Paper surface modelling and characterisation

1. Are 3D surface standard parameters discriminant for paper ? Christophe Mercier Jean-Francis Bloch Contact: mercier.christophe1@googlemail.com

2. Outline  Context / Objectives  Definition of the surface parameters  Simulation  Conclusion / Perspectives

3. What is paper ? Non-c aland e r ed paper, 512*512, pixel: 2 μm , Reverdy-Bruas N , E FPG / ESRF Calandered p aper 512*512, pixel 2 μm , Reverdy-Bruas N, EFPG / ESRF

4. Context Context: paper surface topography is involved * converting stages: printing, coating * final quality: gloss Up to now Needs for non-contact 3D measurement

5. Objective Is-it possible to have surfaces which have same surface parameters, and if possible amplitude distribution, but they are visually different ?

6. Outline  Context / Objectives  Definition of the surface parameters  Simulation  Conclusion / Perspectives

7. Surface parameters Parameters: * Amplitude parameters : 4 * Spatial parameters : 4 * Hybrid parameters : 3 * Functional parameters volumes : 3 Abbott curve : 3 fonctionnels : 3 17

8. Amplitude parameters Sq : Root Mean Square Deviation of the Surface. This is a dispersion parameter defined as the root mean square value of the surface departures within the sampling area. Statistically it the standard deviation of the height distribution. Sz : Ten Point Height of the Surface. This is an extreme parameter defined as the average value of the absolute heights of the five highest peaks and the depths of the five deepest pits or valleys (eight neighbours method) within the sampling a rea. Ssk : Skewness of Topography Height Distribution. This is the measure of asymmetry of surface deviations about the mean plane. This parameter can effectively be used to describe the shape of the topography height distribution. Sku : Kurtosis of Topography Height Distribution. This is a measure of the peakedness or sharpness of the surface height distribution and characterises the spread of the height distribution. A gaussian surface has a kurtosis value of 3.

9. Spatial parameters Sds Density of Summits of the Surface. This is the number of summits of a unit sampling area (eight neighbours method) Str Texture Aspect Ratio of the Surface This is a parameter used to identify texture strength i.e. uniformity of texture aspect. It is defined from auto-correlation function. Str can be defined as its ratio of the fastest to slowest decay to correlation lengt h Sal The Fastest Decay Auto-correlation Length.This is a parameter in length dimension used to describe the auto-correlation character of the AACF. It is defined as the horizontal distance of the AACF which has the fastest decay to 0.2. In other words the Sal Std Texture Direction of the Surface. This is the parameter used to determine the most pronounced direction of the surface texture with respect to the y axis within the frequency domain, i.e. it gives the lay direction of the surface.

10. Hybrid parameters SDq Root mean square value of surface slope within the sampling area Ssc Arithmetic Mean Summit Curvature of the Surface. This is defined as the average of the principal curvatures of the summits within the sampling area. The sum of the curvatures of a surface at a point along any two orthogonal directions is equal to the sum Sdr Developed Interfacial Area Ratio. This is the ratio of the increment of the interfacial area of a surface over the sampling area. The developed interfacial area ratio reflects the hybrid property of surfaces.

11. Functional parameters Sbi Surface Bearing Index. This is the ratio of the Sq parameter over the surface height at 5% bearing area. A larger surface bearing index indicates a good bearing property. Sci Core Fluid Retention Index. This is the ratio of the void volume of the unit sampling area at the core zone (5% ~ 80% bearing area) over the Sq parameter. A larger Sci indicates a good fluid retention. For a Gaussian surface, this index is about 1.56. Svi Valley Fluid Retention Index. This is the ratio of the void volume of the unit sampling area at the valley zone (80% ~ 100%) over the Sq parameter. A larger Svi indicates a good fluid retention in the valley zone. Sm Material Volume of the Surface. The material volume is defined as the material portion enclosed in the 10% bearing area and normalised to unity. The material volume and the material volume ratio are not only geometrical descriptors of the surface Sc Core Void Volume of the Surface. A core void volume is enclosed from10% to 80% of surface bearing area and normalised to the unit sampling area. Sv Valley Void Volume of the Surface. The valley void volume of the unit sampling area is defined as a void volume at the valley zone from 80% to 100% surface bearing area. The void volume is proposed here to provide a direct inspection of lubrication and fl

12. Selected Surface Parameters Parameters: * Amplitude parameters : 4 * Spatial parameters : 4 * Hybrid parameters : 3 11

13. Amplitude distribution

14. Outline  Context / Objectives  Definition of the surface parameters  Simulation Texture 1 Texture 2  Conclusion / Perspectives

15. Texture 1: measured surface

16. Texture 1: method

17. Texture 1: results

18. Texture 1: results Real surface Virtual surface

19. Texture 1bis: method Paper cross-section

20. Texture 1bis: method z = 0 6.75µm 13.5µm 20.25µm

21. Texture 1bis: results Measured surface Virtual surface

22. Texture 1b: visual comparison

23. Outline  Context / Objectives  Definition of the surface parameters  Simulation Texture 1 Texture 2  Conclusion / Perspectives

24. Texture 2: measured surface

25. Texture 2: method µm µm Four stages:  Definition of a motive  amplitude distribution  Orientation  Noise

26. Texture 2: results Parameters Amplitude distribution Measured surface Virtual surface

27. Texture 2: Visual comparison

28. Texture 2: differenciation Areal autocorrelation function Virtual surface Measured surface

29. Outline  Context / Objectives  Definition of the surface parameters  Simulation  Conclusion / Perspectives

30. Conclusion S imulations proove : S urfaces could have comparable * standard parameters * amplitude distributions and exhibit different visual aspects.

31. Perspectives I n the case of paper surface , t he control of topography needs further improvements. Hence, considering only the used parameters, classical in surface quality control, one could conclude that the different surfaces are similar.

32. Acknowledgments

33. Questions

34. Texture n°1ter: results

35. Texture n°1ter: method