User:Ditaylor/draft Gloss

See also List of optical topics.

What is Gloss?

Gloss is an optical property, which is based on the interaction of light with physical characteristics of a surface. Although we may think of gloss as ‘mirror-like reflection’, mirrors are not considered particularly glossy.^[1] A better definition of gloss may be ‘the reflection of highlights’. Gloss perception, a psychophysical phenomenon, incorporates surface finish, texture, view and illumination.

Figure 1: results for several settings of Phong’s model. General decrease in reflectance with angle is diffuse reflectance. Glossy reflectance is a ‘spike’ of varying sharpness.

Two formal definitions of gloss are:

1. The attribute of surfaces that causes them to have shiny or lustrous, metallic appearance.
2. The mode of appearance by which reflected highlights of objects are perceived as superimposed on the surface due to the directionally selective properties of that surface.

Hunter^[2] describes gloss in six distinct ways. These involve not only specular reflectance (reflectance at an angle opposite that of illumination about the surface normal), but also reflectance from the material bulk after scattering within it. The six descriptions include lustre, haze and contrast gloss. Phong^[3] modelled surface reflectance with angle for computer graphics (Figure 1) showing how specular reflectance only partly describes gloss - with the diffusely reflected light, and the light reflected about the specular angle also being significant.

Specular and diffuse reflectance

Metals reflect and scatter most incident light from the first few atomic surface layers. Metallic optically-flat surfaces reflect typically >90% of light specularly, making them mirror-like. Non-metals mainly reflect light diffusely from deeper within the substance by an amount proportional to the cosine of the angle from the surface normal. The specular reflectance of glossy ceramic may be only 4% of incident light. The highest possible reflectance at the specular angle will be when the surface is perfectly smooth.

Surface Roughness

Figure 2:Specular reflection of light from a rough surface

Specular reflectance decreases with surface roughness. Figure 2 shows reflection at angle $i$ on a rough surface with a characteristic roughness height $h$. The path difference between rays reflected from the top and bottom of the surface bumps is:

$\Delta r=2h\cos i\;$

When the wavelength of the light is λ, the phase difference will be:

$\Delta \phi ={\frac {4\pi h\cos i}{\lambda }}\;$

If $\Delta \phi \;$ is small, the two beams (Figure 2) are nearly in phase and therefore the specimen surface can be considered smooth. But when $\Delta \phi =\pi \;$, beams are not in phase and beam cancellation occurs through interference. If an arbitrary criterion for a smooth surface is $\Delta \phi <{\frac {\pi }{2}}$, then substitution into the equation above produces:

$h<{\frac {\lambda }{8\cos i}}\;$

This smooth surface condition is known as the Rayleigh criterion.

Relating Specular Reflectance to Refractive Index

For a perfectly smooth surface, the Fresnel equation [4] gives the specular reflectance, $R_{s}$, for unpolarized light. $R_{s}$ is the ratio of intensities ${\frac {I_{r}}{I_{0}}}$ for angle $i$ of incidence (and reflectance) with $i$ referred to the surface normal. The equation requires $n$, the refractive index of the surface specimen.

The Fresnel equation is: $R_{s}={\frac {1}{2}}\left[\left({\frac {\cos i-{\sqrt {n^{2}-\sin ^{2}i}}}{\cos i+{\sqrt {n^{2}-\sin ^{2}i}}}}\right)^{2}+\left({\frac {n^{2}\cos i-{\sqrt {n^{2}-\sin ^{2}i}}}{n^{2}\cos i+{\sqrt {n^{2}-\sin ^{2}i}}}}\right)^{2}\right]$

Inserting $n$ values of 1.567 (glass) and 2.419 (diamond) into this equation, at higher (grazing) angles there is little difference in specular reflectance between glass and diamond. At low angles (viewing the diamond surface face on with light source practically behind you), diamond reflects almost four times as much light as glass. This is how diamonds sparkle so, and why glass is no substitute for diamond in jewellery.

Relating Specular Gloss Units to Specular Reflectance

The most popular standard gloss measurement description ASTM D523,^[4] contains the core definition of specular gloss units (SGU):

A glass of refractive index 1.567 at 589.3 nm has a specular gloss value of 100 SGU for any angle of incidence.

At high (grazing) angles, diamond has about 110 SGU, comparing with 360 SGU at low angles.

The Metallic Perfect Mirror Gloss Scale

Metallics are measured with a different scale to the SGU method, setting 100 (at all angles) as the value of a ‘perfect mirror’. The SGU system would yield a number much higher than 100 for a perfect mirror, whereas in the metallic mirror scale the value is defined to be lower, namely 100.

Measuring Gloss

Which Gloss Measurement Method is Appropriate?

Figure 3: SGU measurements of 13 samples of increasing glossiness

Rougher (less glossy) surfaces tend to look glossier at grazing angles. This is why accurate gloss measurement uses more than one angle - selecting the angle according to how glossy the sample is.

Many written standards describe gloss measurement. Most are industry variants of ASTM D523 which uses three measurement geometries (20º, 60º and 85º angles).

To select the appropriate specular geometry to use: First measure sample in 60° geometry. If the gloss value is higher than 70 SGU (high gloss) then re-measure at 20°, if less than 10 SGU (low gloss) re-measure at 85°.

Figure 3 shows how this works in practice. Byk-Gardner^[5] measured 13 samples of increasing glossiness in all three geometries. The cyan line sections show how three geometries are better than one in covering the gloss scale linearly.

Gloss Measurement Instrumentation

There are three basic types of gloss meter which (usually) include a specified light source and a detector emulating the human eye’s response. The first type measures only SGU, the latter two give reflectance values about the specular angle for other gloss measurands such as lustre, haze and contrast gloss.

Fixed Few Detector/Illuminator

Figure 4: A parallel-beam specular reflection instrument

By far the most prevalent gloss meter is the one beam in – one beam out approach shown in Figure 4. Many instruments use sets of illuminators and detectors at 20º, 60º and 85º.

Goniophotometer A more flexible and complex version of the above class of instrument is the goniophotometer (GP) shown in Figure 5.

Figure 5: A goniphotometer

The lamp, (generally the most fragile component in a GP), is fixed while the sample and detector move independently. Both incident and reflected intensities can be measured if the sample is removable. GP measurements take longer than fixed systems.

Multi Detector Array These meters (Figure 6) use a relatively inexpensive detector array to speed up the laborious serial function of GPs by simultaneously measuring intensities at a range of angles about the specular angle.

Figure 6: A multi detector array instrument

References

1. ^ "Best Practice Guide to Gloss measurement" (PDF). Retrieved 2006-07-10.
2. ^ R. S. Hunter (1987). The Measurement of Appearance (2nd ed.). New York: John Wiley & Sons. {{cite book}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
3. ^ T. B. Phong (June 1975). "Illumination for Computer Generated Images". Communications of the ACM. 18 (6): 311–317. doi:10.1145/360825.360839.{{cite journal}}: CS1 maint: date and year (link)
4. ^ D523, Standard Test Method for Specular Gloss. ASTM Gaithersburg. 1999.
5. ^ "Byk-Gardner Technical Note". Retrieved 2006-05-03.
6. CIE Publication 17.4 (1987). International Lighting Vocabulary. Vienna. ISBN 3900734070.{{cite book}}: CS1 maint: location missing publisher (link) CS1 maint: numeric names: authors list (link)
7. E. P. Lavin (1971). "Specular Reflection". Monographs in applied optics (2). Adam Hilder. ISBN 0852741749. {{cite book}}: Check |isbn= value: checksum (help)
8. G.H. Meeten (1986). Optical Properties of Polymers. London: Elsevier Applied Science. pp. 326–329. ISBN 0853344345.