Tuesday, March 14, 2017

On the nature of emitted light, Part 1

This is Part 1 in a long and boring series of blog posts on the nature of emitted light. I apologize to the astute reader who has probably already gleaned that much just from the title. That first sentence was for the non-astute reader, who none-the-less, I am compelled to accommodate by the American Blog Readers with Under-Potentiated Techno-savvy act of 2019.

This series of blog posts was inspired by discussions in print standards groups regarding the light source in viewing booths, the light source in spectrophotometers, and the illuminant used to compute L*a*b* values. I will get to that discussion eventually, but I should lay some groundwork -- actually quote a bit of groundwork -- initially.

This particular blog post in the series, which is eponymously named "Part 1", is about that quintessential bright idea, the light bulb. I will eventually provide information that will make color scientists happy and will help people understand things like "D50 light booth", but all I promise for today is to throw out enough factoids so that everyone can learn a little something about incandescent light bulbs. If you read this whole thing through, and didn't learn nothin', then I will buy you a beer the next time I see you in a bar. Provided that you buy me a beer first.

Photons like it hot

Factoid #1 - Everything that is hot gives off electromagnetic radiation. Marilyn Monroe, Brad Pitt, applied mathematicians, snow cones, everything. Even at the very edge of the universe, beer coolers that are set to a chilly 2.7 degrees above absolute zero are giving off electromagnetic radiation. We call this temperature at the edge of the universe 2.7˚ Kelvin, or abbreviate it to 2.7 K. It is the remnant of the Big Bang. I am still a bit miffed that I wasn't invited to this event.

These may be a knock-off brand, but the jeans are really hot!

Factoid # 1.5 - Note the potential for confusion with "K" meaning thousand. Should I call 1000 degrees Kelvin 1 KK??

Factoid #2 - Degrees Kelvin is defined based on absolute zero, the coldest possible temperature, where all heat is gone. Temperatures near this can only be attained in the laboratory, or on the shoulders of the women I went out with before I met my darling wife. Degrees K can be determined by adding 273 to the Celsius temperature.

At 2.7 K, there is electromagnetic radiation, but we wouldn't properly call it light, since we can't see it. Visible light or just light is that part of the electromagnetic that we can see. To be sure, this is a very anthropocentric definintion, since it is based entirely on our own pathetic eyes, which can't even see into the ultraviolet or infrared. If Flysaac Newton had been the one to play with rainbows, visible light would extend another 100 nm down into the ultraviolet.

BTW, the phrase visible light is redundant, just like the phrase devastatingly attractive color scientist.

Factoid #3 - When matter gets up to maybe a thousand or so degrees Kelvin, it starts emitting electromagnetic radiation that we call that light, since we can finally actually see it. It probably looks red, if we can see it. It might be very dim, but if it is visible, then we would call it red. If you have sat gazing into the coals of a fire in the night, or participated in branding cattle, you will know about this. Or if you have ever toasted a bagel.

My bagel likes it at a toasty 1000 K

As the temperature of a solid object increases beyond that red glow, it starts to turn orange, and eventually yellow. As a reference point, an incandescent light bulb emits light that is around 2900 K.

Factoid #4 - CIE 15.4:2004 is the ISO standard that is like the book of Genesis for color scientists. It defines the spectra of various standardized light sources, including "illuminant A", which is defined as "a gas-filled tungsten filament lamp operating at 2856 K". The original definition of Illuminant A was for 2848 K, but those darn physicists changed the definition of the temperature scale, so the originally tabulated data is actually closer to 2856 K. Many of you were probably wondering about that change.

Factoid #5 - I found the value of "2848 K" in Handbook of Colorimetry, (MIT Technology Press, 1936)  and in The 1931 I.C.I. Standard Observer and Coordinate System for Colorimetry (Deanne B. Judd, 1933). Neither had any explanation of why 2848 K was chosen over 2849 K or the somewhat less hip 2841 K. It was probably an intense lobbying effort.

Making the minor adjustment from 2848 K to 2856 K

Why does a hot object emit light? A simple explanation is that photons get so hot that they just can't take it anymore, and they "boil" off. The more complicated explanation is beyond the scope of this blog -- quantum physics and all that -- which is another way of saying "I am ignorant on this subject, but I don't want to give the impression that I am ignorant."

Factoid #6 - A photon is the smallest unit of light. Each photon can be characterized by its wavelength - its position in the rainbow. This position relates to the amount of energy in the photon. This all relates to the Duality Principle of physics, which says that depending on which question you are answering on your physics exam, you need to either consider light to be a wave or a particle. I usually think of light as being particles. Or as waves.

Factoid #7 - Photons are afraid of the dark. I mean, have you ever seen one chilling out in the dark?

Shameless plug for my blog: Visit the internet's largest compendium of photon jokes!

Walking the Planck

Once upon a time, there was a physicist by the name of Max Planck. He invented incandescent emission. Before he came along, hot things didn't give off light. People were changing light bulbs right and left, but they never got them to work. These times were called the Dark Ages.

Actually, I lied. Planck didn't actually invent incandescent emission. He just noticed it, came up with an explanation of what might be causing it, and based on this explanation, he invented a simple formula that fit well with observations of light emitted by stuff that is hot. Oddly enough, we call this Planck's Law. (This is actually unusual for a scientific discovery to be named after the first discoverer!)

The starting point for his theory is the concept of a black body. This is an object that is tautologically only emitting black body radiation, since black body radiation is the radiation emitted by a black body. This black body radiation has a characteristic spectral emission curve; if you know the temperature, Planck's equation will tell you how much light is emitted at each wavelength.

but it's not exactly what we are talking about.

The plot below shows the relative emission of two black body radiators as a function of wavelength. Note: I scaled the two so as to have the same peak emission. The peak for the 5000 K emission is about 3,000 times as large as the one for 1000 K. Higher temperature, more energy emitted. Makes sense.

A bright idea

Factoid #8 - Remember when your third grade teacher told you that Edison invented the light bulb? Well, you should go find her and tell her that she was wrong. Edison did no such thing. The first practical light bulb was the carbon arc lamp, which was invented by Humphrey Davies in the early 1800's.

Did Edison invent the first incandescent light bulb? Nope again. Edison had 3.7 gazillion patents relating to the light bulb, but none of them were for the basic idea of running a current through a filament to make the filament really hot so that it gives off light. Warren de la Rue created light by running a current through a platinum wire in an evacuated tube in 1840. Thomas Edison was born seven years later.

One of Edison's first patents regarding light bulbs is US #223,898, which was granted in January of 1880. The patent describes the prior state of the art: "heretofore light by incandescence has been obtained from rods of carbon of one to four ohms resistance..." Think: pencil lead. At the time, these pencil lead light bulbs were encased in a glass jar with a little bit of an inert gas, much like incandescent bulbs today.
Edison's patent for a light bulb

Edison saw that the whole "one to four ohm" thing was problematic since heat tends to congregate in parts of the circuit with higher resistance, and "one to four ohms" is not all that high of resistance. So a lot of energy was wasted heating up the wires leading to the bulb. And making those wires hot is not such a good thing anyway.

The clever idea in Edison's patent was a way to make a filament that has higher resistance. Edison started with a cotton fiber, which didn't conduct electricity. This fiber was coated with tar, which also didn't conduct. But, the tar was impregnated with carbon dust. The fact that the tar/carbon layer was thin added resistance. The fact that the layer wasn't solid carbon further increased the resistance.

And another innovation in his patent: The filament was wrapped into a coiled shape. This allowed the filament to be longer, a further increase in resistance. He claimed resistance up to 2,000 ohms. This arrangement also increased the surface area, so that more of the photons were able to more readily escape.

As a side note, much of Edison's patent seems to have been anticipated by Joseph Wilson Swan. He used a carbonized paper filament for his light bulb. This proved to have a very short life since he could not create a good vacuum at the time, and the bulb literally burned out. Later, he used a thread that had been reduced to just carbon. This was likely the low resistance filament that Edison's patent maligned. Contrary to many reports that Edison produced the first commercially viable light bulb. Swan eventually sold about 1,200 light bulbs.

I hope this little story jogged some memories about basic electronics, and I hope that most of my readers were able to appreciate the cleverness that led to this improvement of the light bulb. But that's not the important message that I am trying to get across. I want to emphasize the words "improvement of the light bulb". Here comes the next factoid:

Factoid #9 - Very few patents are for truly ground-breaking inventions. I mean, we are coming up on the ten-millionth patent. Are there really ten million "good-golly wow" sort of inventions out there?

Almost all patents are granted for modest improvements to existing stuff.

Back to the Planck

I will revisit the black body curve. Below is the spectrum of a black body radiator that is at 2856 K. I have extended it way out into the infrared to demonstrate a very important factoid about incandescent light bulbs. (The visible spectrum is roughly from 350 nm to 750 nm.) Far and away the majority of the emitted electromagnetic energy (typically 98%) is in the infrared. This is not only wasted energy; dissipating that extra heat is a design problem and a safety hazard.

Spectral emission of a light bulb at 2856 K

Another issue with incandescent bulbs has to do with color. I bet you were wondering when I would finally get around to that!

If we zoom in on just the visible part of the spectrum (see below), you will see that there is a disproportionate amount of energy at the red end of the spectrum. The difference is roughly ten to one between deep red and deep blue. That's just not fair. And it's a whole lot different than sunlight, which has a much more balanced spectrum. Colors look different under incandescent lighting versus daylight. I have mentioned metamerism before, and I am sure that I will find the need to mention it again in this series!

Computed emission spectrum of a 2856 K radiator (on the left)
and actual measurement of a light bulb (on the right)

Why don't we just crank up the temperature of our light bulbs? The black body equation predicts that this would be a more efficient means of changing electrical energy into visible light. At a higher temperature, we would have a better balance between the blue and red ends of the spectrum, so colors would look more like they do under sunlight. Why don't we just heat the filament of a light bulb up to about 5000 K?

That would be a fabulous idea for about 12 microseconds. Tungsten is the metal used in almost all incandescent light bulbs nowadays. It melts at around 3500 K. So, you can overdrive an incandescent bulb a bit above the standard 2856 K, but the fact of the matter is, if you drive it too far, the filament will melt and stop conducting electricity.

Factoid #9 - Tungsten has the highest melting point of any metal. That makes it an obvious choice for filaments.

Factoid #10 - Tungstent-halogen bulbs rely on some fancy chemistry tricks to make tungsten atoms want to re-deposit on the filament when they evaporate. This allows the bulb to be run at a higher temperature without sacrificing life of the filament.

Unfortunately, the only practical way that has been found to create a black body radiator with a balanced spectrum is to use the Sun. This is easily the most ubiquitous form of illumination, but it doesn't work so well at night.

We would kinda like an artificial light that has more energy at the blue end of the spectrum. Luckily, there are other ways to create artificial light. It's lucky, because that fact gives me topics for future blogs! I promise to eventually get around to explaining the ideas of correlated color temperature and standard lighting for color viewing like D50 and D65.

Are you ready for Part 2 of this long and boring series of blog posts on the nature of emitted light?