Tuesday, July 3, 2012

Flat paint is not flat

I needed to paint the inside of an ambient light exclusion device for an optical mensuration1 experiment. (To the layman, I was trying to paint the inside of a box black.) I had decided on flat black mainly because it would look cool. Flat black really gives A/B plywood an air of scientificalness.
The trouble was, this was autumn and the temperature in my garage2 was 45°. The warning label on the spray paint can advised me against painting at temperatures below 50°, but I threw caution to the wind. In single-minded devotion to the greater cause of Science, I forged ahead, hoping that I did not get caught by the Spray Paint Police.
I can look back on this today and laugh at my naiveté. I was quite frankly surprised by the results. The flat black paint came out glossy.
How can flat paint become glossy?
Naturally, my first reaction was to get out the microscope to investigate the microstructure of the surface. This is what I saw.

The image at the left is the surface that I had just painted. The one on the right was a surface that looked flat black because I had painted it at the regulation temperature. Clearly, the glossy surface on the left is smoother than the matte surface on the right. Ironically, the surface of “flat” black paint is not flat!
My “flat black” spray paint became glossy because the vehicle (the stuff that carries the pigment) evaporated much slower at 45°. This gave the surface of the paint time to smooth out.  
Changing color with colorless water
Seeing these images, I immediately had a flashback to one day when I was five years old. I had found myself with a small plastic bucket filled with water and a paint brush. The young scientist in me bloomed when I painted the wall of our house with water, and found that it turned the house from a chalky light green to a richer green.
Some adult wandered by and asked me what I was doing. When I said that I was painting the house, they frantically went off to find my mom. My little ruse had fooled even them. I probably got spanked before the truth was realized. If only I had known Fresnel’s law at the time, I would have been able to explain the phenomenon to my mother before her hand came down on my precocious little butt.
Fresnel’s Law
Fresnel’s Law3 describes what happens when light goes from one medium to another, in this case from air to the surface of the paint or water. When light goes from air to a surface that is optically “harder” (having a higher index of refraction), some light enters the surface and other light reflects directly from the surface, in billiard ball fashion – with angle of incidence equaling angle of reflectance.
Fresnel’s law predicts what percentage of the light is reflected and what percentage of light enters the second medium. The law takes into account the angle of incidence, the indices of refraction of the two media, and the polarization of the incoming light. All that is fabulously interesting, but all we need to know is that somewhere between two and five percent of the photons act like little billiard balls. We call this specular reflection.
I brought my good friend Smeldon in to demonstrate. He reads his magazine4 with the light behind him, and the magazine tilted slightly away from him. Without even thinking about it, he will orient the magazine so as to avoid the specular reflection. Smeldon could orient the magazine so he sees only the gloss of the magazine, as in the drawing on the right. If he were to do this, the print on the paper would be largely washed out by the specular light.

Smeldon’s magazine was printed on a coated stock. After the paper is formed, it goes through a second process where various additives, like kaolin (a white clay) and calcium carbonate, are affixed to the surface of the paper and then the paper is polished to a glossy finish. The coating makes the surface glossy. Most magazines are printed on coated stock. Newspapers and Sunday paper inserts are printed on uncoated stock.
If Smeldon were to try this same experiment with a newspaper, he would not see the same results. In fact, he would be hard pressed to find a way to orient the newspaper in such a way as to see gloss. (The interested reader will try this before going on. Go ahead. I’ll wait.)
Smeldon is not an accomplished color scientist and applied mathematician like me (and he is not nearly as good-looking as me) but he does have a bit of a scientific bent. His conclusion is that newsprint is an exception to Fresnel’s law. It would appear that newsprint has very little surface reflection.
Holding out on the dark side
Smeldon is inquisitive and intuitive, but in this case, he is wrong. A newspaper has plenty of specular reflection; it’s just hiding in plain sight. I’ll get back to that in a bit.
Anyone who has looked at a magazine and newspaper side by side will notice that the magazine has much richer color. A solid black on newsprint looks almost gray when sitting next to a solid black of a glossy glamour magazine.
Why is this? I have heard many otherwise intelligent people attribute this to “holdout”. As the explanation goes, glossy stock will “hold out” because of its nice smooth and hard surface. That is, it will impede the progress of ink that tries to seep in. Newsprint has no protective coating, so ink will seep into the paper, and some of the cute little pigment particles will hide behind paper fibers.
I am sure this is explanation is true, but hey, flies walk on the ceiling. I am not convinced that this is the predominant effect. I submit the following image as proof. The image is of newsprint. I borrowed my wife’s clear nail polish and painted over the word “FREE”. The black ink with the polish is noticeably darker. I didn’t add pigment. This was clear nail polish. This is not explained by the “ink hiding behind the paper fibers” theory – the cute little pigment particles are still in hiding. Why did it get darker?

Newsprint with splotch of nail polish
The next picture sheds some light on the quandary by shedding light from a different direction. To take the next picture, I left the camera and the newsprint where they were and moved the light over to the specular angle. The splotch of nail polish has suddenly gotten much brighter because the specular reflection has suddenly reappeared.

Same sample, with light at specular angle
Going back to the original pair of microscope images, we saw that the “flat” black ink on the right had a rough texture. Photons hit this rough surface and reflect specularly in all sorts of directions. Contrary to Smeldon’s conclusion, newsprint still follows the magic of Fresnel’s law, it’s just that the specular reflection goes in all directions.
In the first “free estimate” image, it’s not so much that the nail polish made the black ink darker. It’s more that the specular reflection in the other parts of the image made the black ink without the polish look lighter. The nail polish focused the specular reflection so that it all bounced away from the camera.
My conclusion is that smoothness will make a surface appear darker in color. This is not because there is less total light reflected. It is because the specular reflection from a smooth surface generally bounces off in a direction where we don’t normally notice it.
  1.  Notes
1)      No, I didn’t spell that word wrong. “Mensuration” means the act of measuring. All good mensurologists know this word and use it all the time. It’s like a secret handshake.
2)      Due to certain previous incidents, I wasn’t allowed to paint in the basement like other respectable mensurologists do. I guess we can see why I don’t have a Nobel Prize. Yet.
3)      In my humble opinion, Fresnel’s Law is way cooler than Snell’s Law. By the way, Snell’s Law was discovered by Ptolemy. I don’t know who discovered Fresnel’s law, but we know from a previous blogpost that it probably wasn’t Fresnel. As for the Fresnel lens? That idea came from Georges Louis Leclerc, and not Augustin-Jean Fresnel.
4)      Magazines were a technology common in the 20th century that was similar to the iPad. While articles could be read on these devices, you could only check the status of a few celebrities, and one magazine could barely hold a few dozen articles. To their credit, they were produced from a once common renewable resource called “trees”. Ask your grampa to tell you about trees.


  1. Actually what we call Snell's law was not accurately derived ny Ptolemy but by Ibn Sahl in 984 (Rashed, Roshdi (1990). "A pioneer in anaclastics: Ibn Sahl on burning mirrors and lenses". Isis 81 (3): 464–491. DOI:10.1086/355456.)

    While you may consider Fresnel's law way cooler it is far less useful. Snell is used to undepin most ray tracing programs use to design focusing devices in all kinds of modern optoelectronic devices. Fresnel not required.

    Fresnel lenses have nothing in common with the law assigned to his name.

  2. Perhaps next time you will give more attention to the instructions from the coatings chemist concerning the reaction temperature required for his polymer resin to form a conformal coating instead of floculating the extenders and pooling a layer of unpigmented polymer at the surface of the coating.

    Also those in optics prefer the term metrology or metrological to mensuration, even though optics is highly dependent on geometry we prefer to reserve the term mensuration for the practice of measurement in geometric mathematics.

  3. I love the comments! Thank you, Unknown. (Although I suspect you are not quote unknown to me. I think I recognize the lion by his paw.)

    You are correct that I have given too much credit to Ptolemy. He merely characterized the effect of Snell's law, and fit a quadratic to it. He did not analyze this from first principles, apply a trig function, or go beyond measurements of refraction in water.

    Thanks for the info on ibn Sahl. I had not yet met the guy in my studies on applied math history.

    You're right. Fresnel's law is not required when understanding Fresnel lenses.

    I hope you don't think less of me for sometimes favoring "cool" over "useful". :)

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  5. As for those darn flocculating extenders... One thing I have pondered about heatset presses... In order to maximize the amount of product out the door, the press guy tries to run the press as fast as possible, which means he needs to run the dryer at a higher temp. Doing that, he spends more money on natural gas, but (it seems to me) he also loses gloss. This means he needs to run more ink to get the same density.

    I wonder how big this effect is. What are the hidden costs of running faster?

    1. Time on a heatset web is much more costly than ink. (a total guess, knowing that cost is usually the determining factor over quality)