Wednesday, August 20, 2014

When light reflects from stuff

I responded to a recent discussion on LinkedIn, baring my soul about the measurement of the color of metallic stuff. I have never seen a standing ovation on a LinkedIn discussion thread, but... another person responded "Oh?  That's interesting." I will take that as the closest thing to a standing ovation that you can get on professional social media. Or maybe I should say that the mildly pleasant comment was the closest thing to a standing ovation that I can get!

But nevermind. I described some of the plethora of color appearance measurement devices, and Jonkai found it interesting. I decided to blog about this, to explain why we have 0/45 spectrophotometers that are sometimes polarized but sometimes they are 45/0, and we have 8/diffuse spectrophotometers that are SPIN or SPEX, (is your head spinning?), and we have really hoity-toity sounding instruments called goniospectrophotometers, but some of them are abridged. And then there are friendly sounding devices called glossmeters.
A simple goniophotometer, from US Patent 6,249,751

Wouldn't that be a great topic for a blog post?  Absolutely! Too bad that's not the topic of this blog. Before we get to that dessert topic, I need to prepare you, dear reader, with some fundamentals. How does light reflect from objects? Understanding the difference between specular and bulk reflection goes a long way to explain why we have so many different types of geometries for color appearance measurement devices.


I have two articles online where you can go to read about the possible destinies of a photon (a tiny particle of light) encounters an object. In an article in called Four Fates of a Photon, you can read the short answer: a photon may bounce off the surface, it may enter the object and get absorbed, it may transmit all the way through the object, or it may scatter within the object, eventually to be absorbed, transmitted, or scattered again. In another humorous and insightful blog post, I asked the "simple" question of What Color Is Water. The various answers to this question - the different colors of water under different conditions - gave a practical example of these four fates.

A fate worse than absorbance!

Reflective light = specular + bulk

It is normal to think that the colorfullness of an object is due to the light that bounces off the surface. An apple looks red because red light is reflected from the surface, right?  It's also normal for us to think that light doesn't go into solid objects, except for clear solids, like water. Oh, and lemonade or iced tea or Jello.

But that's not quite the case. Light that bounces from the surface of an object (the specular reflection) has basically the same color as the incident light. An apple looks red because a lot of the incident light goes into the skin of the apple and only the red light survives to tell about it. Light that is green or blue gets absorbed into the skin of the apple. This is called the bulk reflection.

Whenever we see an illuminated object, we are viewing a combination of specular and bulk reflection. Uusally, the bulk of the reflection is bulk reflection.

The nature of specular reflection

Specular reflection is also referred to as gloss, glint, glare, and mirror-like reflection. This is not to be confused with "spectral", which is a modifier that refers to a photons position in the rainbow. Or, "spectral" might also mean "having to do with stuff in the spiritual world". Oddly enough, another similar sounding word is "secular", which means "having to so with stuff not in the spiritual world".

Specular light is largely governed by Fresnel's equations and Billiard's law. Fresnel is best known for inventing the Fresnel lens that can be seen in every lighthouse and every geek's wallet. Bobbi Billiard is a busty swimsuit model and former pro wrestler who has nothing to do with Billiard's law.

The math in Fresnel's equations is ugly -- if math can ever really said to be ugly -- but the details are not important. The equations tell us how much light is reflected when it goes from one medium to another and how much enters the second medium. This could mean going from air to glass, or from water to air. Here are the three important consequences of the Fresnel equations:

   1. The "harder" the surface (from the perspective of a photon), the larger percentage of light that reflects specularly.

The first law explains mirrors. If I were a photon, I would believe that metal and mirrors and stuff like that is pretty darn hard. If I saw a piece of metal in my path, I would get out the old crash helmet, cuz I know that I would be changing direction in a few femto seconds. Glass? Not so hard. Maybe I have a 5% chance of going specular. Water, still less.

If I were to want to sound really smart, I would say that the relative hardness of a material from the perspective of a photon is called its index of refraction.

   2. The shallower the angle, the larger percentage of light that reflects specularly.

The second law is all about playing the angles. As I said in the previous paragraph, photons hitting glass straight on have a one in twenty chance of flying right back again. If photons approach the glass from the side (a shallow angle) then glass or even water might just as well be a mirror.

   3. The amount of specular reflection depends on polarization of the light.

Polarized sunglasses. Need I say more?

Well, maybe I do. When light reflects specularly at somewhere near 53 degrees, pretty much all of the light that was polarized in one direction goes into the material. This angle is called the Brewster angle. The 53 degree angle is for glass - the exact number depends on how optically hard the surface is. As a result, the specular light is pretty much all polarized in the other direction. Using the proper polarizing filters can eliminate the glare, at least when you are near the Brewster angle.

Using antispecular specs to hide my glaring personality

For completeness, I add Billiard's law:

   4. Specular light reflects like a billiard ball.

This one is near and dear to my heart, not because of any special attraction to Bobbi Billiard, but because it helps explain why magazines don't look like newspapers. As the diagram below shows that, if a surface is not flat, light will reflect in all different directions.

Red light rays, photographed bounding off a smooth pebble

What does that have to do with magazines and newspapers, you may ask? Both of them are flat. Ahhh! So it would appear, Dear Reader!  At the microscopic level,  Magazines are mostly. As a result, when directional light hits the surface, the specular reflection is also directional. Note that when we read a magazine, we subconsciously orient the magazine so that the gloss goes somewhere else, and we don't see it.

Newspapers are anything but flat, and as a result, the specular reflection is sent out in all directions. No matter how we orient a newspaper, we see the specular reflection, so we don't notice it. And it makes the newspaper inherently lighter in color. Our perception of "glossy" is just specular reflection that has been concentrated into one angle.

Note that our perception of glossy and matte paint works the same way.

The nature of bulk reflection

The last section was about one of the four fates of a photon when it encounters an object: specular reflection. Once a photon has decided to pay the cover charge to enter the medium, the other three fates come into play. A photon may be absorbed or it may be scattered. Failing to do either, the photon may emerge on the other side.

Ideal white paint

An ideal white paint - primer - should only scatter photons. They enter the paint layer, encounter a "particle of white opacity making stuff" (like titanium dioxide, barium sulfate, calcium carbonate, or the infamous lead sulfate), and change directions like pinballs. The photons would stay in play, bouncing around until they finally exit. All photons eventually find their way out, so the paint has 100% reflectance.

In a less-than-ideal white paint, there may not be enough "particles of white opacity making stuff" to block the photons from reaching the layer under the paint. If this happens, then some may be absorbed by the layer underneath, so that the reflectance is something less than 100%. In the worst case, the layer underneath is a rich color whose absorbance is spectrally selective, that is, it absorbs more of one part of the spectrum than another. In this way, it will impart a hue to the layer of paint that is overneath.

Note that the photons that eventually exit will have long since forgotten which direction they were going when they started out. In other words, when they exit, they could be headed in pretty much any direction.

Ideal ink

While an ideal white paint scatters photons without absorbing, an ideal ink is just the reverse. In an ideal ink, photons make their way through the ink to the paper (or other substrate), reflect from the substrate, and then make a second pass through the ink. All along the way, photons run the risk being absorbed, but the motto of the ideal ink is "non dispergam" (never scatter).

This bit about scattering is important. If I print yellow ink atop cyan ink, I want the result to be green, and not yellow. I don't want the yellow ink to hide the cyan ink below.

Oh, by the way... The cyan, magenta, and yellow inks are all spectrally selective. Cyan ink likes to eat photons at the red end of the spectrum. Yellow ink likes to eat photons at the blue end of the spectrum. Magenta ink is partial to photons near the middle, the green photons. How this gives us the gamut of colors that can be printed is a fabulously interesting topic. No doubt I will blog about it some day.

I should mention something about the direction that photons exit from a perfect ink. Such photons will travel through the ink without changing direction, so their angle of exit depends a lot on the characteristics of the substrate. Often this means that this sort of bulk reflection is equally likely to be pointed in any direction, but this may not always be the case.

I should also mention that photons in an ideal ink will follow Beer's law.

The real world

I have carefully avoided talking about paint that isn't white, and ink that isn't transparent. These are the interesting cases, since they involve both scattering and absorbing. These are also complicated cases. Beer's law just won't cut it. It's time to haul out the old Kubelka-Munk equation.


The light that reflects from an object is a combination of light that reflects directly from the surface and light that interacts with the object. The net effect is a combination of the Fresnel equation, the Billiard law, Beer's law, and the Kubelka-Munk equation. Between all these equations, we can characterize the amount of light that reflects from the object as a function of direction of incoming light, direction of exiting light, and wavelength.

A basic knowledge of these rudiments is helpful in understanding the next installment on color appearance measurement devices.

1 comment:

  1. Forget the standing ovation. I'm still trying to figure out if "professional social media" is an oxymoron.

    - DW