Tuesday, April 25, 2017

On the nature of emitted light, Part 3

I said in a previous blog post that I wanted to talk about fluorescent bulbs. I do. Really. And I will... in this very blog post. But before we get to that dessert, we need  to eat our peas and carrots. Let's talk about fluorescence.

The soon-to-be-famous sunburn analogy

I am of Northern European stock. I sunburn easily. Naturally, I wound up in a place where the Sun doesn't shine. Milwaukee. On those rare occasions when the Sun does shine, I absorb ultraviolet light. Later, my skin emits red light.

Lobster, anyone?

That's fluorescence.

Well, not really. I do absorb UV, and my skin does turn red. But that red is a reflective red, rather than a emissive red. My skin doesn't actually give off light. Factoid: sunburnt skin is red due to the increased concentration of hemoglobin at the surface. Hemoglobin absorbs bucketloads of light in the OYGBIV part of the spectrum, and reflects some at the R end. The reflected light is thus comprised chiefly of red light so skin looks red when we burn. (Interested in more about the color of human skin?)

Just in case you were wondering, my normally pasty-white Anglo-Swedish skin matches 2R04 in the Pantone Skintone guide.

If I recall correctly, though, I was talking about fluorescence. My explanation about sunburn shares a lot of the features of fluorescence. Light is absorbed at one wavelength, and is emitted at another wavelength. It is always emitted at a wavelength with less energy, which is to say, at the more relaxed higher wavelengths. For some molecules, the absorbed light is in the UV, and the emitted light could be at the red region of the spectrum. 

My understanding of the fizzicks involved

This will thankfully be a short section. I dunno nothin' about the fizzicks behind fluorescence. I mean, a molecule absorbs a photon, and that photon "kicks it up into a higher energy state". I have no clue what that means. I just know that I don't want to be around when my wife gets kicked up into a higher energy state.

Happy little benzine molecule

Later, the excited molecule gives up that energy, but not all at once. For some reason, it only gives it up a parcel at a time. Hence each fluorescent emission is at a lower energy (higher wavelength) than the excitation.

Note that I said molecule, and not atom. In the last post, kicking an atom up into a higher energy state was all about the orbits of electrons. Now it's about molecules. Surely that's a clue about what is happening when something fluorescences. But I am pretty ignorant when it comes to all that chemistry stuff. I'm the guy who once looked for a quantum mechanic to fix my compact car.

If I really understood any of this stuff, I would explain that
in this diagram from Kurt Nassau's book,
the wavy lines represent fluorescence

But in the spirit of pretending I know something...

There is a closely linked phenomenon called phosphoresence. Actually, it's the same phenomenon with a different name. Light is absorbed and is later emitted at a higher wavelength. The only difference is in how much later the emission happens. If it happens on a time scale where we don't notice (like nanoseconds or milliseconds), it's called fluorescence. If the delay happens on a time scale that we notice, for example if the fluorescent emission continues for seconds or hours after the excitation goes away, then we call it phosphorescence.

The distinction between fluorescence and phosphorescence is thus strictly anthropocentric. Just like the distinction between electromagnetic radiation and light (described in a previous blog post), the distinction is along a continuum and is not based on anything physical other than our meager, pitiful senses.

Examples of phosphorescence

Back in the olden days, engineers made a lot of use of phosphorescence. Cathode ray tubes (CRTs) in electron microscopes and in radar systems had long-persistence phosphors so that the image stayed latent on the tube long enough for us to notice. Quick show of hands... how many in the audience have used one of these devices?

A vintage scanning electron microscope (left) and a vintage radar tube (right)

Ok... let's try to open this up a bit. Show of hands again. How many in the audience have been to a historical museum (or my basement, same thing) and saw a TV that was two feett deep and weighed more than a pregnant and cross-eyed mule? That, my friend, was a cathode ray tube display, with a phosphor on the inside of the display end of the tube. Then again... maybe that was more accurately called a fluorescor, since we definitely didn't want it to persist for more than a 30th of a second.

(By the way, a scanning electron microscope is nearly identical in structure to the cathode ray tube in a television set. In fact, the cathode ray tube display was invented along side the scanning electron microscope. Someday I will blog on that topic.)

Certain lichens and mushrooms will glow in the dark long after the sun has gone down. Perhaps there is an evolutionary advantage to being seen as a part of the night life of the forest? I dunno. When it comes down to it, being a visible part of the night life has never given me much of an evolutionary advantage. It usually kicks my wife up into a higher energy state.

Some minerals fluoresce like an Anglo-Swedish color scientist with sunburn. Party-loving minerals like fluorite come to mind. I wonder where it got that cool name? Come to think of it, where did phosphorous get it's cool name?

Welcome back to the 60's

You can also see phosphorescence if you look at a fluorescent bulb in the dark, just after it has been turned off. Here we see the vague distinction between fluorescent and phosphorescent. Some of the stuff inside the tube is fluorescing, and some of it is phosphorescing. But more on that when I finally get around to discussing fluorescent bulbs.

But by far the most useful application is the little rubber duckie that was sitting on my wife's desk, at least until I absconded with it for a photo shoot. The rubber duckie is impreganted with some phosphor with excitation in the violet to blue part of the rainbow, and emission in the green to yellow part.

You can't claim to be uber-cool until you have one of thes on your desk

Examples of fluorescence

Certain versions of the Pantone guide had a few cards with the ever-popular 800 series inks. These inks all have fluorescent properties.

Picture of my 2005 Pantone guide

One of the more hip of these colors is Pantone 804, which is the orange ink. I almost called this dayglo orange, but that would be a misuse of the word, since Dayglo is a company. They make Dayglo pigments.

To demonstrate the phenomenal fluorescent properties of Pantone 804, I set up my spectrometer, my camera, and dug out my red, green, and blue laser pointers. (Note the repetitive use of the first-person pronoun my. It's all about me. Even when it's not, it's still about me.)

Here is what happens when I point the green laser pointer at Pantone 804. There is a strong peak in the green, at 546 nm. This is the reflection of the light from the laser pointer. But note the broader spectral stuff that appears from 560 nm to 700 nm. Lasers only put out a very narrow range of wavelengths. The broader peak must be fluorescence.


Now have a look at the spectrum emitted when the blue laser pointer is swapped in. The laser wavelength appears way far to the left, tucked away nicely at 390 nm. Then there's a broad peak that looks a lot like the broad peak in the previous spectrum. The excitation wavelength has changed, but the emission spectrum has not. 


Or at least the fluorescent emission spectrum hasn't changed a lot. Have a close look at the region from 460 to 510 nm. We see another bump. Not a big one, but a bump all the same. Why didn't this show up in the experiment with the green laser?

The explanation can be found above. I don't mean in the Heavens, but earlier in this blog post. I wisely said: "each fluorescent emission is at a lower energy than the excitation." The green laser just didn't have the gumption to excite emission in the blue part of the spectrum.

This should help us explain the frankly quite boring results with the red laser pointer that are shown below. We see a red peak, which is way up at 688 nm. Ho-hum. Any fluorescence would have to be above that, so we get bupkis in the way of fluorescence.


Fluorescent whitening agents

How about another example? I have previously touched on the topic of additives that make paper whiter. I mentioned it in a blog about color-related standards in the print industry. I also blogged about how different spectros deal with the problems caused by the whitening stuff. And I blogged about a conference with a sub-conference on the little buggers.

The image below shows the reflectance spectrum of one paper stock. You might notice something a bit peculiar about it, especially around 430 nm. Go ahead. Have a look. And take note of the scale on the left-hand side. The observant reader will have noticed that over 120% of the light that hits the surface is reflected back. For the mathophobes in the crowd, 120% is more than 100%. So... this paper is creating light?

Note the attractive little bump at the blue end of the spectrum

So, here's the scam. Paper normally looks like a brown paper bag. You can make it whiter by various means, including bleaching it, but that's expensive. Not horribly expensive, but there is cost involved. And people like their paper to be white. In fact, studies have shown that people prefer paper that is just a tad on the blue side of true white.

A cheaper way to get white (and the only way to get blue) is to add fluorescent whitening agents to the paper. There is a family of compounds known under the name of stilbenes. Below is the excitation / emission spectra of stilbene stolen from a TAGA paper by Dr. David Wyble and some Anglo-Swedish guy who likes to think of himself as a color scientist. The blue line shows the amount of energy that the stilbene absorbs, as a function of wavelength. Note that this is in the UV region, mostly all between 300 nm and 400 nm. The red line is the wavelengths where that energy is fluorescently emitted. Pretty much what we would call the blue region of the spectrum, from 400 nm to 500 nm. 

Yest'day I's fluorescin', and today, I still-been fluorescin'

Adding stilbene to a paper stock will boost the blue. Since drab, dull, yellowish paper is blue-deficient, this will make it look whiter. Well, provided there is some UV light to get it excited. Paper is not creating light, it's redistributing the energy from the UV to higher wavelengths.

The image below illustrates that. There are three sheets of paper here. I wrote on them, annotating the amount of FWAs. On the right side, I took a picture of the three sheets under regular old garden-variety light. The three look similar. On the left we have a picture of those same three sheets under a UV flashlight. OMG! It is pretty obvious that there is some sorta difference going on! 

Three sheets to the fluorescent wind

BTW, FWA AKA OBA. Someone got the bright idea to call these brighteners OBAs. This stands for Optical Brightening Agents. I agree, the term fits. Stilbene brightens paper optically. But so does bleach, calcium carbonate, and titanium dioxide, and a good coat of white paint. These four will all increase the reflectance of paper in the blue region. But only stilbene does it with a fluorescent flair. So, if you hear someone call stilbene an OBA, wag your finger at them and tell 'em John the Math Guy says that they are using the term improperly.

Remember back when I took note of the little bump in the spectrum when I used the blue laser pointer? You may have guessed by now. It was stilbene. The paper that the Pantone book is printed on has quite a bit of FWAs. It's kinda hard to find paper today that doesn't.


Well. Look at the time! It's about time to wrap up this blog post on the nature of emitted light. Today I taught you everything I know (and a little bit more) about things that fluoresce in the night. There was something else I wanted to say about fluorescent light... Can't remember what it was. I guess it can wait until the next blog post. That one will be about fluorescent bulbs. I promise.

Wednesday, April 12, 2017

On the nature of emitted light, Part 2

I'd like to talk about one of the most ubiquitous light sources, the fluorescent bulb. I mean, not only are they ubiquitous, they're all over the place. And at least until the recent new wave of LED illumination, they were the number two light source that tried harder. (They try harder than the #1 light source, incandescent, which was featured in my last blog post.) And for those of you who are excited by viewing booths (and quote frankly, who isn't?) I'm sure you have been just chomping at the bit, waiting for a blog post about fluorescent lights, since almost all light booths use fluorescent bulbs.

As I said, I'd like to talk about fluorescent bulbs. But I have to talk about a different sort of light emitting thingie first. You see, florescent bulbs are kinda complicated. There is a combination of two physics thingies going on: gas excitation and fluorescence. Today's blog will be about gas excitation. If that phrase caused you to snicker, then ... well, so be it.


Neon bulbs

The simplest gas excitation bulb is the neon bulb. You start with a couple of electrodes close together, but not touching. You form a glass bulb around them, and squirt in a tiny amount of neon just before you seal it. Maybe you add a tiny tiny amount of argon as well. Now, you put a high voltage across the electrodes (at least 50V, but likely 110V). Lo and behold, a faint orange glow appears.

Neon bulbs have gained popularity as indicator lights. A recent Rasmussen poll put their popularity somewhere just above that of Mel Gibson. Why are they so popular? First off, they're cheap. You can buy a handful of these little puppies for about a dime apiece on Amazon. Second, they are very simple to hook into a device that plugs into household current (110V AC). All you need is a current limiting resistor, which is included in your investment of one thin dime on Amazon. Third, they draw a tiny amount of power. You would need about 1500 of them to draw the power of a 60W bulb. Fourth, they put out a pleasing warm glow that is very effective at telling someone that the power strip is live, that the soldering iron is on, or that the circuit is live.

A collection of indicator lights chosen to subliminally convey my machismo

Getting your knee on

I have no idea what is mean by the title of this section, but it has some sort of cool vibe. As does neon. I mean, it is one of the noble gases! This prestigious group of elements includes helium, neon, argon, krypton, xenon, and radon. Helium, of course, is the party gas, since it makes us talk funny. Krypton is so cool that it has a fictitious planet named after it, and it is so powerful that it makes Superman cower. And radon? What safety conscious household doesn't have a radon detector in its basement? Truly this is a noble group to belong to.

The group is characterized as those elements which have a full outer shell of electrons. (As you know, you don't want to be that guy who is one electron short of a full outer shell!) This means that they are inert, very reluctant to react. As a result, they don't get invited to many pep rallies or often get selected as game show contestants. But they do get selected for applications where engineers are trying to avoid chemical reactions. Such as light bulbs that are hot and that we want to last a long time. Argon's senior picture has the caption: most likely to be selected to make an appearance inside an incandescent bulb.

The shell game

I'm gonna start with a quote from Wikibooks, under the heading "General Chemistry, Shells and Orbitals": "Each shell is subdivided into subshells, which are made up of orbitals, each of which has electrons with different angular momentum." As I was going to Saint Ives... I sure wish I could talk purdy like that. Honestly, I have no idea what this means, but nonetheless, I will give my explanation.

Imagine a guitar string. It has a certain resonant frequency. Like, the G string will vibrate easily at around 200 Hz.(I am tempted to throw in a joke about how I frequently resonate with G strings, but that would be totally inappropriate. So I won't say anything.) This is a natural vibration mode for the string, where the whole string is moving back and forth the same way.

The G string will also vibrate at one octave above 200 Hz, around 400 Hz. If you were to watch a high speed video of the string at 400 Hz, you would see that the center of the string is not moving, and that the right and left side of the string are moving opposite from each other. Similarly, the G string has an affinity for vibrating at 600 Hz, where there are two points on the string that are immobile. This third mode of vibration is shown below. The astute reader will recognize this concept from a blog post of mine from almost exactly three years ago on the vibration of piano wires.

G string vibrating at 600 Hz

Atoms are like guitar strings. (I just googled that sentence, in quotes. Google is not aware of that sentence ever having been typed before. High fives all around! Just wait until next week!!) Just like a G string doesn't take kindly to vibrating at 260 Hz, the electrons that orbit an atom only exist in certain energy states. (Oh yeah. I forgot to mention that each frequency has a different energy level associated with it. It takes more energy to get something to vibrate quickly, so the higher the frequency, the higher the energy level. Each energy state corresponds to a specific frequency/wavelength.)

So, you got this atom. Let's get just for example that an electron in this particular type of atom can be at energy states of 13 banana units, 15 banana units, and 20 banana units. An electromagnetic field induces the electrons way up to the 20 banana unit state. Eventually, the electrons will grow tired of hanging around up there, and they will drop down to another state.

If they drop down to the 15 banana unit state, they will lose 5 banana units of energy. Since energy is conserved, a little packet with 5 banana units of energy needs to be spit out. It gets spit out as a photon with 5 banana units of energy. Since energy and wavelength are related, this photon proudly moves to its proper place in the rainbow - the location that corresponds to 5 banana units of energy.

If an electron drops all the way down from the 20 to the 13 banana unit state, it will lose 7 banana units of energy. Now we have photons that are at the 5 and 7 banana unit locations of the rainbow.

There is one other possibility - an electron that dropped to the 15 banana unit state could drop a second time and wind up at the 13 banana unit state. Hence we also see some photons in the 2 banana unit state. A third position on the rainbow.

Going through the possibilities, we can expect there to be photons at three discrete positions (that is to say, wavelengths), corresponding to 2, 5, and 7 banana units of energy, as illustrated below.

Monkeys falling from tree branch to tree branch
The size of the yellow circle represents how loud of an uf-da the monkey makes

Emission lines

If you were looking for the section on transmission lines, I suggest you might want to check out a different blog. On the assumption that you are actually interested in how all this orbital decay stuff ties into neon bulbs, then read on.

Based on this business about discrete energy levels leading to discrete energy levels for the emitted photons, we kinda expect that the spectral output of a neon bulb to be equally discrete. Here is my expectation, based on some website somewhere that looks like it's reliable. They use big words, anyway.


I got put my ultra-sophisticated spectrometer, for which I paid about two years' salary, and put one of my neon light sources in front of it. The spectra below shows what I saw. Strong peaks, but not really the very narrow lines that we might expect. I am going to blame that on my spectrometer. Although it reports every nanometer, the spectral resolution is around twelve nanometers. 


My spectrometer looks at neon

Tech note: There is a spectral blur in any spectrometer that has to do with a design trade-off. Most spectrometers require collimated light, which is accomplished by focusing light on a slit aperture. The narrower the slit, the finer the spectral resolution, but also the smaller the amount of available light. Less light means either longer integration time or more noise.

Actually, a neon bulb can be used to measure the spectral resolution of a spectrometer. I looked through the data to find the wavelengths on either side of the peak where you reach 50% of the max: 579 nm and 592 nm. The difference between these is the FWHM resolution. FWHM stands for "Full Width at Half Max".

Do my peaks line up with the advertised values?

Mine Theirs
585 585.2
612 609.6
637 640.2
669
702 703.2
724

Actually, I am rather impressed. The two peaks in the official-looking plot which are most isolated (585.2 nm and 703.2 nm) are almost right on the money. 

But why are the others off? The key is that we need isolated peaks to test for correct placement of emission peaks. Because the resolution of my spectrometer blurs the spectrum, several peaks got averaged together, and so the center got shifted.

Another tech note: This is the technique used to calibrate spectrometers. Typically, the factory calibration lab will have a set of  gas discharge lamps such as neon, but also maybe krypton, xenon, argon, and/or mercury.

How about doing color matching under neon bulbs?

Neon bulbs are very efficient and inexpensive. Individually, they don't emit a whole lot of light, but they're small and cheap. Presumably, I could wire up a gazillion or so of these to make a really groovy light booth for evaluating color. And since we know the spectrum so accurately, it should make for really accurate evaluation of critical color, right?

The short answer is no. And the long answer is "good golly gosh, no!" Take another gander at the spectral emission plot of the neon bulb. Note in particular what we see happening below 570 nm. Nothin'. Virtually no light at all.

Consider a yellow ink. Above 550 nm, it looks almost indistinguishable from the paper it's printed on. So, I would argue that a neon bulb color booth is about as useful as Braille on the keypad of a drive-through ATM.

Yellow ink 

They have a measure that is an index of how good a light source is at properly rendering color. Ironically, it's called the Color Rendering Index, or CRI for short. The color rendering index of a neon bulb is zero. That's on a scale from 0 to 100. So, kinda not so good.

A few similar bulbs

You know those orangey-yellow lights that are used for street lights? High-pressure sodium vapor lights, also known as HPS by the cool people. Not to be confused with high-pressure sodium vapor light salesmen, who tell you how great the bulbs are cuz they are very efficient.

But have you ever tried to find your car at night in a parking garage with these kind of lights? I bet that high-pressure sodium vapor light salesman never told you that the HPS lights have a CRI of 20. Color is greatly distorted.

You'll never guess what gas is used in these puppies!

How about those really bright bluish-white lights that are used as security lights, as overhead lights in high-bay factories and stores, and as floodlights in a stadium? Those are likely to be metal halide bulbs. As with all the other gas excitation bulbs, these have a gas and a high voltage which causes electrons to jump around to different energy levels, giving off light at specific discrete wavelengths. Theses bulbs come in at a whopping 54 CRI.

Rock concert? Make sure you get the heavy metal halide floodlights!
  
By the way, just to make sure I am not misunder-terpretted, getting a score of 54 on a 100 point test is not so good. Of the bulbs in this blog. the metal halide bulb does the best job of making colors look right, but note that even metal halide is kinda short of energy on the red end. That's where it lost a lot of points on the CRI test. But, I should point out that the spikes don't help a lot either. 


Next time, I'll talk about fluorescent bulbs. I promise.

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.

Very attractive black radiator, which does radiate heat...
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.

Raise your hand if you had a science kit like this

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?

Tuesday, January 31, 2017

The Triumph of Science over science

February the 17th, 2017 marks the 417th anniversary of the death of Giordano Bruno. I know that many of my ardent readers are still trying to get over that.

Giordano Bruno's rather angelic looking Senior picture

Aristotle taught that the Earth is the center of the Universe. His proclamation cemented this idea into Western thought for almost 2,000 years. This is just one of the many examples of things that Aristotle said that mere observation would readily demonstrate to be just flat out wrong. Aristotle did lower-case science by decree. His attitude was that if reality disagrees with what he says, then reality is wrong.

Giordano Bruno challenged the idea of geocentricity (Earth being the center of all things) by proclaiming the heretical notion that the Earth travels around the Sun, rather than the other way around. He also proclaimed that the stars are just Suns like our own, but are just really darn far away. And (get this) Bruno said that those distant suns might have planets of their own, complete with living beings.

His challenge to conventional thought didn’t go over so well. He was burned at the stake by the Inquisition in 1600.

My attempts at marketing BBQ sauce have not proven successful

If Pew or Gallup were to do a poll asking people about Bruno, I’m gonna take a wild guess that most people would identify him as a pro wrestling promoter. Even if one were to restrict the poll to the scientifical and intellectual cream of the crop (which is to say, those people who regularly read my blog posts) I am gonna take another wild guess that a pretty small percentage would recognize the name Giordano Bruno. Yes, even the seven of you dear readers who have read more than one of my blogposts might say “who?”

But I should add that Bruno does have a crater on the Moon named after him. Kind of a small consolation what with his untimely death and all. I doubt if I ever get that honor. But if I do, I promise to look surprised.

Giordano Bruno, the lunar pimple

Some historians of science see Bruno as a martyr to the cause of Science. Perhaps he was killed for refusing to recant his beliefs about the universe?  But, perhaps not. I didn’t mention that he said quite a few nasty things about religion. More pointedly, he questioned some of the core beliefs of Christianity. The tamest of these was that the Bible is all about morals and stuff like that, and shouldn’t be treated like a textbook on astronomy. I’m not gonna get into all the other stuff that rankled the leaders of the church. Suffice it to say that his pontifications on religion were likely enough for the Inquisitors to get out their book of matches.

I think that explanation for his martyrdom is quite likely, but I’m going to make a different argument about why I don’t think Bruno was a martyr for Science. I argue that what he did wasn't Science. Bruno had some brilliant hypotheses that were way ahead of his time, but he didn’t do a lot of testing of those hypotheses. Testing of hypotheses is at the crux of Science. 

Copernicus

Bruno was not the first person to talk about the Earth revolving around the Sun. Aristarchus of Samos proposed this in 270 BC. An astronomer from India by the name of Aryabhata claimed this around 400 AD. The first person in “modern” times to make such a claim was Nicholas of Cusa in the early 1400’s. This time period was the start of the Renaissance, when people started questioning the dogma that Aristotle had left us with. (Note the forming of a theme here concerning Artistotle.)

Show of hands… Who remembers Aristarchus or Aryvhata? Anyone? Who remembers sending out Nicholas-of-Cusa-Day cards? He was the guy who updated the Alfonsine astronomical tables? Yeah, I didn’t think you remembered him either.

This is not one of the Alfonsine Tables

How about another Nick… Nicolaus Copernicus? Ahhh… now I am seeing some name recognition. I think a lot of people who paid attention in Science class will at least vaguely remember the name. Something to do with the Solar System and planets and stuff? Yup. That’s the guy. A few people reading this may actually remember some self-proclaimed math guy who blogged about Copernicus.

Copernicus was a true Scientist, with a capital S. Aristotle and Giordano Bruno and Nicholas of Cusa? They were all scientists of the lower case variety. They were pontificators. They had an interest in Science, and pontificated about it. They had great intuition. With the exception of Aristotle, their intuition often proved correct. (Yet another subtle jab at Aristotle.)

But they weren’t capital S Scientists in that they didn’t follow the scientific method. They got the first part of the method: observe some junk and hypothesize about an explanation. Then they went forth and pontificated on their hypotheses. That might be lower case s science, but it’s not upper case S Science.

Copernicus took it to the next step. He also pondered on the possibility of a Solar System with the Sun at the center, but he went out and found data. In this case, it was largely data about the positions of the planets that was consolidated a zillion years ago by Ptolemy. Copernicus demonstrated in his posthumous book (On the Revolutions of the Heavenly Spheres, 1543) that “the Earth and the Planets travel around the Sun, and the Moon travels around the Earth” provided a simple explanation that fit the data.

This was how Science is supposed to work. It's all about data and hypothesis testing. When observations contradict a theory, the theory doesn't get all defensive and call the data a loser. The theory is rejected. And when a hypothesis arises that is simpler but provides as good of an explanation of the data, the older hypothesis is moved to the side. 

By the way, Copernicus also has his own crater on the Moon and one on Mars. Two heavenly spots for vacation homes.

Copernicus' summer home is the large complex in the center of the crater

As a side note… I have a big pile of files on my computer that contain books that I almost finished writing, one of which is a history of science. In order to find what I had previously written about Copernicus, I used a program to search my computer that is ironically named Copernic. True story. Good program, by the way.

A few more Scientists

It can also be said that Ptolemy (around 200 AD) did some Science. He started with a hypothesis, Aristotle’s geocentric universe, collected a lot of data, and found a mathematical explanation of the data. This is the way Science is supposed to work.

But much to the detriment of Western thought, Ptolemy went through gyrations (quite literally Spirographic gyrations) to describe the various motions in terms of Aristotle’s geocentric universe. He built an overly complicated model based on the assumption that Aristotle's tweets about the Universe were infallible, but I would still argue that Ptolemy was doing capital S Science, what with all the hypothesis testing and real data stuff.

Ptolemy's explanation of the course of the planets 

(I want to point something out here, just to make sure I haven’t been too subtle. Aristotle is the bad guy in this blog post. I also heard that he has small hands.)

Galileo also did capital S Science. You will likely remember Galileo for doing a bunch of stuff with pendulums and rolling balls down inclines. You might also remember that bit about when his press agent told everyone that he leaned over and dropped some balls onto a tower of pizzas. Don't always believe press agents! But I want to point out some Science of his that did not get as much press.

Galileo had heard of Copernicus’ work. He was taken by the idea of a heliocentric solar system. When he came upon the first telescope in 1609, he anxiously built one, and pointed it to the skies to look for evidence. He used the telescope to observe many things that the Roman Catholic church did not want to hear: the moon has craters (and was not perfect), the Sun had spots (and was not perfect), the planet Venus has phases (so it must rotate around the Sun), and Jupiter has bodies revolving around it (rather than all bodies revolving around the Earth). These ideas all went against the accepted doctrine of the time.

This was capital S Science, where observational data trumps hypotheses.

All great Scientists have beards. I have a beard. Draw your own false syllogisms.

And by golly, did the whole Inquisition crowd get ticked off when Galileo published Dialogue Concerning the Two Chief World Systems! Galileo wasn’t invited to a barbecue like Bruno was, but he was put under permanent house arrest. I am happy to report that the Catholic church quickly reversed this. It took them a mere 325 years to pardon Galileo.

Ironically, this guy who discovered the craters on the Moon -- Galileo -- doesn’t have a single crater named after him. All the rest of his gang got one. The injustice! All he got was "a large, dark surface feature" on Ganymede, one of Jupiter's moons. If ever there was an example of Stigler's law of eponymy, Galileo's craters are it.

Johannes Kepler is another guy who did capital S Science. He looked at data on the positions of Mars and deduced that the orbit of Mars around the Sun is elliptical. He also developed some laws regarding the speed that planets move around the Sun. Data and theory going hand-in-hand. Capital S Science.

Does Kepler have a lunar crater to call his own? Ya, you betcha. And the obligatory second one on Mars, and then gobs of other stuff in outer space.


How about Isaac Newton? No question about it, he did some capital S Science, in a large and bolded font. Newton took Kepler’s laws and had the Greatest Synthesis of All Science – he determined that Kepler’s laws were a consequence of the inverse square law of gravity, and vice versa. In other words, a simple rule about the relationship between distance and gravity replaced Ptolemy's Spirograph set as an explanation of how the celestial bodies move. And he invented calculus just to figger that out! Data begets a simple theory to explain a whole lotta stuff. Science don’t get no better’n that.


Newton got a crater on the Moon, and also one on Mars, just like Copernicus and Kepler. It's a shame though, that he didn't get a few asteroids and exo-planets. Newton doesn't even have is very own disambiguation page on Wikipedia like Kepler.

The triumph

This story has a happy ending. In the end, Science has triumphed over some smarty-pants guy who spouted off about a lot of bogus stuff that he just made up. Granted, it wasn't so happy along the way for some of the courageous people who challenged alternative facts with gosh darn real facts. But in the end, we wound up with Science that truly explains how the world really is. And there are no craters (that I know of) that are named after Aristotle.

Let us hope that we have the wisdom to let facts and data guide our course in the future.

Tuesday, January 24, 2017

The long, medium, and short of the cones

Color is three-dimensional. I've said that before. Almost four years ago, I blogged about how it is not possible to arrange all your crayons in a line. This led to a discussion about how you need three numbers to uniquely identify any color, because color is three dimensional. Hence, when we describe a color, we need three attributes.

In an RGB camera or on a computer monitor, those attributes are the intensity of red, green, and blue. In the Munsell color system, the attributes are hue, value, and chroma. In the CIELAB system, the three coordinates are L*, a*, and b*. In any color space, there are three.

Actual photomicrograph of the strawberry, lime, and blueberry cones in the eye

Why is color three-dimensional?  Simply put, it's because we have three types of color sensors (called cones) in our eye.

In case this is starting to sound familiar, I have talked about the three sensors before. I blogged about how having three color sensors can lead to something called metamerism, where two objects can have identical colors under one light, but look different under another. I have blogged about colorblindness which is caused by missing one or more of the three cones. This came out in a blog about apps for testing for colorblindness, And then a followup blog post about colorblindness, and in one which asked the metaphysical question about whether two people see color the same way.

But today, I want to talk more about what those three cones look like.

Rainbowology 101

Time to pound some Fezziks into your head

Below is an artist's rendition of a rainbow. I like saying that my drawings are artist's renditions cuz it makes me feel like an artist. But perhaps it would be better if I call this a scientist's rendition, since I did actually put a little effort into making it anatomically correct. I am referring to the spacing and positions of the colors and the numbers on the scale below the rainbow.


The scale at the bottom is in wavelength and is measured in nanometers (abbreviated nm). A nanometer is a really tiny unit of measurement ... like about the width of a dent in a hair on a freckle on the butt of a baby flea that is the runt of the litter. A nanometer is the distance I will move over in the middle of the night when my wife tells me I'm hogging the bed. There is a whole lotta Fezziks behind wavelength and nanometers and how they got involved with rainbowology, but that would be getting off the topic. For our purposes, a nanometer refers to a position in the rainbow. At one end (400 nm) light is violet, and at the other end (700 nm) it's red.

If I wanted to be pedantic, I might extend the rainbow a bit. We can see light, however faintly, as low as 380 nm, and all the way up to 780 nm. So, I am lying when I say that my rainbow is anatomically correct. But it is a useful lie.

Strawberry, lime, and blueberry?

The obvious first guess is that there must be one set of cones in the eye that respond to the red part of the spectrum, one set that respond to the green part of the spectrum, and one set that respond to the blue part of the spectrum. Go RGB! 

Let's assume that the blue cones respond to light that is between 400 nm and 500 nm, the green cones respond to light that is between 500 nm and 600 nm, and the red cones respond to light between 600 nm and 700 nm. The top half of the picture below shows a graph of the sensitivity of each of the three cones as a function of position in the rainbow. Below that, we see the hypothetical rainbow that such an eye would see.

First guess at the response of the cones.

I don't know what you see when you look at a rainbow, but my rainbow has more that three colors. So, saying that the three cones respond each to their own 100 nm wide part of the rainbow is not just a lie. It's a lie that isn't even useful. The worst kind, if you ask me.

One of the difficulties with the first guess model is that it has the cones responding equally to all wavelengths within their respective ranges. That is why the first guess rainbow looks so blocky, and to be honest, very few light sensors in the real world have such a flat response.

So, let's tweak our hypothesis a bit. The graph below shows a second guess at sensitivity of the three hypothetical cones in the eye. So, as before, the blue cones will collect light that is in the range from 400 nm to 500 nm, but they are less sensitive near the ends of the ranges.

Second guess at the response of the cones

Note that the hypothetical rainbow has a decidedly more natural look, but it still doesn't look like a rainbow. I like my rainbows (and my brandies) with a little splash of orange. And then there's the dark areas. I don't ever recall seeing black listed as one of the colors of the rainbow.

Strawberry, strawberryish-lime, lime, limish-blueberry, and blueberry?

You know when you get one of those triple scoop cones? The fun part is when you are transitioning from one ice cream to another. You get a bite with some strawberry and some lime. You're not sure how much of each will be in the bite, and you're not sure how peacefully the two flavors will coexist in your mouth. But it will be fun. 

We can try that with our hypothetical cones... mush together the responses of the strawberry with the lime, and the lime with the blueberry. In this third guess, the responses of the cones have a significant overlap. So, if light at 500 nm comes in, both the green and the blue cones stand up and proudly wave their little neurons to say that they see the light.

Third guess at the response of the cones

I think that this has enough of the rainbow vibe to get Kermit the Frog to reach for his banjo. But when it comes to anatomical details, I think we can do a little better. Note that the yellow in the third guess rainbow is at 600 nm, when in reality, it's zip code is pretty close to 570 nm under cool lighting and 580 nm under warm lighting. Sky blue is another color that doesn't quite land in the right spot. I would really like for it to slide down from 510 nm to maybe 470 or 480 nm.

Based on that, I adjusted the width and position of the three hypothetical cone responses. Here is what I come up with - my final guess at the spectral sensitivity of the three cones in the human eye. Note that this analysis is pretty rudimentary. This was just a Gedanken - thought experiment. No lab rats were inconvenienced by the experiments described herein.

My fourth and final guess

The real answer

How close did I come? This last image shows one reliable estimate of the response of the three cones.

A guess from some real experts

I am rather pleased with my guess. I did of course, have the benefit of knowing what the real response looked like, and all the time in the world to rationalize my own estimate. But, I think the point has been made that the response of the three cones in the eye is not as simple as red-green-blue.

In fact, the responses of the cones really aren't red, green, and blue. There was a movement to call them by the Greek letters rho, gamma, and beta. Clever... you know? But the official designation is now to call them L, M, and S cones. L stands for long, or long wavelength, and it is the curve that is furthest to the right - the one we would be tempted to call red. M stands for medium, and it is the one in the middle. I still kinda think of it as green. And S is the short wavelength cone, the one that is furthest to the left. Speak kindly to it. It's kinda blue.

Why?

Why do I bother with all this explanation? First off, just cuz it's fascinating. Anything to do with color is gosh-darn interesting.

But this overlap between the L and M cones is kind of a head-scratcher. In those brief moments when I think like an engineer, I often think about stuff like how reducing the correlation between sensory channels increases the entropy of the system - the efficiency of information gathering. Based on that, I would think that the engineers who designed the human eye would have avoided overlap, especially such an egregious overlap.

But while Dr. Eva Lution (the designer of the human eye) doesn't always come up with the best designs, the poor designs are mercilessly discarded. I am left with the conclusion that maximizing entropy might not be the only worthwhile goal.

Note that as we slowly move upward in the rainbow from green to red, the response from the M cones is decreasing while the response from the L cones increases. This has the effect of accentuating the change, since the human visual system relies on comparison of L and M to discern greenish to bluish. Thus we see very rapid change, with green, yellow-green, yellow, orange, reddish-orange, and red all packed into 70 nm. If you are a photon out to have a wild time, this is where the action is.

There was one blogpost of mine about why we evolved to have three different colors sensors. I argued in this post that the addition of the L cones allowed us to see the difference in leaves as they change color. The additional cone also makes our eyes sensitive to a change in hemoglobin at the surface of the skin. This has some clear advantages for a social animal who does not have fur on its face. (With the exception of color scientists, who have beards and have yet to evolve into anything useful.)

Oh... what a little L cone can do

And that, dear reader, is why the L and M cones have such flagrant overlap.