TIPO Y NOMBRE DE LA ACTIVIDAD Speckle 2012: V Internatioanl Conference on Speckle Metrology

LUGAR Y FECHA (Duración) Vigo, España. 10‐12 de septiembre 2012.

OBJETIVOS Reunir a científicos e ingenieros que trabajan en todo el mundo en el campo

de metrología speckle y que encuentran aplicación en diferentes campos de

la ingeniería, la física, la biología y la medicina.

PARTICIPANTE (S) Dr. Abdiel Osvan Pino Docente‐Investigador Facultad de Ciencias y

Tecnología

ASPECTOS RELEVANTES EN EL 

DESARROLLO DE LA ACTIVIDAD

Se dictaron conferencias invitadas por importantes expositores de relevancia

mundial en el campo de la metrología speckle, como las ponencias generales

en los diversos tópicos, como también la presentación de poster.

RESULTADOS OBTENIDOS    (Contacto 

con futuros expositores, becas, firma de 

convenio, etc.)

La publicación de nuestro trabajo en los Proceeding del Congreso y en la 

sección especial de la SPIE Digital Library.  Además, establecimos contacto 

con colegas de Brasil: Roberto Braga Jr. (Autor de Libro de 

Biospeckle/Universidad Federal de Lavras ), Armando Albertazzi( 

Universidad Federal de Santa Catarina) entre otros. 

CONCLUSIONES Esta conferencia fue una nueva oportunidad para que los investigadores

académicos e industriales con interés en el desarrollo y aplicación de láser en

base a las técnicas de metrología speckle puediesen presentar y discutir sus

últimos resultados y experiencias, ponerse al día con información sobre el

avance actual en el campo, establecer nuevos contactos y encontrar socios

potenciales para la cooperación internacional.

RECOMENDACIONES Seguir incentivando la participación de los investigadores panameños de

otras areas de la ingenería, para que participen y conozcan los métodos de

inspección óptica, y que es un campo de potencial desarrollo para el país. 

ANEXOS Nuestros articulos cientificos publicados, ya estan siendo citado por 

investigadores de otras universidades, como fue el evento: Saratov Fall 

Meeting 2012 International School for Junior Scientists and Students on 

Optics, Laser Physics and Biophysics (Rusia) realizado del 25‐28 de 

septiembre de 2012.

Firma y cédula del participante:  8‐351‐692

Fecha de entrega del informe:   01/10/2012

UNIVERSIDAD TECNOLÓGICA DE PANAMÁ

INFORME DE VIAJEEl presente formato tiene el objetivo de consolidar toda la información obtenida por los colaboradores, que de una u

otra forma se hayan beneficiado para realizar viaje al exterior, el cual, a la vez será reportado al Ministerio de la

Presidencia para justificar la gestión realizada, en correlación con el presupuesto ejecutado.

Conferencia Internacional de Metrología: Speckle 2012(Fotos)

Measurement of the roughness surface using the normalized autocorrelation function of the fields of the texture of speckle pattern

A. O. Pino [1], J. Pladellorens [2]

[1] Natural Sciences Department, Technological University of Panama Technological University of Panama Avenue, Bethania, Panama, abdiel.pino@utp.ac.pa

[2] CD6 Optics and Optometry Department, Polytechnic University of Catalonia Rambla de Sant Nebridi 10, Terrassa, Spain 08222, pladellorens@oo.upc.edu

Introduction

Measurement principle

References

Experimental Setup

Conclusions

Results

( ) ( ) ( )2, ,i n o n hπϕ α β α βλ

= − ⋅ + ⋅

We characterized the roughness of 14 different types of papers with Ra between 3,3 and 6,9 mµ

and similar optical proprieties using one optical method (a confocal microscope optical 3-D profilometer operating in confocal mode). The software used to capture and analyze the images of speckle patterns included AVT Active FirePackage (Allied Vision Technologies, Taschenweg, Stadtroda, Germany), MATLAB (Digital Image Toolbox) from MathWorks (Natick, MA, USA), and Origin (OriginLab, Northampton, MA, USA)13,14,15. We characterized the roughness of 14 different types of papers with Ra between 3,3 and 6,9 mµ

and similar optical proprieties using one optical method (a confocal microscope optical 3-D profilometer operating in confocal mode). The software used to capture and analyze the images of speckle patterns included AVT Active FirePackage (Allied Vision Technologies, Taschenweg, Stadtroda, Germany), MATLAB (Digital Image Toolbox) from MathWorks (Natick, MA, USA), and Origin (OriginLab, Northampton, MA, USA)13,14,15.

5,5 mµ

4,2 mµ

3,4 mµ

Measurement of the roughness surface using the normalized autocorrelation function of the fields of the texture of speckle

pattern

Abdiel O. Pino [1], Josep Pladellorens [2] [1] Natural Sciences Department, Technological University of Panama

Technological University of Panama Avenue, Betania, Panama, abdiel.pino@utp.ac.pa [2] CD6 Optics and Optometry Department, Polytechnic University of Catalonia

Rambla de Sant Nebridi 10, Terrassa, Spain 08222, pladellorens@oo.upc.edu

ABSTRACT

We present a new method of measure of the roughness based on the analysis of the texture of speckle pattern on the surface. Images of speckle pattern over the surface are captured by means of a simple configuration using a laser, beam expander, and a camera charge coupled device (CCD). Using the properties of the normalized covariance function that we obtain from the image of the speckle through the inverse Fourier transform, we relate the values of the normalized covariance function. We compare the results obtained with the results obtained with a confocal microscope. This method can be considered as a noncontact surface profiling method and is easy to implement and can be used during the manufacturing process. Keywords: Arithmetic average, speckle, texture, normalized covariance function, inverse Fourier transform.

1. Introduction The characterization of surface topography involves the identification of the general features of a surface. This is essential for controlling the manufacturing process and the fundamental performance of a surface. Surface roughness parameter measurement and determination of statistical properties of rough surfaces have very important applications in several fields of engineering and sciences. Different parameters can be used for the characterization of surface roughness. Statistical parameters such as the arithmetic mean of the roughness, aR and the root mean square surface roughness, qR or Rσ , are most frequently used. Theoretically, Ra is the arithmetic average value of departure of the profile from the mean line throughout the sampling length1, 2.

Figure 1. Definition of average roughness (Ra).

( )1 0

1 1 LN

a i ai

R h or R y x dxN L

δ=

= =∑ ∫ (1)

Speckle 2012: V International Conference on Speckle Metrology, edited by Ángel F. Doval, Cristina Trillo, J. Carlos López-Vázquez, Proc. of SPIE Vol. 8413, 84131P

© 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.978077

Proc. of SPIE Vol. 8413 84131P-1

An alternative measure of the average variation in surface height is the root-mean-square roughness. This is the quantity commonly used in the optics industry. It is defined as1, 2:

( )12 22

1 0

1 1 LN

R i Ri

h or y x dxN L

σ δ σ=

⎡ ⎤= = ⎡ ⎤⎢ ⎥ ⎣ ⎦⎣ ⎦∑ ∫ (2)

There will obviously be some definite relationship between aR and Rσ . However, this will depend on the particular statistical distribution of surface height present in any given case. In the industry, the relationship usually assumed is3:

1,11R aRσ = (3) In our work, the examined materials were a series of samples of paper, on which were created speckle patterns. Roughness of paper surface is an important parameter in paper manufacturing4, 5. At the moment, air leak methods are standardized and employed in paper industry as roughness rating methods. We use of optical techniques based on the second order statistical properties of speckle patterns, scattered from a rough surface can be used for an accurate determination of surface quality. In particular the degree of correlation of the intensities of speckle patterns can be applied to measure surface roughness since it depends on the variance of the surface height distribution.

2. Measurement of the roughness surface using speckle Surface roughness measurement can also be accomplished by a speckle-based instrument. A surface speckle pattern, which is a grainy structure produced by light scattered from a rough surface when illuminated by coherent light, contains rich information about the surface roughness. With the advent of lasers in the 1960s, researchers have discussed the relationship between surface roughness and the statistical properties of speckle pattern6, 7. We have seen that speckle metrology has the potential to obtain measurements of the surface roughness. Researchers have been developed and used different methods to study the surface roughness by speckle techniques. These are based on the study of speckle contrast8 and others use the speckle correlation9, 10, 11, 12, which have been shown to give good results, for studying metal surfaces, dielectric fluids, and paper.

3. Methodology. 3.1 Setup system configuration The setup is built with a CCD camera Pike F-032B with 640 x 480 effective pixels, with 8 bits per pixel, a 5mW He-Ne laser with a wavelength of 632,8 nm, and a beam expander, the power of which can be adjusted to avoid the digital camera signal saturation. The field of view is 10×10 mm. The camera is located in the sample normal direction. The format of the images was 180×180 pixels, with 256 gray levels and a 10 mm diameter speckle pattern. The angle between the incident laser light beam and the normal direction was fixed to be as small as practical to reduce the effect of the direction of surface microstructure in the surface roughness evaluation. In the setup, the angle is 15°. By means of the simple setup, different speckle pattern images from paper surface roughness samples were obtained13, 14, 15.

Proc. of SPIE Vol. 8413 84131P-2

3.2 Theory When we pdepends onthe surface by variatiooversimplifheight by a delay assoc

where “ϕ ”

unitary vect

Making app

hσ through9

The comple

y

project a mononly on the diff

and the amplns of surface

fied model thageometrical a

ciated with pro

” is the phase

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Figur

covar

proximations t9, 10:

ex coherence f

ochromatic plaferences of mlitude variatioe slope and tat implies thatapproximationopagating to th

( ),ϕ α β

e, ( ),h α β is

nce, reflection

re 3. The intens

riance function

the variance o

2ϕσ

⎡= ⎢⎣

factor of the f

Figure 2

ane wave overeasurement co

ons of the scattheir effect ont the scattered n that assigns he surface and

(2 i nπλ

= − ⋅ +r r

the surface h

n, and normal

sity in the plan

of the waves le

of the phase sh

(2 . .i n o nπλ

⎡ − +⎣

r r r r

field leaving th

2. Experimenta

r a surface thaoordinates, thttered wave isn reflection, complex ampa phase “ϕ ”

d scattering fro

) ( ,o n h α β+ ⋅r r

height, “λ ” i

to the surface

ne ( ),x y is the F

eaving the surfa

hifts ϕσ is rela

)2

2hn σ⎤

⎥⎦r

he surface is d

al system

at is assumed hen the relatios, in general, multiple scat

plitude just abto the scatter

om the surfac

)

is the wavelen

e, respectively

Fourier transfor

ace in the plane

ated to the var

defined as:

to be rough anonship betwee

an extremely ttering, and s

bove the surfaced complex ame9, 10.

ngth and “ ir

”

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rm of the norm

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riance of the s

nd its correlatn the height vcomplex one

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he Figure 3.

malized

surface height

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We adopt an o the surface is the phase

(4)

“ nr ” are the

fluctuations

(5)

Proc. of SPIE Vol. 8413 84131P-3

( ) ( )1, 1 2 22

; ,, a

aincr I

α β α βμ α β

ΓΔ Δ = (6)

“ aΓ ” is the autocorrelation function of the field, “ r ”is the average amplitude reflectivity of the surface, and “ incI ”

is the intensity incident on the scattering area. Simplifying, assumption is usually made that the surface height fluctuations are a Gaussian random process. In this case, the complex coherence factor takes the relatively simple form:

( ) ( )( )2, exp 1 ,a hϕμ α β σ ρ α β⎡ ⎤= − −⎣ ⎦ (7) This result provides us with a specific relationship between the correlation properties of the reflected fields and the correlation properties of the reflecting surface. If the normalized correlation function of the surface heights is also of Gaussian form:

2

( ) exp ah a

c

rr

rρ

⎡ ⎤⎛ ⎞⎢ ⎥= −⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(8)

( )2

2exp 1a

c

rr

a ar eϕμ σ⎛ ⎞

−⎜ ⎟⎜ ⎟⎝ ⎠

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟= − −⎢ ⎥⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(9)

Where 2 2ar α β= Δ + Δ and cr is a constant. The greater “ ϕσ ”, more rapidly “ aμ ” will tend zero “ ar ” grows

( a cr r ). So we can relate the sum of the values of “ aμ ” far from the center ( ar > 20 cr ) to “ ϕσ ” through Eq. (9)

and we may define “ ϕσ ”, as:

( )20

1lna

a arrϕσ μ

>

⎛ ⎞⎜ ⎟=⎜ ⎟⎝ ⎠∑

(10)

3.3 Calculation of the aμ

The Van Cittert–Zernike theorem9, 10 is a result of the coherence theory that states that under certain conditions the Fourier transform of the mutual coherence function of a distant, incoherent source is equal to its intensity. When applied to the fields leaving the scattering surface of paper, the Van Cittert–Zernike theorem provides us with a connection between the normalized autocorrelation function of the fields leaving the scattering surface of paper and the average intensity distribution observed in the image plane of a positive lens

( ) ( ) ( )2 /, , j x y faI x y e d dπ α β λμ α β α β

∞− Δ + Δ⎡ ⎤⎣ ⎦

−∞

∝ Δ Δ Δ Δ∫ ∫

(11)

where “ aμ ” is the normalized autocorrelation function, “ f ” is the focal length of the positive lens used, and “ λ ” is

the wavelength of the laser used. Thus, if ( ),I x y is carefully measured, using a detector that is large enough to

average over many individual speckles, a normalized inverse Fourier transform of the intensity distribution would provide “ aμ ” at the scattering surface.

Proc. of SPIE Vol. 8413 84131P-4

4. Results.

We characterized the roughness of 14 different types of papers with Ra between 3,3 and 6,9 mμ and similar optical proprieties using one optical method (a confocal microscope optical 3-D profilometer operating in confocal mode). The software used to capture and analyze the images of speckle patterns included AVT Active FirePackage (Allied Vision Technologies, Taschenweg, Stadtroda, Germany), MATLAB (Digital Image Toolbox) from MathWorks (Natick, MA, USA), and Origin (OriginLab, Northampton, MA, USA)13,14,15.

Figure 4, shows three images of the speckle pattern variations for different rugosities. This implies that the speckle pattern texture properties change with the surface roughness, and it is possible to extract the surface roughness from the speckle pattern texture images using the normalized autocorrelation function.

F26LC50TCF_1a Ra=5,5μm T47_7a Ra=4,2μm verge_8a Ra=3,4μm

Figure 4. Speckle pattern variations against the paper surface roughness.

The table I, shows the results obtained with 14 paper sheets, which include white base paper, yellow base paper, medium porosity filter paper, low porosity filter paper, verge paper, and velin paper.

Table I. Results of the measurement of the roughness obtained with confocal microscope,

sum of the values of aμ ( ar > 20 cr ) and the equivalent roughness for 14 papers.

Samples Ra Confocal (μm) ( ) 2

2010

a

aa ar

rμ −>∑

1

1lna

σ μ⎡ ⎤⎛ ⎞

= ⎢ ⎥⎜ ⎟⎝ ⎠⎣ ⎦∑

F24HP100_7a 6,9 0,0284 2,45 F24HP100_2a 6,2 0,0261 2,44 F22HP35_1a 6,1 0,0284 2,42 F22HP35_3b 6,0 0,0304 2,41 F22HP35_6a 6,0 0,0256 2,44

F26LC50TCF_7a 5,7 0,0282 2,42 F26LC50TCF_1a 5,5 0,0333 2,39

T47_7a 4,2 0,0366 2,37 T47_9a 3,8 0,0373 2,36 velin_7a 3,7 0,0458 2,32 verge_8a 3,4 0,0508 2,30

BB36NT_10a 3,4 0,0523 2,29 BB36NT_9a 3,4 0,0531 2,29

verge_7a 3,3 0,0501 2,30

a We multiply by 10-2 to avoid negative numbers in the logarithm

In the figure 5, we show the values of μa ( ra > 20rc ) for three different papers and in the figure 6; we show the comparison between the measurements using confocal microscope and our method:

Proc. of SPIE Vol. 8413 84131P-5

2,48

2,46

2,44

2,42

2,40

2,38

2,36

2,34

2,32

2,30

2,28

3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5 7,0

hnes

sou

gs

rrm

Ra (μm)

Figure 5. Values of the covariance function for three Figure 6. Comparison between the measurements using different papers confocal microscope and our method R2 = 0,9249

5. Conclusions In this work, we have developed a method to find the roughness of paper using speckle. Using the properties of the normalized covariance function that we obtain from the image of the speckle through the inverse Fourier transform, we relate the values of the normalized covariance function far from the center with the roughness of the paper. In order to test the method we have characterized the roughness of 14 papers in the range between 3,3 mμ and 6,9 mμ

using a confocal microscope. The results present a good correlation between them 2 0,9249R = . The method is easy to implement and can be used during the manufacturing process.

6. References [1] ASME B46.1-2002 (Revision of ASME B46.1-1995) surface texture (surface roughness waviness, and lay). The American Society of Mechanical Engineers, Three Park Avenue, New York, NY 10016-5990, 2003. [2] ISO (4287:1997). Geometrical Product Specifications (GPS). Surface texture: Profile method, Terms, definitions and surface texture parameters. [3] T. Kuparinen, “Paper Surface Roughness Measurement Using Machine Vision”, Master’s thesis. Department of Information Technology, Lappeenranta University of Technology, Finland, 2005. [4] T. Cresson and P. Luner, “The characterization of paper formation. Part 2. The texture analysis of paper formation,” Tappi J. 73 (12), 175–184 (1990). [5] H. F. Rance, Handbook of Paper Science, Vol. 2: The Structure and Physical Properties of Paper, Elsevier Scientific Publishing (1998). [6] P. J. Chandley and H. M. Escamilla, “Speckle from a rough surface when the illuminated region contains few correlation areas: the effect of changing the surface height variance,” Opt. Commun. 29, 151–154 (1979). [7] H. M. Pedersen, “Theory of speckle dependence on surface roughness,” J. Opt. Soc. Am. 66, 1204–1210 (1976). [8] D. D. Duncan, S. J. Kirkpatrick, and R. K. Wang, “Statistics of local speckle contrast,” J. Opt. Soc. Am. A 25 (1), 9–15 (2008). [9] J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications, Roberts & Company Publishers (2006). [10] J. C. Dainty, “Laser speckle and related phenomena,” Vol. 9 of Topics in Applied Physics, Springer-Verlag (1984). [11] D. Leger and J. C. Perrin, “Real-timemeasurement of surface roughness by correlation of speckle patterns,” J. Opt. Soc. Am. 66 (11) (1976). [12] B. Ruffing, “Application of speckle-correlation methods to surfaceroughness measurement: a theoretical study,” J. Opt. Soc. Am. A 3, 1297–1304 (1986). [13] A. Pino, J. Pladellorens, J.F. Colom, O. Cusola, A. Tosas, “Using laser speckle to measure the roughness of paper". Tappi Journal, The Paper and packaging industries technical resource. VOL. 10 NO. 3 (2011). [14] A. Pino, J. Antó, J. Pladellorens, "Determinación de propiedades superficiales del papel utilizando el análisis de la textura del patrón de speckle", Óptica Pura Aplicada, 43 (1) 43-48 (2010). [15] A. Pino, J. Pladellorens, O. Cusola, J. Caum, “Roughness measurement of paper using speckle”. Optical Engineering 50(9), 093605, 2011.

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