AN INTRODUCTION TO THE SURFOPTIC IMAGING REFLECTOMETER

Transcription

1 AN INTRODUCTION TO THE SURFOPTIC IMAGING REFLECTOMETER N J Elton 1. INTRODUCTION The Surfoptic Imaging Reflectometer is a new generation of instrument for polarised light reflectometry of industrial materials. In this context, reflectometry means the measurement and analysis of the properties of visible polarised light reflected and forward scattered from surfaces. The technique is fast, non-destructive and can provide useful data about the characteristics and properties of the reflecting surface. Reflectometery has application in industries wherever surface appearance is important. Applications include coated and printed paper, paint, varnish, plastics and films, automotive finishes and ceramic glazes. Reflectomter data have proved helpful in production support and troubleshooting, product development and general industrial R&D. Reflectometry, as exploited in the Imaging Reflectometer, provides quantitative data on: 2-D angular distribution of the forward scattered light. Effective Refractive Index (a measure of surface composition and porosity). Distribution of surface slopes (Macroroughness, a measure of surface roughness greater than the wavelength of light). Microroughness (a measure of surface roughness smaller than the wavelength of light ). Gloss according to various standard definitions plus other reflectance properties such as reflectance haze. Surface reflectance anisotropy. 2. ROUGHNESS AND REFRACTIVE INDEX The visual appearance of materials is of critical importance in many industries. Generally, under some given geometry of illumination and viewing, the gloss of an object s surface is determined by just two parameters the refractive index and the surface roughness. Before describing how the Imaging Reflectometer works, it is useful to review some background on roughness and refractive index. 2.1 Refractive index The refractive index is a parameter describing how light is reflected, refracted and absorbed at an interface. Figure 1 illustrates what happens when light is reflected off a smooth surface. The incident light (denoted k i ) is partly reflected from the surface (ray denoted k r ) and partly transmitted into the material (ray denoted k t ). Light reflected from a smooth surface is said to be reflected specularly i.e. mirror-like 1

2 the angle of the reflected ray with respect to the surface is the same as the angle of the incident ray and is known as the specular angle. The transmitted ray however is deflected. This behaviour is termed refraction. The amount of defection is determined by the refractive index and the angle of incidence. Further, the relative intensity of the reflected and transmitted rays is also determined by the angles and the refractive index. k i n k r n 1 θ i θ r Figure 1 Geometry of reflection and refraction at a smooth interface n 2 θ k t For an absorbing material the refractive index describes not only how light is reflected and refracted, but how it is absorbed. Selective absorption for different wavelengths is what creates colour. At the atomic scale, the reflection and transmission of light at a surface is a consequence of the interaction of the light wave with the atoms or molecules in that surface. A light wave hitting an atom sets its electrons into oscillatory motion. Then in turn, the vibrating electrons radiate the light onwards. The light is actually re-emitted into all directions, but the waves cancel out through interference effects in all but the directions of reflection and refraction. Because light is reflected and refracted via an interaction with the atomic structure of the material, the properties of the reflected or transmitted light depend on what specific atoms are present in the material and how they are bound together. Thus the refractive index is, in fact, a material property related to the material s composition and physical internal structure. A measurement of refractive index can be useful in many industrial situations where some knowledge of changes in the surface composition of a material is required, but where a full chemical (or other sophisticated and often expensive or time-consuming analysis) is not practicable or warranted. Spectroscopic ellipsometry is one method of obtaining refractive indices by reflection. This method can provide a great deal of information, including absorption coefficients over a range of wavelengths. However, the technique is specialised and mainly used for highly reflective surfaces. Reflectometry is a simpler approach which can provide useful information on refractive index at one or two wavelengths and which offers benefits in speed and practicality, but can also be used in combination with other optical techniques to extract information on roughness and gloss. A straightforward measure of refractive index can often give powerful insights into changes in structure or composition at a surface. For example, in mixtures of materials the refractive index of the mixture is usually a linear combination of the refractive indices of the individual components. Or in microporous materials, refractive index often correlates directly with surface porosity (because the refractive index measured is a combination of the material refractive index and that of air). 2.2 Surface Roughness When a surface is perfectly smooth, light is reflected specularly as described above. Most of the time, however, material surfaces are not perfectly smooth. Roughness comes in many forms and sizes. And indeed, what is perceived as roughness often depends on how the surface is measured. 2

3 One common way of measuring surface roughness is to use the technique of stylus profilometry. In this method a very fine needle is dragged over the surface moving up and down according to the profile of the surface being measured. The movements of the stylus are recorded as a trace of the surface roughness. However, as illustrated in Figure 2, a large stylus may report a different roughness to a very sharp stylus for a given surface. Figure 2. surface roughness measured by stylus profilometry the measured profile and hence degree of roughness depends on the relative length scales of the stylus and the surface This is an important point that roughness depends on how it is measured. A second consideration is that roughness comes in many different forms. Scratches, dig marks, pits, bumps, surface waviness and steps are all types of roughness, but their properties are rather different, the methods of measuring and characterising them are usually different and their effect on the appearance of an object are also distinct. A very common type of roughness which is important for optical appearance is random roughness. A randomly rough surface is one where the variations in height about a mean plane are random. Many surfaces of industrial interest have random roughness. An everyday example of a randomly rough surface is glossy magazine paper. Many printed and painted surfaces fall is this category. A randomly rough surface is described by a statistical distribution function plus (usually) two parameters a mean height and a characteristic length scale (known as the correlation length) which describes (in a statistical way) the wavelength of surface features (Figure 3). T h i Mean plane 3

4 Figure 3 Random surface roughness is described by height above a mean plane and a (statistical) length scale characterising the wavelength of surface features. When light falls on a rough surface, it is not all reflected in the specular direction as in the case of a perfectly smooth surface (Figure 1). Instead it is scattered. The amount of scattering depends on the wavelength of the light, the angle of incidence and the surface roughness. For a slightly rough surface, most of the light is still reflected in the specular direction, but as roughness increases, the scattering becomes greater, until at some point the light is scattered diffusely in all directions (Figure 4). Figure 4 From left to right (a) light reflected from a smooth surface is reflected specularly. (b) A small amount of surface roughness causes some scattering of light about the specular direction. (c) More roughness results in more scattering, but the general direction of the scattered light is still about (or close to) the specular direction. (d) For an extremely scattering surface, light is scattered uniformly in all directions. It was illustrated in Figure 2, that what is perceived as roughness depends on how the surface is measured. The same is true for light scattering. For a given surface roughness and angle of incidence, light of a longer wavelength is scattered less than light of a shorter wavelength. In the analogy of Figure 2, the shorter the wavelength, the finer the probe. In general, the scattering of light from a rough surface is a complicated mathematical problem. However, in the case where the scale of roughness is much larger than the wavelength of light, the problem becomes relatively simple. In this case the surface can be imagined as being made up of many tiny facets each of which reflects light as a would a smooth surface of the same composition (Figure 5). Then the angular orientation distribution of the reflecting facets directly determines the angular distribution of the scattered light. One example of such a case might be the reflection of sunlight from ripples on water or from the dimpled textures in the surface of an orange. Figure 5 Illustrating the facet model of light scattering 4

5 Roughness features much greater than the wavelength of light shall henceforth be referred to as macroroughness. Scattering of light by a macrorough surface is independent of wavelength or angle of incidence. When the scale of roughness is of the same order of magnitude as that of the wavelength of light (or smaller) the scattering behaviour is more complicated and the intensity distribution of the scattered light is highly wavelength (and angle) dependent. Roughness at this scale (around or smaller than the wavelength of light) shall be denoted microroughness. Figure 6 For a given surface roughness and angle of incidence, shorter wavelength light (here blue) is scattered more than light of a longer wavelength (red). This wavelength dependent behaviour is useful because it provides a potential way of obtaining information about a surface. By measuring light scattering intensity at two or more wavelengths (or angles of incidence), it is possible to deduce the magnitude of surface roughness around the scale of the wavelength of light (Figure 6). The idea that a surface roughness can be described by a two-scale model (macroroughness + microroughness), has practical value in that simple light scattering measurements can provide a rapid measure of the roughness at the two scales. 2.3 A Practical Example of a surface with two-scale roughness: coated paper It is possible to find surfaces of industrial materials which exhibit purely microroughness or macroroughness. For example, some glazed ceramic tiles have very glossy surfaces with relatively little microroughness. However, they may exhibit considerable surface waviness by manufacturing design or accident. Etched glass may be very macrosmooth but have a fine scale roughness determined by the action of the etching chemical on the structure of the glass. Figures 7 and 8 illustrate the general appearance of the angular distribution of scattered light for these two kinds of surface. Note that the intensity scales are arbitrary here the plots have been adjusted so they have the same intensity value. A macrorough surface produces a broad scattering pattern whose angular width is determined by the orientation distribution of the surface facets. The scattering pattern for the microrough surface is rather curious consisting of a very narrow sharp spike at the specular angle sat on a very broad hump. Here some fraction of the light intensity is reflected just like from a perfectly smooth surface while the remainder is scattered widely creating a fairly broad scattering background. The pattern in figure 7 is largely independent of incidence angle or wavelength. However that of figure 8 is strongly angle and wavelength dependent. The angle of incidence for Figures 7 and 8 was 75 from the surface normal (i.e. 15 to the surface itself). At high angles, the specular spike of figure 8 may disappear leaving 5

6 a broad hump more resembling that of figure 7. This behaviour has a considerable effect on the appearance of objects. A piece of ground or etched glass (or some painted surfaces) viewed from above may appear quite matt with no distinct reflections, but viewed at a very shallow angle may reflect images with little distortion. Intensity (arbitrary scale) angle (degrees) Intensity (arbitrary scale) angle (degrees) Figure 7 Scattered intensity vs angle for light incident at 75 on a macrorough (random wavy) surface. Figure 8 Scattered intensity vs. angle for a macrosmooth but microrough surface. Many surfaces of practical interest possess roughness at several scales and the optical characteristics result from the combined effects of these different roughnesses. This complexity can be difficult to deal with rigorously, but a useful simplification in many cases is to describe a surface as being composed of microrough facets i.e. a combination of roughness at just two scales. One everyday material which illustrates this approach well is glossy paper (of the type used in glossy magazines or mail order catalogues for example). Figure 9 shows an cross-section through such a piece of paper viewed under an optical microscope. Basically, coated paper consists of a sheet of interwoven and tangled wood fibres to which has been applied a coating of fine white mineral pigment (usually kaolinite clay or calcium carbonate). The mineral pigment coating serves several purposes it makes the sheet whiter and brighter, it fills and levels voids and bumps in the surface creating a smoother sheet and it presents a relatively well defined microporous layer ideal for high quality colour printing. 6

7 Microroughness profile Macroroughness profile 5 µm Clay coating Paper fibres Clay coating Figure 9 20 µm Optical microscope cross-section through a clay-coated lightweight magazine paper. The base sheet fibres define a large-scale roughness profile (sketched in green). However, the mineral pigment in the coating later defines a microscopic roughness scale (sketched in inset enlargement in blue). The distribution of light scattered from the surface of glossy paper resembles that of figure 7. A detailed analysis shows that the macroroughness largely defines the gross angular distribution of the scattered light, but that the intensity of distribution is modified due to the microroughness of the pigment coating. Analysis of reflectometry data can quantify the macroroughness and microroughness and experience has shown that this two parameter model of roughness is very useful for understanding coated paper properties. By also measuring refractive index, information is obtained relating to surface composition and microporosity, which, coupled with the roughness data, provides much useful information about the surface of the coated paper. Many other industrial materials can be treated in a similar way painted and printed surfaces in particular have many similarities with the above example. 3. HOW THE IMAGING REFLECTOMETER WORKS Collimated light is directed at the specimen surface at a fixed angle of incidence, nominally 75 to the surface normal. At the surface, the light is scattered and its angular intensity distribution measured with an imaging photodetector, which collects scattered light over a range of about ± 10 about the forward specular direction (Figure 10). The angular distribution of the scattered light is called the Reflectogram. The imaging detector captures the full 2-D reflectogram within its angular range, but for analysis it is generally more useful to present the scattering pattern as two 1-D reflectograms slices through the 2-D distribution in the plane of reflection and out of the plane of reflection (Figure 11) In earlier reflectometry measurements, data were typically collected using a photodiode mounted on a mechanical goniometer (e.g. Gate et al., 1973, Gate & Leaity, 1991). This approach can be versatile, but is very slow and not particularly user-friendly. The key advantage of the imaging detector is the elimination of moving parts: benefits include fixed alignment and improved speed of measurement and robustness. 7

8 Scattered light collected by imaging detector Incident collimated beam 75 2-D scattering pattern (reflectogram) Figure 10 illustrating the basic principle of operation As described in section 2, surface roughness on a scale significantly greater than the wavelength of light can be expressed as an orientation distribution of surface facets. Roughness at this large scale is independent of wavelength and angle of incidence. However, light scattering by roughness features around or smaller than the wavelength of light can be strongly wavelength dependent. Generally the shape of the reflectogram is largely determined by the macroroughness. The microroughness contributes to broadening of the wings of the scattering pattern, but the effects are not usually noticeable unless the microroughness is very large. If microroughness effects can be neglected in the shape of the reflectogram, it can be inverted to obtain the distribution of slopes in the material surface. Comparison of in-plane and out-of-plane reflectogram FWHM can provide information on macroroughness anisotropy in the sample surface. (a) (b) Intensity (c) Detector angle (degrees) 8

9 Figure 7 Typical image of scattered light from a sample of coated paper. The intensity distribution is known as the 2-D reflectogram The data may be displayed in various ways. (a) Grey scale image (raw data), (b) 3-D representation. More useful for analysis are slices through the 2-D distribution in the plane of incidence (c) and normal to it. These 1-D reflectograms lend themselves to statistical analysis. Reflectograms may also be transformed into a distribution of facet angles (surface slopes). Macroroughness can be quantified as the FWHM surface slope distribution. The integrated intensity of the scattered light contained within some specified acceptance angle can be used to calculate gloss (by reference to a suitable standard). A further advantage of the imaging detector is that it is easy to calculate gloss according to a variety of acceptance angles. Microroughness is estimated by comparing the reflected intensity at two wavelengths. The difference in intensity can be used to calculate the microughness. The reflectance of light of different polarisation states is described by the Fresnel equations and depends upon the refractive index of the surface. By comparing reflected intensities for light polarised normal and parallel to the surface, it is possible to derive the refractive index. Mapping beam Optics (option) Lasers Reference beam CCD Camera and Scattered light detectors Photometric and Imaging detectors Polarising optics specimen Angle mapping optics Figure 12 Simplified schematic of Imaging Reflectometer showing principal components A typical reflectometric measurement consists of measuring the reflectance at various polarisation and wavelength states to derive the full range of information available from the reflecting surface. Data acquisition takes about 0.3 s and all measurements are fully automated under PC control. The reflectometer may be equipped with a motorised x-y stage to allow mapping of reflectometric parameters over the surface of a specimen. Thus the instrument is imaging in several senses principally in that it produces directly an image of the angular distribution of the forward scattered light but also in the sense that it can produce images of refractive index and roughness over a specimen surface. A general schematic for the instrument is shown in Figure 12. The instrument is also provided with a CCD camera for direct viewing of the specimen under various illumination conditions (useful for setting up and for locating features for analysis). The theoretical background is described in the Surfoptic Technical Paper TP2 Reflectometer Theory. The Imaging Reflectometer is calibrated using a block of highly polished glass of known refractive index. The automatic calibration procedure ensures that all measured intensities are referred to this standard which means that gloss, refractive index and microroughness are always referenced to a standard material of known properties. It is assumed for the purposes of the microroughness calibration that the standard is perfectly smooth. In fact the reflectometer is relatively insensitive to extremely small roughness levels (owing to the geometry) and this assumption is perfectly satisfactory. Figure 13 illustrates the linearity of refractive index determination across the range

10 1.8 Measured RI glass standards Figure 13 Measured refractive indexes for a range of reference materials illustrating good linearity after calibration. 1.3 water film True RI The instrument geometry and alignment is factory set. An angular calibration is carried out during commissioning. Macroroughness and other angular distribution measurements are related to this factory calibration. ACKNOWLEDGMENTS The author is indebted Dr Len Gate for his valuable input. FURTHER INFORMATION Further information on the Imaging Reflectometer instrument, the background theory, and various practical applications may be found on the Surfoptic web site: 10