Materials characterisation by light scattering and reflectometry


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Measurement parameters



This page provides some additional background on the various parameters measured by the Imaging Reflectometer: to explain (in a practical way) what they mean and identify some of the uses and limitations. If you are interested in the theory, you can download a PDF document on that subject from the technical page.










As described in Principles, macroroughness is roughness on a scale much greater than the wavelength of light. Such features give rise to scattering of light which is largely independent of wavelength and angle of incidence.


The shape of the scattering pattern produced by macroroughness (called a reflectogram) is related directly to the distribution of surface slopes in the specimen. The analysis software can display either the scattering pattern, or the distribution of slopes derived from it. The software also calculates the full width at half maximum (FWHM) of the distribution of surface slopes in the plane of incidence and orthogonal to it.  These values of the FWHM are used as single number representations of the macroroughness (e.g. for comparing specimens or plotting maps).






The scattered light reflectogram always appears elliptical with an aspect ratio of approximately 4:1 owing to the high angle of incidence (75°). The distribution of slopes is more generally circular. However, the FWHM of the distribution in the x (plane of incidence) and y (orthogonal) directions provide direct information on the anisotropy of surface macroughness in a single measurement. For example, in coated paper, it is usually easy to detect the difference between machine and cross-machine directions.


The speckliness within a reflectogram is largely due to “laser speckle” – an interference phenomenon caused by the coherence of the laser light and does not contain directly  useful information about the surface.


A surface with a greater distribution of surface slopes (i.e. rougher) will produce a broader reflectogram as light is scattered into a wider range of angles. This is illustrated in the figure below, which shows three reflectograms for coated papers calendered to different degrees. Very rough materials (for example uncoated paper) may produce significant scattering outside the angular range of the Imaging Detector. In this case the analysis software employs various tricks to estimate the width of the distribution, but in extreme cases may only be able to report width in the out-of-plane direction.








Macroroughness vs microroughness




The distinction of microroughness and macroroughness may seem rather arbitrary as it is defined by the analysis method rather than the properties of the specimen. However, the distinction is of practical value, for there are many industrial materials which do exhibit a two-scale roughness. One good example is coated paper: the wood fibres in the base sheet define a macro-scale of roughness, with features of the order of ten of microns, while the coating layer, being composed of micron or sub-micron mineral particles defines a much finer scale of roughness. Some paints have similar surfaces where the extender pigments (or substrate) add macroroughness and finer pigments (or weathering) contribute microroughness.








Microroughness is roughness on a scale less than (or around) the wavelength of light. In the reflectometer, the wavelengths of light used are 635 and 670 nm, and microroughness features are normally in the range around 80-200 nm.


Roughness features around the wavelength of light produce scattering which is dependent on both wavelength and angle of incidence. The Reflectometer estimates microroughness by comparing the scattered intensity at 635 and 670 nm. For various practical reasons, the determination of microroughness is rather exacting and the method is only applicable to reasonably glossy materials. For example, it produces satisfactory results for coated-calendered papers, but generally not for uncoated or uncalendered sheets. It is also correlated to some extent with macroroughness, but in practice this latter effect does not limit its usefulness, at least a relative measure of fine-scale roughness.


The microroughness is reported as a root-mean-square (rms) amplitude in nm.  Measurements are referred to a highly polished glass standard. Good correlation has been observed with atomic force microscope measurements on coated papers.








Effective Refractive Index




The refractive index (RI) of a material is determined by the material’s composition and physical structure. RI determines how light is reflected and refracted at an interface for a given angle of incidence. For example, glass, with a relatively high RI (RI ~ 1.55) reflects and refracts more strongly than water (RI ~ 1.33). 


The textbook definitions and theory are always presented in terms of smooth and homogeneous surfaces. But the same theory can be applied to surfaces which are neither smooth nor homogeneous, and in doing so, one can learn useful information about the surface. The Imaging Reflectometer determines an approximate real refractive index. The method is valid for many materials, but not for metals, or materials with very high absorption coefficients (see Theory or ellipsometry downloads for more information).




A surface that is inhomogenous (i.e. composed of a mixture of components) reflects light as if the effective refractive index was a linear combination (by volume fraction) of the individual refractive indices of the components.  By measuring the intensities of reflected p and s polarised beams, the effective RI can be measured and will provide information on the surface composition.


A surface that is microrough or porous is a special case of the inhomogeneous surface – it is one where air is one of the components. Of course, such a surface will also scatter the light over a range of angles, but this does not directly affect the determination of effective RI. The effective RI of a porous surface can provide information on the surface porosity, or specifically the surface void fraction.


For a material like coated paper, where coating colour components generally have similar RI (typically around 1.5 – 1.6), the effective RI is very sensitive to surface porosity and can reveal, in a relative sense, how closed or compacted a surface is.


For paper coatings of a given pigment type, a good correlation has been observed between effective RI and the pore diameter as measured by mercury porosimetry.  An Applications Note on this topic can be downloaded from the technical page.










Gloss, haze, calculated gloss






Gloss is a very familiar measurement, basically a measure of reflected intensity relative to some standard material. The Imaging Reflectometer determines gloss at (nominally) 3° and 20° acceptance angles and derives (based on the reflectogram shape) additional glosses at 2° and 5° acceptance angles. Gloss is referred to a glass standard of refractive index 1.54 (at sodium d line).


Reflection haze is a measure of specularity, the percentage of intensity in 2° acceptance angle to that in 1° acceptance. A broad reflectogram gives a large haze, but haze does not offer more information than the FWHM of the scattering pattern (macroroughness). It is a measure sometimes used by the plastics industry and useful for some comparisons.




The measured parameters, effective RI, macroroughness and microroughness are largely independent of each other, and together provide a complete description of reflectance within the model used. Thus, these three parameters may be used to calculate the expected gloss… which of course can then be compared with the observed values. As the figure adjacent shows, the simple model works remarkably well for such a complex material as coated paper. Deviations of observation from the model may themselves provide indirect information about the sample – indicating that the model assumptions are being violated, or indicating sources of measurement error.





© Dayta Systems 2011