Amplitude

The amplitude Ê is a measure for the intensity (brightness) of light. For from a graphical point of view the amplitude describes the height of a wave crest, respectively the depth of a wave valley, measured from an imaginary horizontal line running right through a sinusoidal curve, light with a large amplitude is bright light, while darker light has got smaller amplitude.

"Die Amplitude einer Schreibtischlampe ist größer als die einer Streichholzflamme, die Amplitude des Sonnenlichts wiederum größer als diese beiden.

Mit der Entfernung ändert sich die Amplitude des Lichts. Nahe bei seiner Quelle ist das Lichts stärker und wird immer schwächer, je weiter es sich davon entfernt. Das erklärt sich durch die Tatsache, daß sich Licht auf seiner Reise ausbreitet. Die Energie einer ganzen Wellenfront bleibt zwar gleich, aber die Intensität wird geringer, da die Front eine größere Fläche abdeckt. Sind wir z. B. doppelt so weit von der Lichtquelle entfernt, als vorher, beträgt die Intensität nur noch ein Viertel."

[The amplitude of a desk lamp ist larger than the amplitude of a match's flame. The amplitude of sunlight is larger than both of them.

The amplitude of light changes with the distance. Close to its source light is stronger and gets weaker the farther it removes. This circumstance is explained by the fact that light propagates on its journey. The energy of all of a wave front remains the same, but the intensity gets smaller, for the front covers a larger area. For light departs twice the distance from its source, its intensity amounts just a quarter.]

Referred to the graphical illustration of the sinusoidal curve this means: "[...] if one wave has twice the amplitude of another, the first light has four times the intensity of the second."

"Das ist das Gesetz vom inversen Abstandsquadrat, welches besagt, daß die Lichtintensität umgekehrt proportional zum Quadrat der Entfernung abnimmt. Bei dreifacher Distanz beträgt die Intensität also nur noch ein Neuntel."

[This is the law of inverse square of the distance, which says, that light intensity declines inverse proportional to the square of the distance.]

Fig. Law of inverse proportional light intensity

The following figure would like to illustrate the above described:

Fig. Intensities of different light waves

The waves in (a) and (b) have got the same wave length, but the light in (a) is more intense (brighter) than in (b) - (a) has got a larger amplitude than (b). The ratio between these to waves is about 2:1. Therefore light (a) is four times (2²) brighter than light (b). (c) has got he same intensity as (b), but a larger wave length. (d) again has got the same intensity as (b), but a shorter wave length.

The sinusoidal is therefore a graphical illustration of intensity variation of the energy of light, that travels as a particle photon wave-like through space and time.

Fig. Light photon passes two cycles

It passes a whole cycle, starting at »off« (zero point), passing »on« (wave crest), back to »off« (zero point), passing »on« (wave valley), and back to »off« (zero point).

Wave nature of light

Christian Huygens, Augustin Fresnel and Thomas Young are considered as the three main protagonists, who construct a theory of light between 17th and early 19th century, which is looking for help of explanation on the water. Using the example of waves on the surface of the water the nature of light is demonstrated.

"This theory does not depend on knowing what light really is, but on the assumption that it consists of transverse waves, as do water waves, and that the basic wave phenomena occur in much the same way in both cases. This simple theory of the behaviour of light is completely satisfactory for understanding all of the aspects of holography [...]"

This very simple and easy to understand analogy should serve as a paragon to explain for holography fundamental characteristics of light.

When a stone hits the surface of the water, it causes oscillations.

Fig. Propagation of water waves outgoing from a point source

The caused waves propagate in all directions - outgoing from a point source. They move up and down, vertical to the direction of propagation.

"For this reason, such waves are said to be transverse. (In contrast, sound waves in air consist of regions of compression and rarefication along the direction of travel and are called longitude waves). That water waves are transverse is shown convincingly by considering a bobber on the surface, rising and falling vertically as the traveling waves pass it."

Fig. Propagation of water waves - bird's-eye view and cross section

The left part of the figure shows circular propagation of waves from a bird's-eye view. The dotted lines indicate wave valleys, the consistent lines indicate wave crests. To pay a correct terminology back in its own coin, these circles should be named wave fronts. The right part of the figure shows a wave front in cross section as sinusoidal curve. Using the example of sinusoid some terms should be explained, which are going to be used afterwards.

The distance between two wave valleys, respectively two wave crests, describes the wavelength (in figure distance A-A', and B-B'). For a stone now hits the surface of the water exactly at the same position in exact equal intervals, a pattern of a sinusoid curve occurs (respectively a pattern of waves on the surface of the water), which remains steady. For the sinusoid is divided right in its middle by an imaginary horizontal line (dotted line in figure), the distance between the line an maximum of a wave crest, or the maximum of a wave valley, is called amplitude (not illustrated in figure). The passage from zero point to the top of a wave crest, back to zero point, to the low of a wave valley, back again to zero point describes one complete oscillation - one cycle. The frequency measures the amount of times a cycle passes a certain point in one second. It is specified in hertz (hz).

The just explained terms are valid for any kind of sinusoidal curves - anyway if sound, water or light. One significant difference between a water wave and a light wave should not remain unmentioned, to avoid any potential misunderstanding in coming entries about interference and the recording of wave fronts. While a water wave moves up and down, which means at a certain position wave crest and wave valley alternate, a light wave is a standing wave. The wave pattern - position of wave crest and wave valley - does not change.

History of light

As long humans were thinking about the nature of light, as many different theories of light there were and still are. The way of these attempts establishing a universal theory should be kept track abridged and partially.

Greek optics

Long before there is ever a possibility of transcription of thoughts and ideas, humans admire a sun god. The greeks take a try in ancient times, explaining nature not in religious, but in a rational way.

To begin with Anaximander (610-546 B.C.), who regards day light from the sky and sun light as two different kinds of light, being independent form each other. To him darkness has got an own physical and material existence and is not just the absence of light.

Pythagoras (536-497 B.C.) continues egyptian tradition, in which lights stands for the good and darkness representing the evil.

Anaxagoras (500-428 B.C.) and Empedocles (490-424 B.C.) are the first ones regarding darkness as the absence of light. By means of the phases of the moon, he explains that the moon reflects sun light, instead of emitting light by itself. Even for him it is the other way round, day light and sun light is connected. He is the first one trying to explain vision as the unity of fire in the eyes with the fire of the objects. From this point of time the theory of light is closely linked to the theory of vision.

While Democrit's (460-370 B.C.) intromission theory - based on his theory of atomic particles - assumes light rays emitting from the objects and received by the eyes, Plato (427-347 B.C.) establishes an extramission theory a little later, according to which the eyes emitting light rays to see the objects. But both theories are not able to explain certain phenomenons. The intromission theory e.g. can not satisfactory explain, how surfaces of large objects get into the eye without losing their shape. The extramission theory on the other hand has got no answer to the question, how rays from the humans' eyes can make it to far distant stars.

Aristotle (384-322 B.C.) constructs an intromission theory with one significant difference. To him the key to the nature of light lies in transparent bodies, which work as a medium, transferring not light, but colour. This medium contains a substance, that becomes transparent, e.g. by a luminous body like the sun. Aristotle's theory of light and vision is part of a comprehensive and unifying picture of the world and seems strange and hard to understand in nowadays. However it shows early approaches of a wave theory of light. Even his thoughts involve an intromissiontheory, there's a fundamental difference to Democrit's theory, in which atomic particles move from the regarded object to the eye. From this point of time on the intromission theory splits further into a particle and a wavetheory. This separation proceeds till modern times.

In his book Optica Euclid (330-370 B.C.) tries to put the nature of light into an exact mathematical formula. The result is geometric optics, which assumes a radial straight-line propagation of light in space. Extramission theory as a basis enables Euclid to forecast a variety of laws of perspective and geometric optics.

The last to be mentioned in a row of famous greek optics protagonists is Ptolemy (90-168 A.D.), who continues Euclid's tradition. Even he also favors an extramission theory, his deliberations are more physically shaded, than the Euclid's pure mathematical theory. Ptolemy adds experiments of refraction and diffraction to his theory and concludes that rays of vision from the eyes are of the same nature as light rays being emitted from a luminous body.

With that finally theory of light and theory of vision converge at the end of greek science.

Optic in the middle ages

After the fall of the roman empire science - incl. optics - falls into a long and deep sleep. In this period of time the arabic world becomes a locus of new scientific discoveries and preservation of classic writings from greek-roman times.

Al-Kindi (801/813-866; sources vary) is the first arabian contributor to the field of optics. As a supporter of Plato's extramission theory he develops a technique to analyse light rays on a point-to-point basis. He regards every single point of a luminous body as an emitter of rays, which propagates in all directions, independent of other nearby illuminating points. This technique is still used in geometric optics today.

As probably one of the greatest arabian scientists of the middle ages, Alhazen (965-1040) succeeds in combining Euclid's geometric optics and Ptolemy's intromission theory of vision - on the basis of Al-Kindi's point-to-point analysis. Besides his theory of vision - as maybe one of his greatest triumphs - he does further important discoveries on the field of theoretical and experimental optics.

Roger Bacon (1214-1292) adapts Alhazen's theory of vision almost in its entirety. To construct a consistent theory he takes a piece of almost every other author who writes about optics before.

The greatest advance in understanding about the nature of light brings Renaissance jarring and pulling down Aristotle's concept of the universe.

Renaissance of optics

In the 16th and early 17th century Nicolaus Copernicus (1473-1543), Johannes Kepler (1571-1630) and Galileo Galilei (1564-1642) dismantle the aristotelian concepts of astronomy and mechanics and lay the foundations of modern science. Kepler is initially successful in giving a comprehensive description of the mechanics of the eye, considering every light ray falling into it. He completes attempts of a unification of geometric optics with the help of intromission theory of vision, that Alhazen starts 300 years before.

French philosopher René Descartes (1596-1650) is considered to be one of the most influential scientific thinkers of his time. Like Aristotle 2.000 years prior, he tries to establish an uniform system of the world, that is able to explain every possible events in nature. Therefore he assumes a matter, which fills all space - the ether. In his theory light has got infinite speed and is not motion, but a tendency of motion. The impression of light in the eye is caused by little bodies crashing into each other.

Corpuscular theory

In 1705 Isaac Newton (1642-1727) publishes a book called Optics, in which he accepts Descartes' idea of the ether, but not the fact, that light is a result of disturbances - crashing particles - in the ether. This contradicts his assumption of straight-line propagation of light as rays. He concludes this from his observations of shadows cats by a candle lit object. This shadow is an exact image of the object, without distortion. He thinks of light as little particles - corpuscles - emitted by a luminous body and moving like bullets through the ether. He thinks that bullets moving in straight lines can best explain sharp zoned shadows of objects. If corpuscles bump onto an object, they recoil an change direction.

Newton does not change his opinion about that, even Francesco Grimaldi's (1613-1663) observation, which is published two years after his death, contradicts his theory. Grimaldi observes not exact defines shadows of the objects, cause by refraction and diffraction. This observation contradicts a particle theory of light and is to be considered as an evidence of the wave theory of light.

Wave theory

In his book Traité de la lumière (1690) Christian Huygens (1629-1695) establishes a theory in which light - like sound and water - propagates as a wave. With this he neglects geometric optics and ascribes the appearance of light to a universal principle - which is valid for every wave phenomena in nature. This principle assumes waves propagating from an epicenter in all directions.

Before Huygens' wave theory can assert against Isaac Newton's authority, one more century has to pass. Optical phenomena refraction and diffraction help wave theory to get its recognition.

At this point the history of light does not end yet even after 2.300 years. A variety of electromagnetic and quantum mechanic theories still try to disclose the secret of light. But of these theories should not be told any further. With the wave theory the history of light has come to a chapter, which is satisfactory as a basis for the understanding of mechanics of holography.

Light

As fundamental light is for the recording and the reconstruction of a hologram, as fundamental is the knowledge of what light is and the understanding of how it works. The coming posts are about:

• history of light
• wave nature of light (amplitude, wavelength, frequency)
• interference
• coherence
• diffraction
• laser

Even these coming entries are not about phantasms, they would like to provide a service giving everyone an understanding of the properties of light, who isn't much into it or into physics and mathematics.

Here is a track called Lightwave by VNV Nation, going perfectly with the entries to come - by title and even musically.

Project Natal

Johnny Chung Lee is currently working with Microsoft on Project Natal - a new technology of game controlling without a gamepad. It's a continuation and advancement of Lee's work on the Wii Remote hand tracking system.

It works quite in the same way as his Wii Remote project does. With one significant difference. The video game is just controlled by hands, feet, head and voice without any other kind of device, except a sensor, which is placed near the TV.

The sensor is able to recognize moves of several people in front of the TV. Besides a number of built-in microphones - to ensure communication by voice from any point in the room with the console - it has got two attached cameras. An ordinary Red-Blue-Green colour camera, and 3D camera, which allows to locate the user's position an recognize his moves.

Project Natal Xbox 360 announcement

The new device is expected to be available by autumn/winter 2010 under a name that is not know yet.

In June 2009 Shinoda Lab presents on SIGGRAPH Touchable Holography using Johnny Lee's Wii Remote hand tracking system. Next SIGGRAPH conferences are going to take place in Los Angeles, 25-29 July and Seoul, 15-18 December. Right now there are no announcements, that Shinoda Lab is going to present a further developed version of its Touchable Holography.

Nevertheless it would be very interesting to see, what it would look like.