Abstract

Goniospectrophotometric space curves were obtained by summation of spatially under-sampled bidirectional reflectance distribution function over all directions and repeating this for all wavelengths in the visible spectral region. This gives a 3D goniospectrophotometric curve called an xDNA graph. Systematic analysis applying 19 measurement geometries confirms existence of characteristic shapes of the graph for all optically similar samples. This enables distinguishing between differently rough samples, an interference effect on various transparent layers, and selective spectral absorption of light in differently thick pigmented coatings. Therefore, the considered goniospectrophotometric space curves could serve as an appearance fingerprint of such samples.

© 2013 Optical Society of America

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    [CrossRef]
  29. M. Klanjšek Gunde, “Optical effects in IR spectroscopy: thickness-dependent positions of absorbance lines in spectra of thin films,” Appl. Spectrosc. 46, 365–372 (1992).
    [CrossRef]
  30. M. Klanjšek Gunde and M. Maček, “Infrared optical constants and dielectric response functions in silicon nitride and oxynitride films,” Phys. Stat. Sol. A 183, 439–449 (2001).
    [CrossRef]
  31. M. Klanjšek Gunde, M. Žveglič, N. Hauptman, and G. Golob, “Measurement possibilities of interference layers on a paper,” Adv. Print. Media Technol. 35, 429–436 (2008).
  32. R. Kulčar, M. Friškovec, N. Hauptman, A. Vesel, and M. Klanjšek Gunde, “Colorimetric properties of reversible thermochromic printing inks,” Dyes Pigm. 86, 271–277 (2010).
    [CrossRef]

2012

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- and out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, A. M. Rabal, J. Campos, A. Pons, and M. L. Hernanz, “Spectral and geometrical variation of the bidirectional reflectance distribution function of diffuse reflectance standards,” Appl. Opt. 51, 8535–8540 (2012).
[CrossRef]

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[CrossRef]

A. Ferrero, A. M. Rabal, J. Campos, A. Pons, and M. L. Hernanz, “Variables separation of the BRDF for better understanding color variation in special effect pigment coatings,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

2011

E. Perales, E. Chorro, W. R. Cramer, and F. M. Martínez-Verdú, “Analysis of the colorimetric properties of goniochromatic colors using the MacAdam limits under different light sources,” Appl. Opt. 50, 5271–5278 (2011).
[CrossRef]

L. Simonot, M. Hébert, and D. Dupraz, “Goniocolorimetry: from measurement to representation in the CIELAB color space,” Color Res. Appl. 36, 169–178 (2011).
[CrossRef]

N. Dekker, E. J. J. Kirchner, R. Supèr, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

V. B. Podobedov, M. E. Nadal, and C. C. Miller, “Improving the performance of NIST five axis goniospectrometer for measurements of bidirectional reflectance distribution function,” Proc. SPIE 8065, 80651l (2011).
[CrossRef]

2010

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

R. Kulčar, M. Friškovec, N. Hauptman, A. Vesel, and M. Klanjšek Gunde, “Colorimetric properties of reversible thermochromic printing inks,” Dyes Pigm. 86, 271–277 (2010).
[CrossRef]

2009

J. Suomalainen, T. Hakala, J. Peltoniemi, and E. Puttonen, “Polarised multiangular reflectance measurements using the Finnish geodetic institute field goniospectrometer,” Sensors 9, 3891–3907 (2009).
[CrossRef]

2008

M. Klanjšek Gunde, M. Žveglič, N. Hauptman, and G. Golob, “Measurement possibilities of interference layers on a paper,” Adv. Print. Media Technol. 35, 429–436 (2008).

2007

L. Simonot and G. Obein, “Geometrical considerations in analyzing isotropic or anisotropic surface reflections,” Appl. Opt. 46, 2615–2623 (2007).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Supèr, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

2005

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, T-1–T-10 (2005).
[CrossRef]

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275–282 (2005).
[CrossRef]

2004

Q. Z. Zhu and Z. M. Zhang, “Anisotropic slope distribution and bidirectional reflectance of a rough silicon surface,” J. Heat Transfer 126, 985–993 (2004).
[CrossRef]

2002

W. R. Cramer, “Examples of interference and color pigment mixtures green with red and red with green,” Color Res. Appl. 27, 276–281 (2002).
[CrossRef]

2001

G. Obein, T. Leroux, and F. Viénot, “Bi-directional reflectance distribution factor and gloss scales,” Proc. SPIE 4299, 279–290 (2001).
[CrossRef]

M. Klanjšek Gunde and M. Maček, “Infrared optical constants and dielectric response functions in silicon nitride and oxynitride films,” Phys. Stat. Sol. A 183, 439–449 (2001).
[CrossRef]

1999

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

1996

1992

1990

H. J. A. Saris, R. J. B. Gottenbos, and H. van Houwellingen, “Correlation between visual and instrumental colour differences of metallic paint films,” Color Res. Appl. 15, 200–205 (1990).
[CrossRef]

Baba, G.

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275–282 (2005).
[CrossRef]

Bousquet, R.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, T-1–T-10 (2005).
[CrossRef]

Campos, J.

Chorro, E.

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- and out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Cramer, W.

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[CrossRef]

Cramer, W. R.

Dekker, N.

N. Dekker, E. J. J. Kirchner, R. Supèr, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

Dupraz, D.

L. Simonot, M. Hébert, and D. Dupraz, “Goniocolorimetry: from measurement to representation in the CIELAB color space,” Color Res. Appl. 36, 169–178 (2011).
[CrossRef]

Ellens, M. S.

J. K. Nisper, T. M. Richardson, M. S. Ellens, and C. Huang, “Method and system for enhanced formulation and visualization rendering,” U.S. patent 0213120 A1 (27August2009).

Ferrero, A.

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- and out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Friškovec, M.

R. Kulčar, M. Friškovec, N. Hauptman, A. Vesel, and M. Klanjšek Gunde, “Colorimetric properties of reversible thermochromic printing inks,” Dyes Pigm. 86, 271–277 (2010).
[CrossRef]

Golob, G.

M. Klanjšek Gunde, M. Žveglič, N. Hauptman, and G. Golob, “Measurement possibilities of interference layers on a paper,” Adv. Print. Media Technol. 35, 429–436 (2008).

Gottenbos, R.

N. Dekker, E. J. J. Kirchner, R. Supèr, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Supèr, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Gottenbos, R. J. B.

H. J. A. Saris, R. J. B. Gottenbos, and H. van Houwellingen, “Correlation between visual and instrumental colour differences of metallic paint films,” Color Res. Appl. 15, 200–205 (1990).
[CrossRef]

Hakala, T.

J. Suomalainen, T. Hakala, J. Peltoniemi, and E. Puttonen, “Polarised multiangular reflectance measurements using the Finnish geodetic institute field goniospectrometer,” Sensors 9, 3891–3907 (2009).
[CrossRef]

Hauer, K.-O.

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

Hauptman, N.

R. Kulčar, M. Friškovec, N. Hauptman, A. Vesel, and M. Klanjšek Gunde, “Colorimetric properties of reversible thermochromic printing inks,” Dyes Pigm. 86, 271–277 (2010).
[CrossRef]

M. Klanjšek Gunde, M. Žveglič, N. Hauptman, and G. Golob, “Measurement possibilities of interference layers on a paper,” Adv. Print. Media Technol. 35, 429–436 (2008).

Hébert, M.

L. Simonot, M. Hébert, and D. Dupraz, “Goniocolorimetry: from measurement to representation in the CIELAB color space,” Color Res. Appl. 36, 169–178 (2011).
[CrossRef]

Hernanz, M. L.

Höpe, A.

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

Huang, C.

J. K. Nisper, T. M. Richardson, M. S. Ellens, and C. Huang, “Method and system for enhanced formulation and visualization rendering,” U.S. patent 0213120 A1 (27August2009).

Kirchner, E.

E. Kirchner and W. Cramer, “Making sense of measurement geometries for multi-angle spectrophotometers,” Color Res. Appl. 37, 186–198 (2012).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Supèr, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Kirchner, E. J. J.

N. Dekker, E. J. J. Kirchner, R. Supèr, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

Klanjšek Gunde, M.

R. Kulčar, M. Friškovec, N. Hauptman, A. Vesel, and M. Klanjšek Gunde, “Colorimetric properties of reversible thermochromic printing inks,” Dyes Pigm. 86, 271–277 (2010).
[CrossRef]

M. Klanjšek Gunde, M. Žveglič, N. Hauptman, and G. Golob, “Measurement possibilities of interference layers on a paper,” Adv. Print. Media Technol. 35, 429–436 (2008).

M. Klanjšek Gunde and M. Maček, “Infrared optical constants and dielectric response functions in silicon nitride and oxynitride films,” Phys. Stat. Sol. A 183, 439–449 (2001).
[CrossRef]

M. Klanjšek Gunde, “Complete optical analysis to obtain the absorption coefficient of the interstitial oxygen vibration in silicon,” Appl. Spectrosc. 50, 1156–1160 (1996).
[CrossRef]

M. Klanjšek Gunde, “Optical effects in IR spectroscopy: thickness-dependent positions of absorbance lines in spectra of thin films,” Appl. Spectrosc. 46, 365–372 (1992).
[CrossRef]

Kulcar, R.

R. Kulčar, M. Friškovec, N. Hauptman, A. Vesel, and M. Klanjšek Gunde, “Colorimetric properties of reversible thermochromic printing inks,” Dyes Pigm. 86, 271–277 (2010).
[CrossRef]

Leroux, T.

G. Obein, T. Leroux, and F. Viénot, “Bi-directional reflectance distribution factor and gloss scales,” Proc. SPIE 4299, 279–290 (2001).
[CrossRef]

Macek, M.

M. Klanjšek Gunde and M. Maček, “Infrared optical constants and dielectric response functions in silicon nitride and oxynitride films,” Phys. Stat. Sol. A 183, 439–449 (2001).
[CrossRef]

Maile, F. J.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

Martínez-Verdú, F. M.

Miller, C. C.

V. B. Podobedov, M. E. Nadal, and C. C. Miller, “Improving the performance of NIST five axis goniospectrometer for measurements of bidirectional reflectance distribution function,” Proc. SPIE 8065, 80651l (2011).
[CrossRef]

Nadal, M. E.

V. B. Podobedov, M. E. Nadal, and C. C. Miller, “Improving the performance of NIST five axis goniospectrometer for measurements of bidirectional reflectance distribution function,” Proc. SPIE 8065, 80651l (2011).
[CrossRef]

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, T-1–T-10 (2005).
[CrossRef]

Nisper, J.

J. Nisper, T. Richardson, and B. Teunis, “Major advances in the reliable measurement of the color and appearance of special effect paints and coatings,” presented at the American Coatings Conference, Charlotte, North Carolina, 1 April (2008).

Nisper, J. K.

J. K. Nisper, T. M. Richardson, M. S. Ellens, and C. Huang, “Method and system for enhanced formulation and visualization rendering,” U.S. patent 0213120 A1 (27August2009).

J. K. Nisper, P. S. Rood, B. A. Pawlanta, T. M. Richardson, and B. D. Teunis, “Measuring an appearance property of a surface using a bidirectional reflectance distribution function,” U.S. patent 0291993 A1 (20December2007).

Njo, L.

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Supèr, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Obein, G.

L. Simonot and G. Obein, “Geometrical considerations in analyzing isotropic or anisotropic surface reflections,” Appl. Opt. 46, 2615–2623 (2007).
[CrossRef]

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, T-1–T-10 (2005).
[CrossRef]

G. Obein, T. Leroux, and F. Viénot, “Bi-directional reflectance distribution factor and gloss scales,” Proc. SPIE 4299, 279–290 (2001).
[CrossRef]

Pawlanta, B. A.

J. K. Nisper, P. S. Rood, B. A. Pawlanta, T. M. Richardson, and B. D. Teunis, “Measuring an appearance property of a surface using a bidirectional reflectance distribution function,” U.S. patent 0291993 A1 (20December2007).

Peltoniemi, J.

J. Suomalainen, T. Hakala, J. Peltoniemi, and E. Puttonen, “Polarised multiangular reflectance measurements using the Finnish geodetic institute field goniospectrometer,” Sensors 9, 3891–3907 (2009).
[CrossRef]

Perales, E.

Pfaff, G.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

Podobedov, V. B.

V. B. Podobedov, M. E. Nadal, and C. C. Miller, “Improving the performance of NIST five axis goniospectrometer for measurements of bidirectional reflectance distribution function,” Proc. SPIE 8065, 80651l (2011).
[CrossRef]

Pons, A.

Puttonen, E.

J. Suomalainen, T. Hakala, J. Peltoniemi, and E. Puttonen, “Polarised multiangular reflectance measurements using the Finnish geodetic institute field goniospectrometer,” Sensors 9, 3891–3907 (2009).
[CrossRef]

Rabal, A. M.

Reynders, P.

F. J. Maile, G. Pfaff, and P. Reynders, “Effect pigments-past, present and future,” Prog. Org. Coat. 54, 150–163 (2005).
[CrossRef]

G. Pfaff and P. Reynders, “Angle-dependent optical effects deriving from submicron structures of films and pigments,” Chem. Rev. 99, 1963–1982 (1999).
[CrossRef]

Richardson, T.

J. Nisper, T. Richardson, and B. Teunis, “Major advances in the reliable measurement of the color and appearance of special effect paints and coatings,” presented at the American Coatings Conference, Charlotte, North Carolina, 1 April (2008).

Richardson, T. M.

J. K. Nisper, P. S. Rood, B. A. Pawlanta, T. M. Richardson, and B. D. Teunis, “Measuring an appearance property of a surface using a bidirectional reflectance distribution function,” U.S. patent 0291993 A1 (20December2007).

J. K. Nisper, T. M. Richardson, M. S. Ellens, and C. Huang, “Method and system for enhanced formulation and visualization rendering,” U.S. patent 0213120 A1 (27August2009).

Rood, P. S.

J. K. Nisper, P. S. Rood, B. A. Pawlanta, T. M. Richardson, and B. D. Teunis, “Measuring an appearance property of a surface using a bidirectional reflectance distribution function,” U.S. patent 0291993 A1 (20December2007).

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- and out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Saris, H. J. A.

H. J. A. Saris, R. J. B. Gottenbos, and H. van Houwellingen, “Correlation between visual and instrumental colour differences of metallic paint films,” Color Res. Appl. 15, 200–205 (1990).
[CrossRef]

Simonot, L.

L. Simonot, M. Hébert, and D. Dupraz, “Goniocolorimetry: from measurement to representation in the CIELAB color space,” Color Res. Appl. 36, 169–178 (2011).
[CrossRef]

L. Simonot and G. Obein, “Geometrical considerations in analyzing isotropic or anisotropic surface reflections,” Appl. Opt. 46, 2615–2623 (2007).
[CrossRef]

Suomalainen, J.

J. Suomalainen, T. Hakala, J. Peltoniemi, and E. Puttonen, “Polarised multiangular reflectance measurements using the Finnish geodetic institute field goniospectrometer,” Sensors 9, 3891–3907 (2009).
[CrossRef]

Supèr, R.

N. Dekker, E. J. J. Kirchner, R. Supèr, G. J. van den Kieboom, and R. Gottenbos, “Total appearance differences for metallic and pearlescent materials: contributions from color and texture,” Color Res. Appl. 36, 4–14 (2011).
[CrossRef]

E. Kirchner, G. J. van den Kieboom, L. Njo, R. Supèr, and R. Gottenbos, “Observation of visual texture of metallic and pearlescent materials,” Color Res. Appl. 32, 256–266 (2007).
[CrossRef]

Takagi, A.

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of color-shift paint finishes,” Color Res. Appl. 32, 378–387 (2007).
[CrossRef]

A. Takagi, A. Watanabe, and G. Baba, “Prediction of spectral reflectance factor distribution of automotive paint finishes,” Color Res. Appl. 30, 275–282 (2005).
[CrossRef]

Teunis, B.

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Figures (10)

Fig. 1.
Fig. 1.

DNA calculation procedure at a selected λ . The example considers 45° illumination and six in-plane detecting directions. The measurements are illustrated by arrows in the measuring directions with lengths equal to the corresponding reflectance factors (a). The vector sum (red line with arrow) defines the point, where the z -axis is oriented in the specular direction and the y -axis lies in the plane of incidence (b).

Fig. 2.
Fig. 2.

Description of viewing (detection) direction for illumination at ϑ ill in a polar coordinate system by polar ( ϑ det ) and azimuthal angles ( ϑ az ) and by applying American Society for Testing and Materials (ASTM) notation by aspecular ( φ as ) and azimuthal ( φ az ) angles (see also Table 1).

Fig. 3.
Fig. 3.

SEM micrographs of unpolished silicon wafers: samples A (a), B (b), and C (c).

Fig. 4.
Fig. 4.

SEM micrographs of (a) calendered and (b) noncalendered side of the paper. The platy kaolin clay particles are visible on both surfaces.

Fig. 5.
Fig. 5.

SEM micrograph of the interference layer on paper; the thin layer of varnish adsorbed on a paper surface. The micrograph was taken in the vicinity of the cross cut where the layer breaks and enable to measure its thickness.

Fig. 6.
Fig. 6.

xDNA graphs of polished and unpolished silicon wafers (samples A, B, and C) in (a)  y z (in-plane), and (b)  x z (off-plane) planes. See also Fig. 3 and Table 2.

Fig. 7.
Fig. 7.

xDNA graph of calendered and noncalendered sides of white paper.

Fig. 8.
Fig. 8.

xDNA graphs in x z [ z ( x ) , open circles] and y z [ z ( y ) , solid circles] projections (left) and corresponding reflection curves (right) for 220 (a) and (b), 390 (c) and (d), and 635 nm (e) and (f) thick silicon nitride films, respectively. The measurement geometries of the highest reflectance spectra are denoted.

Fig. 9.
Fig. 9.

xDNA graphs in y z (a) and x z planes (b) as measured for thin varnish layer on black and white cardboards (L/B and L/W, respectively). The graphs of the black and white substrates are also shown (BS and WS, respectively). The reflectance spectra of the layer on black (c) and white (d) substrates are shown with notation of the most important geometries.

Fig. 10.
Fig. 10.

xDNA graphs in y z [ z ( y ) ] and x z [ z ( x ) ] projections for thin layers of the magenta ink printed on white glossy paper (a). Each color refers to a sample of specific layer thickness. The reflectance spectra of the thinnest (b) and thickest (c) samples are also shown. The spectra with the same color are measured in the same geometries.

Tables (2)

Tables Icon

Table 1. Measurement Geometries (Degrees) of the MA98 Multiangle Spectrophotometer; the X-Rite Notation Applies Illumination ( ϑ ill ), Aspecular ( φ as ), and Azimuthal ( φ az ) Anglesa

Tables Icon

Table 2. Data of the Unpolished Silicon Wafer Surfaces: Average Roughness ( R a ) Describes the Average Vertical Deviation from the Mean Surface Levela

Equations (1)

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xDNA = R μ .

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