Light, Vision and Imagery
By: David Wood - November 28, 2001
Light, its properties and behavior, is what the human visual system and all the imagery techniques are based up. In order to understand the various imagery techniques and how they work with the human visual system, we must first understand light itself. Light is something that we take for granted but haveyou ever stopped to wonder what it is actually made of? "What is light?" - an easy question to ask but not an easy one to answer! Lots of people with lots of letters after their names spend their whole careers working on long formulato understand what light is. So without further ado, lets get on with the math...
Only joking! This article is not intended to be a course in quantum physics or anything like that, although this attempt to explain what light is will end up being an introduction to it. Don't worry, the math like that above will be avoided.
What is Light?
Practically every scientist since Aristotle believed that white light was a single entity. Isaac Newton believed otherwise. Sir Isaac Newton is known by most for his theories of gravity, but he did a lot of work with light too. He was one of the first people to separate a beam of white sunlight into a rainbow of different colors using a prism. From this he concluded that white light was not a single entity at all, but made up of multiple components. Later he published a paper in 1672 on light and color in which he attempted to prove through experiment that light was made up of a stream of small particles.
This theory was not well received by Christiaan Huygens; a mathematician was doing a lot of work into the geometry of curves and circular motion. Although Huygens respected Newton as a scientist he did not agree with his theories on light, to him light seemed to behave more like a wave than a stream of individual particles. In 1678 Huygens published his Traite' de la Lumiere in which he argued in favor of a wave theory of light. Huygens was able to use his wave front theory of light to explain many observable optical effects, something that Newton's theory could not do. However neither theory could completely explain all the behavior and properties of light. Here was a dilemma, two contradictory theories, and nobody was sure which to believe for another century.
In 1801 Thomas Young demonstrated that light waves could interfere with each other and in certain conditions cancel each other out. This was significant because this effect could be explained mathematically using the wave theory of light but not with the particle theory. Young's theories revolved around the idea that light was a wave that traveled in aether (a substance that the structure of universe was thought to be made of). Young was able to use his theories to explain many optical phenomena. However, Young was discredited because his theories at the time were not consistent and he changed his mind frequently. Few people at the time paid attention to his theoretical research. It was not until a few years later when Augustine Fresnel repeated and verified some his experiments and used his theories to explain polarization that Young's work was noticed.
Scottish physicist James Clerk Maxwell was to play an important role between 1864 and 1873. During this time Maxwell was the first person to unify the theories of electricity and magnetism by showing that electric and magnetic fields continually interact with each other to form an electromagnetic wave (or "E.M. wave" for short). Maxwell also observed that these waves appeared to travel at approximately the speed of light and so concluded that light too was an electromagnetic phenomenon. In doing so, Maxwell had unified not only the laws of electricity and magnetism but those of optics as well. Maxwell also theorized that what we perceive as visible light is only a small part of the entire spectrum of possible electromagnetic radiation. Maxwell's theory was later confirmed by Heinrich Hertz in 1888 when he produced the first artificial radio waves.
Unlike waves that are ripples in water, light is an EM wave that requires no medium of transport, but it is still a wave and you can do predictable experiments to show it behave as such. So there you go, light is a wave, problem solved! … Well, not quite, but light does exhibit many wave like characteristics…
Light as a Wave
All waves have amplitude - the height of the wave, a wavelength - the distance between the start and end of each wave, and a frequency - the number of waves per second. The frequency of a wave multiplied by the wavelength will give the speed of the wave. Since the speed of light is a known constant you can work out the wavelength of light from its frequency and its frequency from its wavelength. Like how sound is a vibration wave that travels in a range of frequencies that we call "pitch", Light is an electromagnetic (EM) wave that travels in a range of frequencies which we call the EM Spectrum. The EM Spectrum can be scaled by wavelength (metres) or frequency (Hertz).
The Electromagnetic (EM)Spectrum
The EM spectrum is a continuum of the frequencies of EM radiation. Human beings have decided to name the different frequencies of the EM spectrum; many of the names should look familiar...
At the lower frequencies we have things like radio waves, and microwaves, towards the middle we have infrared, visible light (that we can see), then ultraviolet, and all the way up to X rays and gamma rays. It is important to realize that all these different names describe the same thing. The same stuff that you see is the same stuff that cooks your food or sends signals to your TV. X-rays are the same thing as microwaves, ultraviolet is the same stuff as infrared. It is all the same phenomenon, we just give different names to different frequencies. In a way your eyes and your car radio aren't much different, they are both devices that are sensitive to a particular range of EM radiation. If human eyes could see EM radiation in the range 600-200 meters (500-1500 kHz) then we would be able to actually see AM radio waves! Radio transmitters would probably appear as bright towers that would illuminate the whole countryside in light that pulsated with the music they were broadcasting. We commonly use the word "light" to describe only the part of the EM spectrum that is visible to us but really, as you can see, the word "light" can be used to describe all of it.
As mentioned before light behaves like a wave (even though it isn't one) and we can manipulate it as such. Studying and manipulating light according to its wave-like properties is called optics. Our most common encounters with optics include spectacles, magnifying glasses, binoculars etc.
You have heard the phrase "it's all done with mirrors"? Well often it is; optics form the core basis of the tricks done by many famous illusionists and magicians. Optics also explain some of the natural world around us - what are mirages? why is the sky is blue? In this part of the article I will give an overview of basic optics, explain mirages, explain why the sky is blue, and I am going to reveal a variant of a technique used by many illusionists. I would also go on to prove that there is no Santa Clause, but he would get mad and bring me coal this year (again). Lets look at some of the ways in which light behaves like a wave.
Light waves, like any other wave, can interfere with each other, as Thomas Young showed in the early 1800s.
The diagram on the right shows two light waves converging to form a single wave where they join that has twice the amplitude. This is really as simple as 1+1 =2. Two light bulbs placed close together will look like a single point of light that is twice as bright. Or if you take sound waves as an analogy, then two speakers receiving the same mono audio signal will produce twice the volume of a single speaker. For waves to "add" together like this they must match in frequency and in phase. When waves are in phase and identical like this they are said to be coherent.
In this picture the waves are not coherent. Although they appear identical, one wave is out of phase with the other. When one wave is going up, the other is going down and visa-versa. When two equal but opposite waves like this converge they cancel each other out. This is like adding 1 then subtracting 1, or subtracting 1 then adding 1. Either way the end result is zero. Any waves can cancel each other out like this including light and sound. "Anti-sound" is a marketing term for the application of this effect, where a computer emits a tone through the car's stereo system that is an equal but opposite wave of the sound of the car's engine. The end result is that the audible noise coming from the car's engine is reduced to almost nothing.
In the real world the interference patterns are much more complex than the examples above, they consist of many waves interacting to an extent where there is no obvious mathematical pattern behind it. White light is like this; it is a mixture of many different waves from different sources mixing together to produce a wave to which there is no obvious order or pattern.
Interference patterns can give clues as to the object that created it. For example if you converge two beams of coherent light after one beam has bounced off the surface of an object, then the resulting interference pattern will be determined by the three dimension shape of the object it reflect off. Interesting things happen when interference patterns like this reflect or refract light, as we will discover later.
A light wave does not necessarily travel up and down as shown in the diagrams; it does travel in a wave but usually as a mixture of these waves in a variety of orientations. A polarized screen allows us to select which wave orientations we want to let pass and to block the others. For example, we may want to allow light waves that are vertically oriented to pass, but block any that are horizontally orientated. The light we allow through will be all oriented in the same direction, we call this "polarized light."
Once light is polarized you can block it or let it pass with another polarized filter. For example, light that is polarized vertically will only pass through a polarized filter in the vertical position. Two beams of polarized light at opposing 90-degree angles will have minimal interference with each other, which makes it useful for stereoscopic 3D, as we will see later. The human visual system is not sensitive to light polarization, however polarized light is sometimes used in home decoration as it appears less harsh or glaring when polarized horizontally. The windshields of cars are also polarized to reduce the glare from the sun and overhead streetlights.
Reflection occurs when light bounces off some matter. When we hear the word "reflection" we probably think of a mirror. Everyone knows that a mirror "reflects", but as I will discuss here, pretty much everything is reflective.
There are only two ways in which we see something in the world around us, either it emits light (light bulbs, the sun, the phosphor on your PC monitor), or more commonly it reflects light that originated from another source. Consider this picture (shown right) of one of my son's favorite toys:
We can "see" this object because it reflects light. We can also see that parts of it are black, some white, and some red. The way that the material of the object reflects or absorbs light determines its perceived color. Some of the material on this toy reflects light at any wavelength quite well so this material appears bright and uncolored and we call it "white". Other material on this toy absorbs a lot of visible light, it does not reflect much, so it appears dark and we call it "Black". On the head of the toy is material that seems particularly good at reflecting light in the range between 500 and 700 nanometers on the EM spectrum. We call this "Red". Realize that the only reason things have "color" is because some materials reflect light at certain wavelengths better than others.
Remember that visible light is just part of the EM spectrum. A white piece of paper may appear to be opaque and solid, yet to EM radiation in the "radio waves" range a piece of paper appears as transparent as a piece of glass.
What about mirrors? What is the different between a reflective piece of shiny metal and a white piece of card? Most objects - paper, plastic, wood, dirt, don't allow us to see our reflection. This is because the surface of such object is not perfectly smooth; imperfections on the surface of the material scatter light that is reflected off it. A polished surface, like a piece of chrome steel still has imperfections but they are so small that light can bounce of it with very little scattering, so we can see our face in it. Any highly polished surface is a mirror although the best mirrors have a metallic surface because metallic colors reflect most light at visible wavelengths.
A flat mirror will reflect light at a predictable angle. We can use simple geometry to predict where a beam of light will travel. Here is a diagram of an illusionist I saw on TV once:
The illusionist appeared to have been severed in half and his live torso was squirming on the table in agony. The illusion was quite effective, even when viewed on TV, because the camera rotated around and allowed you to see "under" the table. I doubted most illusionists would really go so far as to saw themselves in half to impress an audience and it didn't take me long to figure out how the illusion was done.
So how was it done? The person on the table was indeed a real person, not a dummy, and there was too little space for the illusionist to curl up his legs underneath the table. Well the only illusion here is that you are looking under the table, in fact you are not, you are look at a box with mirrors on the sides. At first glance you may ignore the candlesticks, but they are in fact there for a purpose. Note the similarity in shape and color of the candle stands and the table legs. In fact you can't see the table leg labeled "A", you are actually looking at a reflection of candle stick B! Using simple math the illusionist has placed these candlesticks in just the right places so that the camera can rotate freely around the "table" and provide an accurate illusion of seeing under it. The blood, of course, was merely special effects. In a way the illusion did rely on the camera somewhat, since if the camera had looked at the mirrors flat on you would have seen the reflection of cameraman in them. Most illusions require that their work be viewed only from certain places or angles for it to be effective. Not really a "camera trick" but certainly "selective camera use".
As well as flat mirrors, you can have a whole load of fun with shaped mirrors. Convex mirrors for example are curved out and will disperse a beam of light outwards when it reflects off the surface. Concave mirrors are the opposite; they are curved inwards and will focus a beam in on itself when it reflects off the surface. By curving a mirror in or out, you can make reflected objects look closer or further away, larger or smaller, thinner or fatter. One only has to visit a hall of mirrors at a carnival to experience this. You can also see other examples of it in your car (e.g. the rear view mirror).
Refraction occurs when light travels across the boundaries of two mediums. The most commonly known example of refraction is a lens. Another example would be how refraction makes fish under the surface of the water appear at a different angle than they actually are. Light can "bend" when it travels between mediums of different densities with different indexes of refraction (e.g. air to glass, or air to water). Depending on how we curve or shape the glass we can bend the light to our liking, for example, making things appear closer than they are. You should already have in your mind an idea of what refraction is, but have you every wondered why it actually works? One would expect a beam of light to travel in a straight line through a piece of glass as if it weren't there because the glass is transparent. In fact it does do this if it strikes a piece of glass face on, but if it reaches it at an angle then this angle is altered.
Although the speed of light in a vacuum is constant, it can take a few nanoseconds longer to get through something dense (like glass) than it does something less dense (like air). This effect explains how refraction works, if a beam of light strikes the surface of a piece of glass then its angle will be altered because of the way the glass "slows down" the light. In the picture below note how the waves are closer together in the glass (because they are traveling slower).
Knowing this we can see how a lens works. As the surface of the lens is curved, light waves are refracted differently depending on what part of the lens they reach. The more curved the lens, the more the light is refracted.
There are two popular types of lenses: convex lenses which bend light in, and concave lenses which bend light out. Lenses that bend light inwards also have the effect of flipping the perceived image upside-down. The simple way to correct this in devices like telescopes and microscopes is to just add another lens to the eyepiece to flip the image the right way up again.
Refraction occurs on the boundary between two materials or at a point where the density of the same material changes. It is really the shape of the surface of the lens that makes it do what it does, the fact that the middle of the lens is thicker or thinner than the edges is unimportant. Mathematician Augustine Fresnel realized this and showed that you could make a "flat" lens with the same curvature of a normal curved sherical lens.
A Fresnel lens can be thought of as being made up of sections of a normal sherical lens. It will bend light in the same way as a sherical lens but has the advantage that it is "flat" and thin. Fresnel lenses are commonly used in over-head transparency projectors and large screen TVs. You can also buy plastic ones that can sometimes be seen on the rear window of coaches and other tall vehicles to allow the driver to see immediately behind the vehicle while reversing.
By making use of reflection and refraction (mirrors and lenses) you can make anything we see appear different in location, size and shape. Refraction is also what causes mirages. In the case of a mirage the refraction occurs because hot air has a different index of refraction than cold air, so where hot air rising from the desert meets an area of cold air above it refraction occurs.
As discovered by Isaac Newton, when white light is refracted it will be split into different angles depending on its wavelength. The shorter the wavelength, the more refraction takes place. So blue refracts more green, green more than red. This can be seen by shining a beam of light through a prism and casting a rainbow on a piece of paper. Most of us have done this experiment in school. One natural example of refraction is a rainbow. Rainbows are made, in part, by the refraction of sunlight by water droplets in the sky. ChromaDepth 3D glasses are also based on refraction and will be discussed later.
Light can be scattered by the molecules or particles that it encounters. How much scattering takes places depends on the size of the particle in relation to the wavelength of the light. When sunlight travels through our atmosphere it will encounter gas molecules (like oxygen and nitrogen) and larger particles like dust. Dust particles are larger than the wavelength of visible light so light will reflect off them. When light hits a gas molecule that is smaller than its wavelength then it will get absorbed. The molecule will then radiate light at this frequency in a different direction. This scattering process is called Rayleigh scattering, named after John Rayleigh who first described the process in the 1870s. Light of higher frequencies is more likely to be absorbed and scattered than light of lower frequencies. So blue light is more likely to be scattered than red light. This explains why the sky is blue:
Light from the sun is scattered by our atmosphere and blue is scattered better than other colors. At noon when the sun is overhead we see blue light scattered through the atmosphere. When the sun is low on the horizon the light passes through more atmosphere and most of the blue and green light is scattered away by the time it reaches us and only the red light is left to be seen. This is why the sky drifts more towards red as the sun sets. If it weren't for this scattering our sky would just be a boring black with a white sun in it (from space the sun looks white, not yellow).
Light as a Particle
There was a problem with the wave theory of light, which was that according to theories of the time, a hot body like a star would radiate an infinite amount of energy. For example, imagine a hot body (like a star) that radiates light in frequencies between 1 and a billion waves per second. This doesn't mean that it is radiating light at a billion different frequencies, we just label these billion points on a scale for our convenience. The light would radiate at 1, 2½, 3¼, 4.2938471…. waves per second and so on - the total number of possible different frequencies in any given range is infinite. If the total number of frequencies of the radiation is infinite then the light energy given off by the hot body must also infinite, which isn't the case. In 1900 a German physicist called Max Planck came up with a way to solve this problem. He theorized that the energy in light was transferred bits at a time in little packets which he called quanta.
Others, including Einstein, then theorized that light was in fact made of packets of energy. Einstein called them photons. This idea caused a stir in the scientific community because it contradicted the wave like properties that light exhibits - if it was a particle, how could it have a wavelength and frequency? How could it be affected like a wave, for example by interference and refraction? Despite these questions most scientists immediately considered this new particle theory of light after Einstein demonstrated how it could be used to explain the photoelectric effect (which solar cells are based upon).
So light, as well as being like a wave, is also like a particle. By studying light as if it were a particle we can get some understanding of how it is actually created at the atomic level. When studying light as a particle, we call these particles photons. There are several sources of photons such as radioactive decay, moving electrical fields and moving magnetic fields, a common point of origin is an electron. Before I go any further I should describe what atoms and electrons are.
Atoms and Electrons
Everything that we see around us, walls, chairs, trees, people, rocks, are made up of tiny invisible particles called atoms. An atom is made up of sub-atomic (even smaller) particles: neutrons, protons and electrons. Neutrons and protons are in turn made up of even smaller particles called quarks but we won't get that detailed. Lets take a simple view of an atom made of neutrons, protons, and electrons. To the right is a representation of an atom.
This diagram is an example of the planetary atomic model. You may remember this from high school physics class. It is called the "planetary model" because it looks similar to the motion of moons orbiting a planet, or planets orbiting a star. In this case the electrons are "orbiting" the nucleus, although the electrons are held in "orbit" by electrical force rather than gravity, which is much too weak on this scale. At the center of the atom is the nucleus; it is made up of protons and neutrons. Protons are shown in red and have a positive electrical charge. Neutrons are shown in green and have no electrical charge. The blue things around the nucleus are the electrons, which have a negative electrical charge. Atoms like to have an even electrical charge (the same number of electrons as protons) so electrons will move from an atom that has too many electrons to an atom that has too few. This flow of electrons we call electricity.
An electron exists in a shell or energy state around the nucleus, shown in the diagram above as the circles around the nucleus. The diagram suggests behavior similar to a moon orbiting a planet, which is not really how an electron behaves, but this simple planetary atomic model will however suffice for this article. Keep in mind that this model is simplistic and does not represent what an atom really looks like. In fact, an atom is too small to ever "see" because photons won't reflect off it as they would a larger object. As you will learn later, this model is about 70 years out of date anyway.
Making Particles of Light
Electrons can exist around a nucleus in one of several distinct energy states. By default an electron will always drop to the lowest state (closest to the nucleus). However, when an electron becomes excited it can move to a higher orbit. To describe this lets take a simpler atom. Hydrogen is a simple atom; it contains one proton and one electron. The electron will always be in the lowest state and will only shift to a higher one if it is excited by supplying it with energy (e.g. heat). This shift from a lower orbit to a higher one is called a "quantum leap" (which has very little to do with the TV series of the same name).
When an electron is excited with sufficient energy (by heat, or by being struck by a photon) the electron will move to a higher state (further from the nucleus). The electron will not remain in this higher state, it will drop to its lower state soon after. No energy in the universe is ever lost, it just gets converted from one form to another, so for the electron to drop to its lower state it must release the energy that put it in the higher state in the first place. An electron releases this energy as a packet of energy: a photon.
A photon will have a frequency, this frequency is relational to the amount of energy it has. A higher energy photon will have a higher frequency and a lower energy photon will have a lower frequency (remember the EM spectrum shown previously?). The frequency of the photon is determined by the size of the drop from the electron's higher state to its lower one.
Einstein and E=mc²
Albert Einstein is famous for his theory of relativity, and for his hair. In his theory he concluded that the speed of light is constant, regardless of the viewers point of reference. Most people know of his famous equation E=mc². This equation is so important to modern physics because it shows a relationship between energy (E), mass (m) and the speed of light (c). Actually, E=mc² is not the full formula, although the rest of it makes very little difference to most calculations below the speed of light. Since we know the speed of light to be constant and finite, we can figure out that as an object approaches the speed of light its mass approaches infinity. This is why light-speed spaceships are considered purely science fiction. As such as ship approached the speed of light, its mass approach infinity, and you would need an infinite amount of energy and fuel to accelerate that mass to the speed of light. Photons travel at the speed of light because they have zero rest mass, and therefore can travel at the speed of light without requiring any energy to accelerate them to that speed. In fact, photons instantly travel at the speed of light from the moment they are born. The important point here is that light has no mass.
Stimulated Emission and Lasers
Stimulated emission is something else that Einstein predicted (that guy sure gets around doesn't he?). It is worth mentioning stimulated emission because without it there would be no such thing as lasers, and lasers are the most important part of creating a hologram. Lasers are also used to make CD Rom drives and DVD players, where would computer gaming be if we still used floppy disks? Anyway... Einstein theorized that if an electron was in an excited state and a photon passed by it, then the interaction of their electromagnetic fields would trigger the electron to release a photon with the same properties as the passing one. If you have a whole bunch of matter with enough excited electrons you basically have a little factory that can churn out millions of photons of exactly the same frequency and energy. This is what a laser does, hence the name "LASER" which stands for "Light Amplification by Stimulated Emission of Radiation". A laser beam is made up of photons of the same frequency traveling in a coherent (uniform) beam. A coherent light source is essential for making holograms, which I will go into later on. Lasers have become much more affordable in recent years thanks to the invention of the semi-conductor diode laser, which you can find in things like laser pointers and CD drives.
If you have a laser pointer take a look at it. All laser devices are required by law to have a little warning sticker on them. The sticker will list the beam length which indicates the frequency of light that the laser emits. This particular laser pointer emits light at a wavelength of 650 nm, which to us is perceived as the color "red". Also on the sticker is the total power of the beam, which in this case is 3 mA (milliamps), which is very weak, but still appears quite bright because the light is all focused to a single spot. This type of laser is pretty harmless, you are unlikely to shoot down incoming nuclear warheads with it, in fact the beam doesn't even feel warm. Despite its lower power, a laser beam is very concentrated and can still cause temporary blindness, which is why the warning sticker tells you to avoid eye exposure.
Lasers are a very significant invention and an important tool in science and industry because they are such precise instruments. For example, lasers were used in construction of the channel tunnel between England and France to ensure that both teams knew exactly which way to dig so that they would meet up in the middle under the seabed. Lasers can be used to measure the distance between the Earth and the Moon by reflecting a beam off the ASLEP instruments (basically a mirror) left on the moon by one of the Apollo missions. Lasers can also be used for precise cutting, in medical applications like eye surgery or industrial applications like scribing a new grain structure on a coil of steel.
As we have seen, both the wave and light theories of light have some credibility to them, but it couldn't be a wave and a particle at the same time. This didn't seem to make sense. Gradually it was realized that no matter how hard you try, light would stubbornly refuse to be classified as wave or particle. It is also erroneous to think of light as "a wave made up of particles" because even if you pick on a single lonely photon it will still refract as if it knows that is supposed to be part of a wave. Known physics at the time was unable to explain the dual properties of light and book of physics itself needed a new chapter. This new field of mathematical physics is called quantum physics.
So what is light? Particle or wave? Well actually it is neither. It is a quantum entity, which can exhibits the properties of both particle and wave, depending on how you look at it. Light is not a particle, it is not a wave, it is something else entirely. Depending on how you look at it, light can behave as a particle or a wave, but if try and conclusively prove light as being either you will probably go mad. Some people probably did go mad, though I haven't done any investigation into the mental health risks of studying the physics of light. My dog tells me to stop worrying about it.
"Light is a quantum entity that behaves like particle and wave"
In modern physics all forms of matter and energy are referred to as quantum entities. In fact matter and energy are completely interchangeable, with the property of mass arising due to interactions of other quantum entities. As you can see the simple planetary atomic model taught in most high schools is incorrect and out of date. Quantum physics is not taught in every school because, unfortunately, a quantum entity is not something that can easily be explained in simple terms. As human beings we tend to comprehend things by drawing a mental image of them in our heads. Light particles can be visualized as tiny specks or ball bearings traveling through the air. Light waves can be understood to some degree by thinking of ripples on the surface of a body of water. Neither of these visualizations accurately represent a quantum entity, mathematics is the only way of truly understanding it and the vastness of the topic makes it beyond the scope of this article.
I should just mention another important characteristic of light: its speed. Obviously it is too fast to perceive with a casual observation and a stopwatch, so scientists set about creating experiments that could measure it. How fast is the speed of light? Well, in 1676 astronomer Olaus Roemer was the first to successfully measure the speed of light by using observations based on the moons of Jupiter. He noted that when a moon came between the Sun and Jupiter that there was a slight delay until it cast its shadow on the planet. He estimated the speed of light as being 140,000 miles/second, which was a very good estimate considering the equipment he was using at the time. Later experiments based on rotating mirrors, shutters and more recently, lasers have lead to better and better measurements. The speed of light is now known as being 186282 miles per second. You don't need to remember that number, just realize that light is fast, very fast! To give you an idea, light can travel from here to the Moon in just over 1 second, or from here to Mars in 12 minutes. NASA's experimental Hyper X scramjet aircraft, which is rumored to be capable of traveling at over seven times the speed of sound, is a snail by comparison.