CrossRef]

2012 (2)

Ø. Svensen, M. Kildemo, J. Maria, J. J. Stamnes, and Ø. Frette, “Mueller matrix measurements and modeling pertaining to Spectralon white reflectance standards,” Opt. Express 20, 15045–15053 (2012).
[CrossRef]

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

2011 (3)

2010 (1)

A. Hope and K. O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

2009 (4)

2007 (3)

2006 (2)

2005 (2)

G. T. Georgiev and J. J. Butler, “The effect of speckle on BRDF measurements,” Proc. SPIE 5882, 588203 (2005).
[CrossRef]

S. Kaasalainen, E. Ahokas, J. Hyyppä, and J. Suomalainen, “Study of surface brightness from backscattered intensity: calibration of laser data,” IEEE Geosci. Remote Sens. Lett. 2, 255–259 (2005).
[CrossRef]

2004 (3)

C. Collet, J. Zallat, and Y. Takakura, “Clustering of Mueller matrix images for skeletonized structure detection,” Opt. Express 12, 1271–1280 (2004).

M. Smith, “Polarization metrology moves beyond home-brewed solutions,” Laser Focus World 40, 123–129 (2004).

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

2002 (2)

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41, 1013–1020 (2002).
[CrossRef]

M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt. 41, 2488–2493 (2002).
[CrossRef]

2000 (1)

1999 (2)

D. H. Goldstein, D. B. Chenault, and J. L. Pezzaniti, “Polarimetric characterization of Spectralon,” Proc. SPIE 3754, 126–136 (1999).
[CrossRef]

D. A. Haner, B. T. McGuckin, and C. J. Bruegge, “Polarization characteristics of Spectralon illuminated by coherent light,” Appl. Opt. 38, 6350–6356 (1999).
[CrossRef]

1998 (1)

1996 (2)

1987 (1)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar pecomposition of its Mueller matrix,” Optik 76, 67–71 (1987).

1986 (2)

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

1981 (1)

1978 (1)

Ahokas, E.

S. Kaasalainen, E. Ahokas, J. Hyyppä, and J. Suomalainen, “Study of surface brightness from backscattered intensity: calibration of laser data,” IEEE Geosci. Remote Sens. Lett. 2, 255–259 (2005).
[CrossRef]

Albella, P.

J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Azzam, R. M. A.

Bernabeu, E.

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar pecomposition of its Mueller matrix,” Optik 76, 67–71 (1987).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

Bhandari, A. A.

Bonsey, S. J.

Brothers, A. M.

Bruegge, C. J.

Buddhiwant, P.

Butler, J. J.

G. T. Georgiev and J. J. Butler, “The effect of speckle on BRDF measurements,” Proc. SPIE 5882, 588203 (2005).
[CrossRef]

Campos, J.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Chen, Z.

Chenault, D. B.

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41, 1013–1020 (2002).
[CrossRef]

D. H. Goldstein, D. B. Chenault, and J. L. Pezzaniti, “Polarimetric characterization of Spectralon,” Proc. SPIE 3754, 126–136 (1999).
[CrossRef]

Chipman, R. A.

Chung, J.

Cloude, S. R.

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

Collet, C.

Corróns, A.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

De Martino, A.

Edgar, H.

Esproles, C.

Ferrero, A.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Foldyna, M.

Fontecha, J. L.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Frette, Ø.

García-Caurel, E.

Georgiev, G. T.

G. T. Georgiev and J. J. Butler, “The effect of speckle on BRDF measurements,” Proc. SPIE 5882, 588203 (2005).
[CrossRef]

Germer, T. A.

T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE 8160, 81600D (2011).
[CrossRef]

Ghosh, N.

Gil, J.

Gil, J. J.

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

J. J. Gil, “Characteristic properties of Mueller matrices,” J. Opt. Soc. Am. A 17, 328–334 (2000).
[CrossRef]

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar pecomposition of its Mueller matrix,” Optik 76, 67–71 (1987).

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

Goldstein, D. H.

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41, 1013–1020 (2002).
[CrossRef]

D. H. Goldstein, D. B. Chenault, and J. L. Pezzaniti, “Polarimetric characterization of Spectralon,” Proc. SPIE 3754, 126–136 (1999).
[CrossRef]

González, F.

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: ellipsometric rule-of-thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Gupta, P. K.

Guyot, S.

Hammer-Wilson, M. J.

Hamre, B.

Haner, D. A.

Hauer, K. O.

A. Hope and K. O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

Hope, A.

A. Hope and K. O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

Hsia, J. J.

Hyyppä, J.

S. Kaasalainen, E. Ahokas, J. Hyyppä, and J. Suomalainen, “Study of surface brightness from backscattered intensity: calibration of laser data,” IEEE Geosci. Remote Sens. Lett. 2, 255–259 (2005).
[CrossRef]

Jung, W.

Kaasalainen, S.

S. Kaasalainen, E. Ahokas, J. Hyyppä, and J. Suomalainen, “Study of surface brightness from backscattered intensity: calibration of laser data,” IEEE Geosci. Remote Sens. Lett. 2, 255–259 (2005).
[CrossRef]

Kildemo, M.

Li, X.

Lu, S. Y.

Manhas, S.

Maria, J.

Martino, A. D.

McGuckin, B. T.

Menzies, R. T.

Mishchenko, I. A.

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

Mishchenko, L. T.

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

Moreno, F.

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: ellipsometric rule-of-thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Muttiah, R. S.

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

Oberemok, Y. A.

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

Ossikovski, R.

Patrick, H. J.

T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE 8160, 81600D (2011).
[CrossRef]

Pezzaniti, J. L.

D. H. Goldstein, D. B. Chenault, and J. L. Pezzaniti, “Polarimetric characterization of Spectralon,” Proc. SPIE 3754, 126–136 (1999).
[CrossRef]

Pons, A.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Rabal, A. M.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Rod White, D.

Rubiño, A. M.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Saiz, J. M.

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: ellipsometric rule-of-thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Sanz, J. M.

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: ellipsometric rule-of-thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

Saunders, P.

Savenkov, S. N.

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

Smith, M.

M. Smith, “Polarization metrology moves beyond home-brewed solutions,” Laser Focus World 40, 123–129 (2004).

Smith, M. H.

Stamnes, J. J.

Suomalainen, J.

S. Kaasalainen, E. Ahokas, J. Hyyppä, and J. Suomalainen, “Study of surface brightness from backscattered intensity: calibration of laser data,” IEEE Geosci. Remote Sens. Lett. 2, 255–259 (2005).
[CrossRef]

Svensen, Ø.

Swami, M. K.

Takakura, Y.

Uppal, A.

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

van de Ven, J.

Voss, K. J.

Weidner, V. R.

Wilder-Smith, P.

Yao, G.

Zallat, J.

Zhang, D.

Zhao, L.

Appl. Opt. (9)

D. Rod White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450–3454 (1998).
[CrossRef]

B. T. McGuckin, D. A. Haner, R. T. Menzies, C. Esproles, and A. M. Brothers, “Directional reflectance characterization facility and measurement methodology,” Appl. Opt. 35, 4827–4834 (1996).
[CrossRef]

D. A. Haner, B. T. McGuckin, and C. J. Bruegge, “Polarization characteristics of Spectralon illuminated by coherent light,” Appl. Opt. 38, 6350–6356 (1999).
[CrossRef]

M. H. Smith, “Optimization of a dual-rotating-retarder Mueller matrix polarimeter,” Appl. Opt. 41, 2488–2493 (2002).
[CrossRef]

K. J. Voss and D. Zhang, “Bidirectional reflectance of dry and submerged Labsphere Spectralon plaque,” Appl. Opt. 45, 7924–7927 (2006).
[CrossRef]

J. Chung, W. Jung, M. J. Hammer-Wilson, P. Wilder-Smith, and Z. Chen, “Use of polar decomposition for the diagnosis of oral precancer,” Appl. Opt. 46, 3038–3045 (2007).
[CrossRef]

X. Li and G. Yao, “Mueller matrix decomposition of diffuse reflectance imaging in skeletal muscle,” Appl. Opt. 48, 2625–2631 (2009).
[CrossRef]

A. A. Bhandari, B. Hamre, Ø. Frette, L. Zhao, J. J. Stamnes, and M. Kildemo, “Bidirectional reflectance distribution function of Spectralon white reflectance standard illuminated by incoherent unpolarized and planepolarized light,” Appl. Opt. 50, 2431–2442 (2011).
[CrossRef]

J. M. Sanz, J. M. Saiz, F. González, and F. Moreno, “Polar decomposition of the Mueller matrix: ellipsometric rule-of-thumb for square-profile surface structure recognition,” Appl. Opt. 50, 3781–3788 (2011).
[CrossRef]

Eur. Phys. J. Appl. Phys. (1)

J. J. Gil, “Polarimetric characterization of light and media,” Eur. Phys. J. Appl. Phys. 40, 1–47 (2007).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

S. Kaasalainen, E. Ahokas, J. Hyyppä, and J. Suomalainen, “Study of surface brightness from backscattered intensity: calibration of laser data,” IEEE Geosci. Remote Sens. Lett. 2, 255–259 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

J. Quant. Spectrosc. Radiat. Transfer (2)

J. M. Sanz, P. Albella, F. Moreno, J. M. Saiz, and F. González, “Application of the polar decomposition to light scattering particle systems,” J. Quant. Spectrosc. Radiat. Transfer 110, 1369–1374 (2009).
[CrossRef]

S. N. Savenkov, L. T. Mishchenko, R. S. Muttiah, Y. A. Oberemok, and I. A. Mishchenko, “Mueller polarimetry of virus-infected and healthy wheat under field and microgravity conditions,” J. Quant. Spectrosc. Radiat. Transfer 88, 327–343 (2004).
[CrossRef]

Laser Focus World (1)

M. Smith, “Polarization metrology moves beyond home-brewed solutions,” Laser Focus World 40, 123–129 (2004).

Metrologia (2)

A. Hope and K. O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio-spectrophotometer for the absolute measurement of the spectral BRDF at in- out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Opt. Acta (1)

J. J. Gil and E. Bernabeu, “Depolarization and polarization indices of an optical system,” Opt. Acta 33, 185–189 (1986).
[CrossRef]

Opt. Eng. (1)

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41, 1013–1020 (2002).
[CrossRef]

Opt. Express (4)

Opt. Lett. (2)

Optik (2)

J. J. Gil and E. Bernabeu, “Obtainment of the polarizing and retardation parameters of a non-depolarizing optical system from the polar pecomposition of its Mueller matrix,” Optik 76, 67–71 (1987).

S. R. Cloude, “Group theory and polarization algebra,” Optik 75, 26–36 (1986).

Proc. SPIE (3)

T. A. Germer and H. J. Patrick, “Mueller matrix bidirectional reflectance distribution function measurements and modeling of diffuse reflectance standards,” Proc. SPIE 8160, 81600D (2011).
[CrossRef]

G. T. Georgiev and J. J. Butler, “The effect of speckle on BRDF measurements,” Proc. SPIE 5882, 588203 (2005).
[CrossRef]

D. H. Goldstein, D. B. Chenault, and J. L. Pezzaniti, “Polarimetric characterization of Spectralon,” Proc. SPIE 3754, 126–136 (1999).
[CrossRef]

Other (3)

H. C. van de Hulst, Light Scattering by Small Particles (Dover, 1981).

OSA, Handbook of Optics, Vol. 1, Chap. 14–16 (McGraw-Hill, 1994).

Labsphere Inc., “A guide to diffuse reflectance coatings and materials,” http://www.labsphere.com/uploads/technical-guides/a-guide-to-reflectance-materials-and-coatings.pdf .

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Figures (12)

Fig. 1.
Fig. 1.

(a) Experimental setup: positioning (incidence on sample, detector arm, synchronous waveplates rotations) and measurements are computer-controlled. (b) Scattering geometry.

Fig. 2.
Fig. 2.

Black dots: MM elements behavior versus scattering angle (θ) for Spectralon SRS-99 standard at normal illumination (λ=520.8nm). Red: Lambertian diffuser behavior.

Fig. 3.
Fig. 3.

Black dots: m11 element behavior versus scattering angle (θ) for Spectralon SRS-99 standard at normal illumination (λ=488.0, 520.8, 530.9, 568.2, and 632.8 nm). Red: Lambertian diffuser behavior.

Fig. 4.
Fig. 4.

P(M) for Spectralon SRS-99 standard at normal illumination. Black dots, Lambertian diffuser; blue circles, λ=488.0nm; green triangles, λ=520.8nm; pink squares, λ=530.9nm; red diamonds, λ=568.2nm; dark-red circles, λ=632.8nm.

Fig. 5.
Fig. 5.

Black dots: MM elements behavior versus scattering angle (θ) for Spectralon SRS-99 standard (AOI=40°; λ=568.2nm). Red: Lambertian diffuser behavior.

Fig. 6.
Fig. 6.

Black dots: MM elements behavior versus scattering angle (θ) for Spectralon SRS-99 standard (AOI=75°; λ=568.2nm). Red: Lambertian diffuser behavior.

Fig. 7.
Fig. 7.

Black dots: MM elements behavior versus scattering angle (θ) for Spectralon SRS-99 standard (AOI=85°; λ=568.2nm). Red: Lambertian diffuser behavior.

Fig. 8.
Fig. 8.

Depolarization parameters versus scattering angle (θ) for Spectralon SRS-99 standard (AOI=75°; λ=568.2nm). Black circles, i=1; red circles, i=2; and green triangles, i=3.

Fig. 9.
Fig. 9.

Black dots: surface-averaged (five positions) MM elements behavior versus scattering angle (θ) for Spectralon SRS-99 standard at normal illumination (λ=632.8nm). Red: Lambertian diffuser behavior.

Fig. 10.
Fig. 10.

Black dots: angular averaged (along 5 deg) MM elements behavior versus scattering angle (θ) for a single measurement of Spectralon SRS-99 standard at normal illumination (λ=632.8nm). Red: Lambertian diffuser behavior.

Fig. 11.
Fig. 11.

m11 at λ=568.2nm versus θ. Black line, Lambertian behavior; black circles, AOI=0°; red triangles, AOI=40°; blue squares, AOI=50°; pink triangles, AOI=75°; green circles, AOI=85°.

Fig. 12.
Fig. 12.

P(M), in semi-logarithmic scale, for Spectralon SRS-99 standard at some oblique illuminations (λ=568.2nm. Black circles, AOI=0°; green triangles, AOI=40°; pink squares, AOI=50°; blue triangles, AOI=75°; red circles, AOI=85°).

Tables (1)

Tables Icon

Table 1. Four Examples of Typical MMs Obtained with the DRCP for Direct Transmission Measurements at Different Wavelengths (Figures are Rounded to the Significant Digit)a

Equations (9)

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M=MΔMRMD
MΔ(m11,di,ai,zi)=m11(1000z1d1a1a2z2a1d2a3z3a2a3d3)=m11(10TPΔmΔ).
P(M)=Tr(MTM)m1123m112.
m11(θ)|norm=m11(θ)0.15m11(Δθ)+0.7m11(0°)+0.15m11(+Δθ).
M=m11(1m12000m22m2300m320m340000).
M|0°=M(θ)m11(θ)|0°=(10.0300000.0500.030000.03000.0400000),
M|0°=MΔMPure=(10000.0020.0570.01400.0010.0140.04800000)(10.030000.0240.7860.5740.2300.0120.3910.1720.9040.0140.4800.8000.360),
M|0°=MΔMRMD=(10000.0020.0570.01400.0010.0140.04800000)(100000.7850.5750.23000.3910.1720.90400.4800.8000.360)(10.030000.03010000100001).
M=m11(1m1200m12m220000m33m3400m34m33).

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