## three-dimensional space

Three-dimensional Cartesian coordinate system with the x-axis pointing towards the observer

Three-dimensional space is a geometric 3-parameters model of the physical universe (without considering time) in which we exist. These three dimensions can be labeled by a combination of three chosen from the terms length, width, height, depth, and breadth. Any three directions can be chosen, provided that they do not all lie in the same plane.

In physics and mathematics, a sequence of n numbers can be understood as a location in n-dimensional space. When n = 3, the set of all such locations is called 3-dimensional Euclidean space. It is commonly represented by the symbol $scriptstyle{mathbb{R}}^3$. This space is only one example of a great variety of spaces in three dimensions called 3-manifolds.

## Details

In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional space by means of three coordinates. Three coordinate axes are given, usually each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in three-dimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two axes.

Other popular methods of describing the location of a point in three-dimensional space include cylindrical coordinates and spherical coordinates, though there is an infinite number of possible methods. See Euclidean space.

Another mathematical way of viewing three-dimensional space is found in linear algebra, where the idea of independence is crucial. Space has three dimensions because the length of a box is independent of its width or breadth. In the technical language of linear algebra, space is three-dimensional because every point in space can be described by a linear combination of three independent vectors. In this view, space-time is four-dimensional because the location of a point in time is independent of its location in space.

Three-dimensional space has a number of properties that distinguish it from spaces of other dimension numbers. For example, at least three dimensions are required to tie a knot in a piece of string.[1] Many of the laws of physics, such as the various inverse square laws, depend on dimension three.[2]

The understanding of three-dimensional space in humans is thought to be learned during infancy using unconscious inference, and is closely related to hand-eye coordination. The visual ability to perceive the world in three dimensions is called depth perception.

With the space $scriptstyle{mathbb{R}}^3$, the topologists locally model all other 3-manifolds.

In physics, our three-dimensional space is viewed as embedded in four-dimensional space-time, called Minkowski space (see special relativity). The idea behind space-time is that time is hyperbolic-orthogonal to each of the three spatial dimensions.

## Geometry

### Polytopes

In three dimensions, there are nine regular polytopes: the five convex Platonic solids and the four nonconvex Kepler-Poinsot polyhedra.

Regular polytopes in three dimensions
Class Platonic solids Kepler-Poinsot polyhedra
Symmetry Coxeter group A3 BC3 H3
Order 24 48 120
Regular
polyhedron

{3,3}

{4,3}

{3,4}

{5,3}

{3,5}

{5/2,5}

{5,5/2}

{5/2,3}

{3,5/2}

### Hypersphere

A two-dimensional perspective projection of a sphere

A hypersphere in 3-space (also called a 2-sphere because its surface is 2-dimensional) consists of the set of all points in 3-space at a fixed distance r from a central point P. The volume enclosed by this surface is:

$V = frac{4}{3}pi r^{3}$

Another hypersphere, but having three dimensions is the 3-sphere: points equidistant to the origin of the euclidean space $mathbb{R}^4$ at distance one. If any position is $P=(x,y,z,t)$, then $x^2+y^2+z^2+t^2=1$ characterize a point in the 3-sphere.

### Orthogonality

In the familiar 3-dimensional space that we live in, there are three pairs of cardinal directions: up/down (altitude), north/south (latitude), and east/west (longitude). These pairs of directions are mutually orthogonal: They are at right angles to each other. In mathematical terms, they lie on three coordinate axes, usually labelled x, y, and z. The z-buffer in computer graphics refers to this z-axis, representing depth in the 2-dimensional imagery displayed on the computer screen.

### Coordinate systems

In mathematics, analytic geometry (also called Cartesian geometry) describes every point in three-dimensional space by means of three coordinates. Three coordinate axes are given, each perpendicular to the other two at the origin, the point at which they cross. They are usually labeled x, y, and z. Relative to these axes, the position of any point in three-dimensional space is given by an ordered triple of real numbers, each number giving the distance of that point from the origin measured along the given axis, which is equal to the distance of that point from the plane determined by the other two 2 axes.

Other popular methods of describing the location of a point in three-dimensional space include cylindrical coordinates and spherical coordinates, though there is an infinite number of possible methods. See Euclidean space.

Below are images of the above-mentioned systems.

## References

1. ^ Dale Rolfsen, Knots and Links, Publish or Perish, Berkeley, 1976, ISBN 0-914098-16-0
2. ^ Brian Greene, The Fabric of the Cosmos, Random House, New York, 2003, ISBN 0-375-72720-5

## Holography

Two photographs of a single hologram taken from different viewpoints

Holography is a technique which enables three-dimensional images to be made. It involves the use of a laser, interference, diffraction, light intensity recording and suitable illumination of the recording. The image changes as the position and orientation of the viewing system changes in exactly the same way as if the object were still present, thus making the image appear three-dimensional.

The holographic recording itself is not an image; it consists of an apparently random structure of either varying intensity, density or profile.

## Overview and history

The HungarianBritish physicist Dennis Gabor (in Hungarian: Gábor Dénes),[1][2] was awarded the Nobel Prize in Physics in 1971 “for his invention and development of the holographic method”.[3] His work, done in the late 1940s, built on pioneering work in the field of X-ray microscopy by other scientists including Mieczysław Wolfke in 1920 and WL Bragg in 1939.[4] The discovery was an unexpected result of research into improving electron microscopes at the British Thomson-Houston Company in Rugby, England, and the company filed a patent in December 1947 (patent GB685286). The technique as originally invented is still used in electron microscopy, where it is known as electron holography, but optical holography did not really advance until the development of the laser in 1960. The word holography comes from the Greek words ὅλος (hólos; “whole”) and γραφή (grafē; “writing” or “drawing“).

Portrait of Yuri Denisyuk, by Dieter Jung

The development of the laser enabled the first practical optical holograms that recorded 3D objects to be made in 1962 by Yuri Denisyuk in the Soviet Union[5] and by Emmett Leith and Juris Upatnieks at the University of Michigan, USA.[6] Early holograms used silver halide photographic emulsions as the recording medium. They were not very efficient as the grating produced absorbed much of the incident light. Various methods of converting the variation in transmission to a variation in refractive index (known as “bleaching”) were developed which enabled much more efficient holograms to be produced.[7][8][9]

Several types of holograms can be made. Transmission holograms, such as those produced by Leith and Upatnieks, are viewed by shining laser light through them and looking at the reconstructed image from the side of the hologram opposite the source.[10] A later refinement, the “rainbow transmission” hologram, allows more convenient illumination by white light rather than by lasers.[11] Rainbow holograms are commonly used for security and authentication, for example, on credit cards and product packaging.[12]

Another kind of common hologram, the reflection or Denisyuk hologram, can also be viewed using a white-light illumination source on the same side of the hologram as the viewer and is the type of hologram normally seen in holographic displays. They are also capable of multicolour-image reproduction.[13]

Specular holography is a related technique for making three-dimensional images by controlling the motion of specularities on a two-dimensional surface.[14] It works by reflectively or refractively manipulating bundles of light rays, whereas Gabor-style holography works by diffractively reconstructing wavefronts.

Most holograms produced are of static objects but systems for displaying changing scenes on a holographic volumetric display are now being developed.[15][16][17]

Holograms can also be used to store, retrieve, and process information optically.[18]

In its early days, holography required high-power expensive lasers, but nowadays, mass-produced low-cost semi-conductor or diode lasers, such as those found in millions of DVD recorders and used in other common applications, can be used to make holograms and have made holography much more accessible to low-budget researchers, artists and dedicated hobbyists.

It was thought that it would be possible to use X-rays to make holograms of molecules and view them using visible light. However, X-ray holograms have not been created to date.[19]

## How holography works

Recording a hologram

Reconstructing a hologram

Close-up photograph of a hologram’s surface. The object in the hologram is a toy van. It is no more possible to discern the subject of a hologram from this pattern than it is to identify what music has been recorded by looking at a CD surface. Note that the hologram is described by the speckle pattern, rather than the “wavy” line pattern.

Holography is a technique that enables a light field, which is generally the product of a light source scattered off objects, to be recorded and later reconstructed when the original light field is no longer present, due to the absence of the original objects.[20] Holography can be thought of as somewhat similar to sound recording, whereby a sound field created by vibrating matter like musical instruments or vocal cords, is encoded in such a way that it can be reproduced later, without the presence of the original vibrating matter.

### Laser

Holograms are recorded using a flash of light that illuminates a scene and then imprints on a recording medium, much in the way a photograph is recorded. In addition, however, part of the light beam must be shone directly onto the recording medium – this second light beam is known as the reference beam. A hologram requires a laser as the sole light source. Lasers can be precisely controlled and have a fixed wavelength, unlike sunlight or light from conventional sources, which contain many different wavelengths. To prevent external light from interfering, holograms are usually taken in darkness, or in low level light of a different colour from the laser light used in making the hologram.

Holography requires a specific exposure time (just like photography), which can be controlled using a shutter, or by electronically timing the laser

### Apparatus

A hologram can be made by shining part of the light beam directly onto the recording medium, and the other part onto the object in such a way that some of the scattered light falls onto the recording medium.

A more flexible arrangement for recording a hologram requires the laser beam to be aimed through a series of elements that change it in different ways. The first element is a beam splitter that divides the beam into two identical beams, each aimed in different directions:

• One beam (known as the illumination or object beam) is spread using lenses and directed onto the scene using mirrors. Some of the light scattered (reflected) from the scene then falls onto the recording medium.
• The second beam (known as the reference beam) is also spread through the use of lenses, but is directed so that it doesn’t come in contact with the scene, and instead travels directly onto the recording medium.

Several different materials can be used as the recording medium. One of the most common is a film very similar to photographic film (silver halide photographic emulsion), but with a much higher concentration of light-reactive grains, making it capable of the much higher resolution that holograms require. A layer of this recording medium (e.g. silver halide) is attached to a transparent substrate, which is commonly glass, but may also be plastic.

### Process

When the two laser beams reach the recording medium, their light waves intersect and interfere with each other. It is this interference pattern that is imprinted on the recording medium. The pattern itself is seemingly random, as it represents the way in which the scene’s light interfered with the original light source — but not the original light source itself. The interference pattern can be considered an encoded version of the scene, requiring a particular key — the original light source — in order to view its contents.

This missing key is provided later by shining a laser, identical to the one used to record the hologram, onto the developed film. When this beam illuminates the hologram, it is diffracted by the hologram’s surface pattern. This produces a light field identical to the one originally produced by the scene and scattered onto the hologram. The image this effect produces in a person’s retina is known as a virtual image.

### Holography vs. photography

Holography may be better understood via an examination of its differences from ordinary photography:

• A hologram represents a recording of information regarding the light that came from the original scene as scattered in a range of directions rather than from only one direction, as in a photograph. This allows the scene to be viewed from a range of different angles, as if it were still present.
• A photograph can be recorded using normal light sources (sunlight or electric lighting) whereas a laser is required to record a hologram.
• A lens is required in photography to record the image, whereas in holography, the light from the object is scattered directly onto the recording medium.
• A holographic recording requires a second light beam (the reference beam) to be directed onto the recording medium.
• A photograph can be viewed in a wide range of lighting conditions, whereas holograms can only be viewed with very specific forms of illumination.
• When a photograph is cut in half, each piece shows half of the scene. When a hologram is cut in half, the whole scene can still be seen in each piece. This is because, whereas each point in a photograph only represents light scattered from a single point in the scene, each point on a holographic recording includes information about light scattered from every point in the scene. Think of viewing a street outside your house through a 4 ft x 4 ft window, and then through a 2 ft x 2 ft window. You can see all of the same things through the smaller window (by moving your head to change your viewing angle), but you can see more at once through the 4 ft window.
• A photograph is a two-dimensional representation that can only reproduce a rudimentary three-dimensional effect, whereas the reproduced viewing range of a hologram adds many more depth perception cues that were present in the original scene. These cues are recognized by the human brain and translated into the same perception of a three-dimensional image as when the original scene might have been viewed.
• A photograph clearly maps out the light field of the original scene. The developed hologram’s surface consists of a very fine, seemingly random pattern, which appears to bear no relationship to the scene it recorded.

## Physics of holography

For a better understanding of the process, it is necessary to understand interference and diffraction. Interference occurs when one or more wavefronts are superimposed. Diffraction occurs whenever a wavefront encounters an object. The process of producing a holographic reconstruction is explained below purely in terms of interference and diffraction. It is somewhat simplified but is accurate enough to provide an understanding of how the holographic process works.

### Plane wavefronts

A diffraction grating is a structure with a repeating pattern. A simple example is a metal plate with slits cut at regular intervals. A light wave incident on a grating is split into several waves; the direction of these diffracted waves is determined by the grating spacing and the wavelength of the light.

A simple hologram can be made by superimposing two plane waves from the same light source on a holographic recording medium. The two waves interfere giving a straight line fringe pattern whose intensity varies sinusoidally across the medium. The spacing of the fringe pattern is determined by the angle between the two waves, and on the wavelength of the light.

The recorded light pattern is a diffraction grating. When it is illuminated by only one of the waves used to create it, it can be shown that one of the diffracted waves emerges at the same angle as that at which the second wave was originally incident so that the second wave has been ‘reconstructed’. Thus, the recorded light pattern is a holographic recording as defined above.

### Point sources

Sinusoidal zone plate

If the recording medium is illuminated with a point source and a normally incident plane wave, the resulting pattern is a sinusoidal zone plate which acts as a negative Fresnel lens whose focal length is equal to the separation of the point source and the recording plane.

When a plane wavefront illuminates a negative lens, it is expanded into a wave which appears to diverge from the focal point of the lens. Thus, when the recorded pattern is illuminated with the original plane wave, some of the light is diffracted into a diverging beam equivalent to the original plane wave; a holographic recording of the point source has been created.

When the plane wave is incident at a non-normal angle, the pattern formed is more complex but still acts as a negative lens provided it is illuminated at the original angle.

### Complex objects

To record a hologram of a complex object, a laser beam is first split into two separate beams of light. One beam illuminates the object, which then scatters light onto the recording medium. According to diffraction theory, each point in the object acts as a point source of light so the recording medium can be considered to be illuminated by a set of point sources located at varying distances from the medium.

The second (reference) beam illuminates the recording medium directly. Each point source wave interferes with the reference beam, giving rise to its own sinusoidal zone plate in the recording medium. The resulting pattern is the sum of all these ‘zone plates’ which combine to produce a random (speckle) pattern as in the photograph above.

When the hologram is illuminated by the original reference beam, each of the individual zone plates reconstructs the object wave which produced it, and these individual wavefronts add together to reconstruct the whole of the object beam. The viewer perceives a wavefront that is identical to the wavefront scattered from the object onto the recording medium, so that it appears to him or her that the object is still in place even if it has been removed. This image is known as a “virtual” image, as it is generated even though the object is no longer there.

### Mathematical model

A single-frequency light wave can be modelled by a complex number U, which represents the electric or magnetic field of the light wave. The amplitude and phase of the light are represented by the absolute value and angle of the complex number. The object and reference waves at any point in the holographic system are given by UO and UR. The combined beam is given by UO + UR. The energy of the combined beams is proportional to the square of magnitude of the combined waves as:

$|U_O + U_R|^2=U_O U_R^*+|U_R|^2+|U_O|^2+ U_O^*U_R$

If a photographic plate is exposed to the two beams and then developed, its transmittance, T, is proportional to the light energy that was incident on the plate and is given by

$T=kU_O U_R^*+k|U_R|^2+k|U_O|^2+ kU_O^*U_R$

where k is a constant.

When the developed plate is illuminated by the reference beam, the light transmitted through the plate, UH is equal to the transmittance T multiplied by the reference beam amplitude UR, giving

$U_H=TU_R=kU_O|U_R|^2+k|U_R|^2U_R+k|U_O|^2U_R+ kU_O^*U_R^2$

It can be seen that UH has four terms, each representing a light beam emerging from the hologram. The first of these is proportional to UO. This is the reconstructed object beam which enables a viewer to ‘see’ the original object even when it is no longer present in the field of view.

The second and third beams are modified versions of the reference beam. The fourth term is known as the “conjugate object beam”. It has the reverse curvature to the object beam itself and forms a real image of the object in the space beyond the holographic plate.

When the reference and object beams are incident on the holographic recording medium at significantly different angles, the virtual, real and reference wavefronts all emerge at different angles, enabling the reconstructed object to be seen clearly.

## Recording a hologram

### Items required

An optical table being used to make a hologram

To make a hologram, the following are required:

• a suitable object or set of objects
• a suitable laser beam
• part of the laser beam to be directed so that it illuminates the object (the object beam) and another part so that it illuminates the recording medium directly (the reference beam), enabling the reference beam and the light which is scattered from the object onto the recording medium to form an intereference pattern
• a recording medium which converts this interference pattern into an optical element which modifies either the amplitude or the phase of an incident light beam according to the intensity of the interference pattern.
• an environment which provides sufficient mechanical and thermal stability that the interference pattern is stable during the time in which the interference pattern is recorded[21]

These requirements are inter-related, and it is essential to understand the nature of optical interference to see this. Interference is the variation in intensity which can occur when two light waves are superimposed. The intensity of the maxima exceeds the sum of the individual intensities of the two beams, and the intensity at the minima is less than this and may be zero. The interference pattern maps the relative phase between the two waves, and any change in the relative phases causes the interference pattern to move across the field of view. If the relative phase of the two waves changes by one cycle, then the pattern drifts by one whole fringe. One phase cycle corresponds to a change in the relative distances travelled by the two beams of one wavelength. Since the wavelength of light is of the order of 0.5μm, it can be seen that very small changes in the optical paths travelled by either of the beams in the holographic recording system lead to movement of the interference pattern which is the holographic recording. Such changes can be caused by relative movements of any of the optical components or the object itself, and also by local changes in air-temperature. It is essential that any such changes are significantly less than the wavelength of light if a clear well-defined recording of the interference is to be created.

The exposure time required to record the hologram depends on the laser power available, on the particular medium used and on the size and nature of the object(s) to be recorded, just as in conventional photography. This determines the stability requirements. Exposure times of several minutes are typical when using quite powerful gas lasers and silver halide emulsions. All the elements within the optical system have to be stable to fractions of a μm over that period. It is possible to make holograms of much less stable objects by using a pulsed laser which produces a large amount of energy in a very short time (μs or less).[22] These systems have been used to produce holograms of live people. A holographic portrait of Dennis Gabor was produced in 1971 using a pulsed ruby laser.[23][24]

Thus, the laser power, recording medium sensitivity, recording time and mechanical and thermal stability requirements are all interlinked. Generally, the smaller the object, the more compact the optical layout, so that the stability requirements are significantly less than when making holograms of large objects.

Another very important laser parameter is its coherence.[25] This can be envisaged by considering a laser producing a sine wave whose frequency drifts over time; the coherence length can then be considered to be the distance over which it maintains a single frequency. This is important because two waves of different frequencies do not produce a stable interference pattern. The coherence length of the laser determines the depth of field which can be recorded in the scene. A good holography laser will typically have a coherence length of several meters, ample for a deep hologram.

The objects that form the scene must, in general, have optically rough surfaces so that they scatter light over a wide range of angles. A specularly reflecting (or shiny) surface reflects the light in only one direction at each point on its surface, so in general, most of the light will not be incident on the recording medium. A hologram of a shiny object can be made by locating it very close to the recording plate.[26]

### Hologram classifications

There are three important properties of a hologram which are defined in this section. A given hologram will have one or other of each of these three properties, e.g. we can have an amplitude modulated thin transmission hologram, or a phase modulated, volume reflection hologram.

#### Amplitude and phase modulation holograms

An amplitude modulation hologram is one where the amplitude of light diffracted by the hologram is proportional to the intensity of the recorded light. A straightforward example of this is photographic emulsion on a transparent substrate. The emulsion is exposed to the interference pattern, and is subsequently developed giving a transmittance which varies with the intensity of the pattern – the more light that fell on the plate at a given point, the darker the developed plate at that point.

A phase hologram is made by changing either the thickness or the refractive index of the material in proportion to the intensity of the holographic interference pattern. This is a phase grating and it can be shown that when such a plate is illuminated by the original reference beam, it reconstructs the original object wavefront. The efficiency (i.e. the fraction of the illuminated beam which is converted to reconstructed object beam) is greater for phase than for amplitude modulated holograms.

#### Thin holograms and thick (volume) holograms

A thin hologram is one where the thickness of the recording medium is much less than the spacing of the interference fringes which make up the holographic recording.

A thick or volume hologram is one where the thickness of the recording medium is greater than the spacing of the interference pattern. The recorded hologram is now a three dimensional structure, and it can be shown that incident light is diffracted by the grating only at a particular angle, known as the Bragg angle.[27] If the hologram is illuminated with a light source incident at the original reference beam angle but a broad spectrum of wavelengths, reconstruction occurs only at the wavelength of the original laser used. If the angle of illumination is changed, reconstruction will occur at a different wavelength and the colour of the re-constructed scene changes. A volume hologram effectively acts as a colour filter.

#### Transmission and reflection holograms

A transmission hologram is one where the object and reference beams are incident on the recording medium from the same side. In practice, several more mirrors may be used to direct the beams in the required directions.

Normally, transmission holograms can only be reconstructed using a laser or a quasi-monochromatic source, but a particular type of transmission hologram, known as a rainbow hologram, can be viewed with white light.

In a reflection hologram, the object and reference beams are incident on the plate from opposite sides of the plate. The reconstructed object is then viewed from the same side of the plate as that at which the re-constructing beam is incident.

Only volume holograms can be used to make reflection holograms, as only a very low intensity diffracted beam would be reflected by a thin hologram.

### Holographic recording media

The recording medium has to convert the original interference pattern into an optical element that modifies either the amplitude or the phase of an incident light beam in proportion to the intensity of the original light field.

The recording medium should be able to resolve fully all the fringes arising from interference between object and reference beam. These fringe spacings can range from tens of microns to less than one micron, i.e. spatial frequencies ranging from a few hundred to several thousand cycles/mm, and ideally, the recording medium should have a response which is flat over this range. If the response of the medium to these spatial frequencies is low, the diffraction efficiency of the hologram will be poor, and a dim image will be obtained. It should be noted that standard photographic film has a very low, or even zero, response at the frequencies involved and cannot be used to make a hologram – see, for example, Kodak’s professional black and white film[28] whose resolution starts falling off at 20 lines/mm — it is unlikely that any reconstructed beam could be obtained using this film.

If the response is not flat over the range of spatial frequencies in the interference pattern, then the resolution of the reconstructed image may also be degraded.[29][30]

The table below shows the principal materials used for holographic recording. Note that these do not include the materials used in the mass replication of an existing hologram, which are discussed in the next section. The resolution limit given in the table indicates the maximal number of interference lines/mm of the gratings. The required exposure, expressed as millijoules (mJ) of photon energy impacting the surface area, is for a long exposure time. Short exposure times (less than 1/1000 of a second, such as with a pulsed laser) require much higher exposure energies, due to reciprocity failure.

General properties of recording materials for holography. Source:[31]
Material Reusable Processing Type of hologram Theoretical maximum efficiency Required exposure [mJ/cm2] Resolution limit [mm−1]
Photographic emulsions No Wet Amplitude 6% 1.5 5000
Phase (bleached) 60%
Dichromated gelatin No Wet Phase 100% 100 10,000
Photoresists No Wet Phase 30% 100 3,000
Photothermoplastics Yes Charge and heat Phase 33% 0.1 500–1,200
Photopolymers No Post exposure Phase 100% 10000 5,000
Photorefractives Yes None Phase 100% 10 10,000

### Copying and mass production

An existing hologram can be copied by embossing[32] or optically.[33]

Most holographic recordings (e.g. bleached silver halide, photoresist, and photopolymers) have surface relief patterns which conform with the original illumination intensity. Embossing, which is similar to the method used to stamp out plastic discs from a master in audio recording, involves copying this surface relief pattern by impressing it onto another material.

The first step in the embossing process is to make a stamper by electrodeposition of nickel on the relief image recorded on the photoresist or photothermoplastic. When the nickel layer is thick enough, it is separated from the master hologram and mounted on a metal backing plate. The material used to make embossed copies consists of a polyester base film, a resin separation layer and a thermoplastic film constituting the holographic layer.

The embossing process can be carried out with a simple heated press. The bottom layer of the duplicating film (the thermoplastic layer) is heated above its softening point and pressed against the stamper, so that it takes up its shape. This shape is retained when the film is cooled and removed from the press. In order to permit the viewing of embossed holograms in reflection, an additional reflecting layer of aluminum is usually added on the hologram recording layer. This method is particularly suited to mass production.

The first book to feature a hologram on the front cover was The Skook (Warner Books, 1984) by JP Miller, featuring an illustration by Miller. That same year, “Telstar” by Ad Infinitum became the first record with a hologram cover and National Geographic published the first magazine with a hologram cover.[34] Embossed holograms are used widely on credit cards, banknotes, and high value products for authentication purposes.[35]

It is possible to print holograms directly into steel using a sheet explosive charge to create the required surface relief.[36] The Royal Canadian Mint produces holographic gold and silver coinage through a complex stamping process.[37]

A hologram can be copied optically by illuminating it with a laser beam, and locating a second hologram plate so that it is illuminated both by the reconstructed object beam, and the illuminating beam. Stability and coherence requirements are significantly reduced if the two plates are located very close together.[38] An index matching fluid is often used between the plates to minimize spurious interference between the plates. Uniform illumination can be obtained by scanning point-by-point or with a beam shaped into a thin line.

## Reconstructing and viewing the holographic image

When the hologram plate is illuminated by a laser beam identical to the reference beam which was used to record the hologram, an exact reconstruction of the original object wavefront is obtained. An imaging system (an eye or a camera) located in the reconstructed beam ‘sees’ exactly the same scene as it would have done when viewing the original. When the lens is moved, the image changes in the same way as it would have done when the object was in place. If several objects were present when the hologram was recorded, the reconstructed objects move relative to one another, i.e. exhibit parallax, in the same way as the original objects would have done. It was very common in the early days of holography to use a chess board as the object and then take photographs at several different angles using the reconstructed light to show how the relative positions of the chess pieces appeared to change.

A holographic image can also be obtained using a different laser beam configuration to the original recording object beam, but the reconstructed image will not match the original exactly.[39] When a laser is used to reconstruct the hologram, the image is speckled just as the original image will have been. This can be a major drawback in viewing a hologram.

White light consists of light of a wide range of wavelengths. Normally, if a hologram is illuminated by a white light source, each wavelength can be considered to generate its own holographic reconstruction, and these will vary in size, angle, and distance. These will be superimposed, and the summed image will wipe out any information about the original scene, just as if you superimposed a set of photographs of the same object of different sizes and orientations. However, a holographic image can be obtained using white light in specific circumstances, e.g. with volume holograms and rainbow holograms. The white light source used to view these holograms should always approximate to a point source, i.e. a spot light or the sun. An extended source (e.g. a fluorescent lamp) will not reconstruct a hologram since it light is incident at each point at a wide range of angles, giving multiple reconstructions which will “wipe” one another out.

White light reconstructions do not contain speckles.

### Volume holograms

A volume hologram can give a reconstructed beam using white light, as the hologram structure effectively filters out colours other than those equal to or very close to the colour of the laser used to make the hologram so that the reconstructed image will appear to be approximately the same colour as the laser light used to create the holographic recording.

### Rainbow holograms

Rainbow hologram showing the change in colour in the vertical direction

In this method, parallax in the vertical plane is sacrificed to allow a bright well-defined single colour re-constructed image to be obtained using white light. The rainbow holography recording process uses a horizontal slit to eliminate vertical parallax in the output image. The viewer is then effectively viewing the holographic image through a narrow horizontal slit. Horizontal parallax information is preserved but movement in the vertical direction produces colour rather than different vertical perspectives.[40] Stereopsis and horizontal motion parallax, two relatively powerful cues to depth, are preserved.

The holograms found on credit cards are examples of rainbow holograms. These are technically transmission holograms mounted onto a reflective surface like a metalized polyethylene terephthalate substrate commonly known as PET.

### Fidelity of the reconstructed beam

Reconstructions from two parts of a broken hologram. Note the different viewpoints required to see the whole object

To replicate the original object beam exactly, the reconstructing reference beam must be identical to the original reference beam and the recording medium must be able to fully resolve the interference pattern formed between the object and reference beams. Exact reconstruction is required in holographic interferometry, where the holographically reconstructed wavefront interferes with the wavefront coming from the actual object, giving a null fringe if there has been no movement of the object and mapping out the displacement if the object has moved. This requires very precise relocation of the developed holographic plate.

Any change in the shape, orientation or wavelength of the reference beam gives rise to aberrations in the reconstructed image. For instance, the reconstructed image is magnified if the laser used to reconstruct the hologram has a shorter wavelength than the original laser. Nonetheless, good reconstruction is obtained using a laser of a different wavelength, quasi-monochromatic light or white light, in the right circumstances.

Since each point in the object illuminates all of the hologram, the whole object can be reconstructed from a small part of the hologram. Thus, a hologram can be broken up into small pieces and each one will enable the whole of the original object to be imaged. One does, however, lose information and the spatial resolution gets worse as the size of the hologram is decreased — the image becomes “fuzzier”. The field of view is also reduced, and the viewer will have to change position to see different parts of the scene.

## Applications

### Art

Early on, artists saw the potential of holography as a medium and gained access to science laboratories to create their work. Holographic art is often the result of collaborations between scientists and artists, although some holographers would regard themselves as both an artist and a scientist.

Salvador Dalí claimed to have been the first to employ holography artistically. He was certainly the first and best-known surrealist to do so, but the 1972 New York exhibit of Dalí holograms had been preceded by the holographic art exhibition that was held at the Cranbrook Academy of Art in Michigan in 1968 and by the one at the Finch College gallery in New York in 1970, which attracted national media attention.[41]

During the 1970s, a number of art studios and schools were established, each with their particular approach to holography. Notably, there was the San Francisco School of Holography established by Lloyd Cross, The Museum of Holography in New York founded by Rosemary (Possie) H. Jackson, the Royal College of Art in London and the Lake Forest College Symposiums organised by Tung Jeong (T.J.).[42] None of these studios still exist; however, there is the Center for the Holographic Arts in New York[43] and the HOLOcenter in Seoul,[44] which offers artists a place to create and exhibit work.

During the 1980s, many artists who worked with holography helped the diffusion of this so-called “new medium” in the art world, such as Harriet Casdin-Silver of the USA, Dieter Jung of Germany, and Moysés Baumstein of Brazil, each one searching for a proper “language” to use with the three-dimensional work, avoiding the simple holographic reproduction of a sculpture or object. For instance, in Brazil, many concrete poets (Augusto de Campos, Décio Pignatari, Julio Plaza and José Wagner Garcia, associated with Moysés Baumstein) found in holography a way to express themselves and to renew Concrete Poetry.

A small but active group of artists still use holography as their main medium, and many more artists integrate holographic elements into their work.[45] Some are associated with novel holographic techniques; for example, artist Matt Brand[46] employed computational mirror design to eliminate image distortion from specular holography.

The MIT Museum[47] and Jonathan Ross[48] both have extensive collections of holography and on-line catalogues of art holograms.

### Data storage

Holography can be put to a variety of uses other than recording images. Holographic data storage is a technique that can store information at high density inside crystals or photopolymers. The ability to store large amounts of information in some kind of media is of great importance, as many electronic products incorporate storage devices. As current storage techniques such as Blu-ray Disc reach the limit of possible data density (due to the diffraction-limited size of the writing beams), holographic storage has the potential to become the next generation of popular storage media. The advantage of this type of data storage is that the volume of the recording media is used instead of just the surface. Currently available SLMs can produce about 1000 different images a second at 1024×1024-bit resolution. With the right type of media (probably polymers rather than something like gigabit-per-second writing speed. Read speeds can surpass this, and experts believe one-terabit-per-second readout is possible. In 2005, companies such as Optware and Maxell produced a 120 mm disc that uses a holographic layer to store data to a potential 3.9 TB, which they plan to market under the name Holographic Versatile Disc. Another company, InPhase Technologies, is developing a competing format. While many holographic data storage models have used “page-based” storage, where each recorded hologram holds a large amount of data, more recent research into using submicrometre-sized “microholograms” has resulted in several potential 3D optical data storage solutions. While this approach to data storage can not attain the high data rates of page-based storage, the tolerances, technological hurdles, and cost of producing a commercial product are significantly lower.

### Dynamic holography

In static holography, recording, developing and reconstructing occur sequentially, and a permanent hologram is produced.

There also exist holographic materials that do not need the developing process and can record a hologram in a very short time. This allows one to use holography to perform some simple operations in an all-optical way. Examples of applications of such real-time holograms include phase-conjugate mirrors (“time-reversal” of light), optical cache memories, image processing (pattern recognition of time-varying images), and optical computing.

The amount of processed information can be very high (terabits/s), since the operation is performed in parallel on a whole image. This compensates for the fact that the recording time, which is in the order of a microsecond, is still very long compared to the processing time of an electronic computer. The optical processing performed by a dynamic hologram is also much less flexible than electronic processing. On one side, one has to perform the operation always on the whole image, and on the other side, the operation a hologram can perform is basically either a multiplication or a phase conjugation. In optics, addition and Fourier transform are already easily performed in linear materials, the latter simply by a lens. This enables some applications, such as a device that compares images in an optical way.[49]

The search for novel nonlinear optical materials for dynamic holography is an active area of research. The most common materials are photorefractive crystals, but in semiconductors or semiconductor heterostructures (such as quantum wells), atomic vapors and gases, plasmas and even liquids, it was possible to generate holograms.

A particularly promising application is optical phase conjugation. It allows the removal of the wavefront distortions a light beam receives when passing through an aberrating medium, by sending it back through the same aberrating medium with a conjugated phase. This is useful, for example, in free-space optical communications to compensate for atmospheric turbulence (the phenomenon that gives rise to the twinkling of starlight).

### Hobbyist use

Peace Within Reach, a Denisyuk DCG hologram by amateur Dave Battin

Since the beginning of holography, experimenters have explored its uses. Starting in 1971, Lloyd Cross started the San Francisco School of Holography and started to teach amateurs the methods of making holograms with inexpensive equipment. This method relied on the use of a large table of deep sand to hold the optics rigid and damp vibrations that would destroy the image.

Many of these holographers would go on to produce art holograms. In 1983, Fred Unterseher published the Holography Handbook, a remarkably easy-to-read description of making holograms at home. This brought in a new wave of holographers and gave simple methods to use the then-available AGFA silver halide recording materials.

In 2000, Frank DeFreitas published the Shoebox Holography Book and introduced the use of inexpensive laser pointers to countless hobbyists. This was a very important development for amateurs, as the cost for a 5 mW laser dropped from \$1200 to \$5 as semiconductor laser diodes reached mass market. Now, there are hundreds to thousands of amateur holographers worldwide.

In 2006, a large number of surplus Holography Quality Green Lasers (Coherent C315) became available and put Dichromated Gelatin (DCG) within the reach of the amateur holographer. The holography community was surprised at the amazing sensitivity of DCG to green light. It had been assumed that the sensitivity would be non-existent. Jeff Blyth responded with the G307 formulation of DCG to increase the speed and sensitivity to these new lasers.[50]

Many film suppliers have come and gone from the silver-halide market. While more film manufactures have filled in the voids, many amateurs are now making their own film. The favorite formulations are Dichromated Gelatin, Methylene Blue Sensitised Dichromated Gelatin and Diffusion Method Silver Halide preparations. Jeff Blyth has published very accurate methods for making film in a small lab or garage.[51]

A small group of amateurs are even constructing their own pulsed lasers to make holograms of moving objects.[52]

Holography kits with self-developing film plates have now entered the consumer market. The kits make holographs and have been found to be fairly error tolerant,[53] and enable holograms to be made without any other specialized equipment.

### Holographic interferometry

Holographic interferometry (HI) is a technique that enables static and dynamic displacements of objects with optically rough surfaces to be measured to optical interferometric precision (i.e. to fractions of a wavelength of light).[54][55] It can also be used to detect optical-path-length variations in transparent media, which enables, for example, fluid flow to be visualized and analyzed. It can also be used to generate contours representing the form of the surface.

It has been widely used to measure stress, strain, and vibration in engineering structures.

### Interferometric microscopy

The hologram keeps the information on the amplitude and phase of the field . Several holograms may keep information about the same distribution of light, emitted to various directions. The numerical analysis of such holograms allows one to emulate large numerical aperture, which, in turn, enables enhancement of the resolution of optical microscopy. The corresponding technique is called interferometric microscopy. Recent achievements of interferometric microscopy allow one to approach the quarter-wavelength limit of resolution.[56]

### Sensors or biosensors

The hologram is made with a modified material that interacts with certain molecules generating a change in the fringe periodicity or refractive index, therefore, the color of the holographic reflection.[57]

### Security

Identigram as a security element in a German identity card

Security holograms are very difficult to forge, because they are replicated from a master hologram that requires expensive, specialized and technologically advanced equipment. They are used widely in many currencies, such as the Brazilian 20, 50, and 100-reais notes; British 5, 10, and 20-pound notes; South Korean 5000, 10000, and 50000-won notes; Japanese 5000 and 10000 yen notes; and all the currently-circulating banknotes of the Canadian dollar, Danish krone, and Euro. They can also be found in credit and bank cards as well as passports, ID cards, books, DVDs, and sports equipment.

### Other applications

Holographic scanners are in use in post offices, larger shipping firms, and automated conveyor systems to determine the three-dimensional size of a package. They are often used in tandem with checkweighers to allow automated pre-packing of given volumes, such as a truck or pallet for bulk shipment of goods. Holograms produced in elastomers can be used as stress-strain reporters due to its elasticity and compressibility, the pressure and force applied are correlated to the reflected wavelength, therefore its color.[58]

## Non-optical holography

In principle, it is possible to make a hologram for any wave.

Electron holography is the application of holography techniques to electron waves rather than light waves. Electron holography was invented by Dennis Gabor to improve the resolution and avoid the aberrations of the transmission electron microscope. Today it is commonly used to study electric and magnetic fields in thin films, as magnetic and electric fields can shift the phase of the interfering wave passing through the sample.[59] The principle of electron holography can also be applied to interference lithography.[60]

Acoustic holography is a method used to estimate the sound field near a source by measuring acoustic parameters away from the source via an array of pressure and/or particle velocity transducers. Measuring techniques included within acoustic holography are becoming increasingly popular in various fields, most notably those of transportation, vehicle and aircraft design, and NVH. The general idea of acoustic holography has led to different versions such as near-field acoustic holography (NAH) and statistically optimal near-field acoustic holography (SONAH). For audio rendition, the wave field synthesis is the most related procedure.

Atomic holography has evolved out of the development of the basic elements of atom optics. With the Fresnel diffraction lens and atomic mirrors atomic holography follows a natural step in the development of the physics (and applications) of atomic beams. Recent developments including atomic mirrors and especially ridged mirrors have provided the tools necessary for the creation of atomic holograms,[61] although such holograms have not yet been commercialized.

## Things often confused with holograms

Effects produced by lenticular printing, the Pepper’s Ghost illusion (or modern variants such as the Musion Eyeliner), tomography and volumetric displays are often confused with holograms.[62][63]

The Pepper’s ghost technique, being the easiest to implement of these methods, is most prevalent in 3D displays that claim to be (or are referred to as) “holographic”. While the original illusion, used in theater, recurred to actual physical objects and persons, located offstage, modern variants replace the source object with a digital screen, which displays imagery generated with 3D computer graphics to provide the necessary depth cues. The reflection, which seems to float mid-air, is still flat, however, thus less realistic than if an actual 3D object was being reflected.

Examples of this digital version of Pepper’s ghost illusion include the Gorillaz performances in the 2005 MTV Europe Music Awards and the 48th Grammy Awards; and Tupac Shakur‘s virtual performance at Coachella Valley Music and Arts Festival in 2012, rapping alongside Snoop Dogg during the latter’s set with Dr. Dre.[64]

During the 2008 American presidential election, CNN debuted its tomograms to “beam in” correspondents including musician will.i.am as “holograms”.

An even simpler illusion can be created by rear-projecting realistic images into semi-transparent screens. The rear projection is necessary because otherwise the semi-transparency of the screen would allow the background to be illuminated by the projection, which would break the illusion.

Crypton Future Media, a music software company that produced Hatsune Miku,[65] one of many Vocaloid singing synthesizer applications, has produced concerts that have Miku, along with other Crypton Vocaloids, performing on stage as “holographic” characters. These concerts use rear projection onto a semi-transparent DILAD screen[66][67] to achieve its “holographic” effect.[68][69][70]

In 2011, in Beijing, apparel company Burberry produced the “Burberry Prorsum Autumn/Winter 2011 Hologram Runway Show”, which included life size 2-D projections of models. The company’s own video[71] shows several centered and off-center shots of the main 2-dimensional projection screen, the latter revealing the flatness of the virtual models. The claim that holography was used was reported as fact in the trade media.[72]

## Holography in fiction

[dubious“>dubious ]

Holograms are often used as plot devices in science fiction. However, very often, sci-fi movies and TV shows incorrectly present different 3D-projection technologies as “holography” (see the above section).

• The Carpathian Castle (1893 novel by Jules Verne), the plot revolves around prima donna La Stilla, represented at the times of the events as a projected image.[relevant?“>relevant? ]
• The Jetsons (1962-3 television series), holograms used as entertainment devices, replacing the television in many episodes
• Star Trek: The Animated Series (1974 television series) episode “The Practical Joker“, the holodeck is introduced
• Star Wars (1977 film), use of the hologram in the movies and video games of the series to display people remotely communicating with each other. It is also present in several other of the films of the series, including the Phantom Menace, Attack of the Clones, and Revenge of the Sith to communicate across the galaxy.
• Hello America (1981 book by J.G. Ballard), holographic technology is used by president Charles Manson to scare nomad peoples along the United States of America, showing images of American pop culture icons such as Gary Cooper, Mickey Mouse, or the Enterprise space ship.
• En Iniya Iyanthira (1980s novel by Sujatha Rangarajan), a character named Jeeva, who is the president of the country, is not real but a holographic image.
• Jem and the Holograms (1985 television series), Jerrica Benton, the lead singer of a band uses hologram projections to help create her alter-ego persona, Jem; micro-projectors in her earrings allow her to project a hologram over herself and produce hologram objects and images in her surroundings
• Star Trek: The Next Generation (1987–1994 television series), uses the holodeck extensively; beginning with this series, various episodes and films throughout the Star Trek series feature holographic characters and ships
• Red Dwarf (1988-2012 television series), after a catastrophic radiation leak inside the Jupiter Mining Corporation spaceship Red Dwarf, crew member Second Technician Arnold Rimmer is resurrected as a hologram. Because he is a “soft-light” hologram, he cannot touch anything and objects just pass right through him. However, much later – in series VI – the Red Dwarf crew meet ‘Legion’, a being with advanced technology, who upgrades Rimmer’s light bee – the small object that projects his hologram by hovering around inside him – changing his projection to what is called in the show “hard-light” giving him a hologramatic equivalent of a physical body.
• Back to the Future Part II (1989 film), a giant projection hologram is used as an advertisement for the (fictional) 2015 film Jaws 19
• Total Recall (1990 film), the main character uses a device, similar to a wrist watch, to produce a hologram[citation needed“>citation needed] of himself and deceive his foes
• Star Trek: Voyager (1995–2001 television series), introduced the Emergency Medical Hologram (EMH) doctor
• Yu-Gi-Oh! (1996–present manga, film, television series, video games), use of holographic[citation needed“>citation needed] technology used in order to make a game called Duel Monsters appear to be more life like; Duel Monsters is a game where players using a wrist mounted Duel Disk summon monsters and cast spells and traps in order to bring a players life points to 0 or diminish all the cards in a players deck; used throughout the entire series.
• Stargate: SG-1 (1997–2007 television series), various characters appear as holograms in various episodes: The Asgard masquerade themselves holographically as Norse gods to the primitive peoples under their protection, Morgan le Fay in “The Pegasus Project” and Myrddin as a Merlin in “Avalon” and “Camelot” as a holographic sentry; Heliopolis “Book”; the puddle jumper starship has a holographic HUD. After the Goa’uld leader Anubis probed the mind of Asgard leader Thor, he was able to acquire their hologram technology and he used it frequently.
• Half-Life (1998 video game), the scientific research company Black Mesa is known to use holograms as recorded messages in their facility
• Lost in Space (1998 film), June Lockhart (Maureen Robinson) appeared as Will’s school principal “Cartwright” in a hologram
• Power Rangers Time Force (2001 television series), their chrono morphers use holographic communication
• Halo (2001 video game) uses “holotanks” to display the avatar of an artificial intelligence construct called Cortana; in Halo: Reach, an armor ability called the hologram allows the user to create an identical decoy
• Vanilla Sky (2001 film), a holographic projection of jazz musician John Coltrane appears in the main character’s apartment during his birthday party
• The First \$20 Million Is Always the Hardest (2002 film), computer geeks develop a \$99 computer using a holographic projector as both the display and user interface
• Treasure Planet (2002 film), Jim as a little boy reads from a 3D hologram book the story about Captain Flint and Treasure Planet; later, Jim as a teenager finds a sphere map and uses it to look at the galaxy map to Treasure Planet
• Pinocchio 3000 (2004 film), Mayor Scamboli owns a 3D hologram map on his table; Cabby and Roto change channels on it; later, at Scamboland, Mayor Scamboli welcomes kids as a giant 3D hologram version for Scamboland carnival opening
• Stargate: Atlantis (2004–2009 television series), the Atlantis city-starship features a hologram room that allows access to the Ancient database in the form of holograms; an Ancient Control Chair contains holographic projectors; in the episode “Rising”, Melia (a member of the Atlantean High Council during the first siege of Atlantis some ten millennia ago) is first seen as a hologram describing the history of the Ancients in the Pegasus Galaxy; Aurora-class battleship can project holograms remotely for communication purposes
• The Island (2005 film), a holographic projector surrounded the military compound where clones were kept to give the illusion of a tropical environment; holographic displays are present on various terminals, including the MSN information terminal in Los Angeles
• Meet the Robinsons (2007 film), Bowler Hat Michael Goob Yagoobian has a discussion with the Bowler Hat Robot about getting revenge and Bowler Hat robot shows him a 3D hologram image of a flying car-plane time machine
• GUIs are explained in the codex to consist of a projected holographic display, combined with the use of force feedback gloves that allow the user to experience simulated tactile sensations when manipulating them; the game’s “omni-tools” are holographic user-interfaces that act as a cell-phone-like device, serving as a port between computers, tablets, and other devices, giving the user many capabilities, including the ability to transfer information via wireless technology to others with an omni-tool
• Dead Space (2008 video game), to replace the player’s HUD, a holographic display shows up in front of the player’s character
• Iron Man (2008 film) and Iron Man 2 (2010 film), holographic displays appear in Iron Man’s suit
• Avatar (2009 film), holographic displays are used extensively on terminals and HUDs
• G.I. Joe: The Rise of Cobra (2009 film), Hawk, Destro, Baroness, and Storm Shadow appear as holographic projections
• Enthiran (2010 film), Chitti the robot can be telecommunicated with using a “virtual calling” where each caller can be seen as a holographic projection in front of the robot during the call

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## Reference sources

• Lasers and holography: an introduction to coherent optics W. E. Kock, Dover Publications (1981), ISBN 978-0-486-24041-1
• Principles of holography H. M. Smith, Wiley (1976), ISBN 978-0-471-80341-6
• G. Berger et al., Digital Data Storage in a phase-encoded holograhic memory system: data quality and security, Proceedings of SPIE, Vol. 4988, p. 104–111 (2003)
• Holographic Visions: A History of New Science Sean F. Johnston, Oxford University Press (2006), ISBN 0-19-857122-4
• Saxby, Graham (2003). Practical Holography, Third Edition. Taylor and Francis. ISBN 978-0-7503-0912-7.
• Three-Dimensional Imaging Techniques Takanori Okoshi, Atara Press (2011), ISBN 978-0-9822251-4-1
• Holographic Microscopy of Phase Microscopic Objects: Theory and Practice Tatyana Tishko, Tishko Dmitry, Titar Vladimir, World Scientific (2010), ISBN 13 978-981-4289-54-2

## lenticular printing

Close-up of the surface of a lenticular print.

Lenticular printing is a technology in which lenticular lenses (a technology that is also used for 3D displays) are used to produce printed images with an illusion of depth, or the ability to change or move as the image is viewed from different angles.

Examples of lenticular printing include prizes given in Cracker Jack snack boxes that showed flip and animation effects such as winking eyes, and modern advertising graphics that change their message depending on the viewing angle. This technology was created in the 1940s but has evolved in recent years to show more motion and increased depth. Originally used mostly in novelty items and commonly called “flicker pictures” or “wiggle pictures,” lenticular prints are now being used as a marketing tool to show products in motion. Recent advances in large-format presses have allowed for oversized lenses to be used in lithographic lenticular printing.[1]

## Process

Lenticular printing is a multi-step process consisting of creating a lenticular image from at least two images, and combining it with a lenticular lens. This process can be used to create various frames of animation (for a motion effect), offsetting the various layers at different increments (for a 3D effect), or simply to show a set of alternate images which may appear to transform into each other. Once the various images are collected, they are flattened into individual, different frame files, and then digitally combined into a single final file in a process called interlacing.

Lenticular printing has been used to produce movie posters, such as this advert for Species II, which morphs between two different character appearances when the angle of viewing changes.

From there the interlaced image can be printed directly to the back (smooth side) of the lens or it can be printed to a substrate (ideally a synthetic paper) and laminated to the lens. When printing to the backside of the lens, the critical registration of the fine “slices” of interlaced images must be absolutely correct during the lithographic or screen printing process or “ghosting” and poor imagery might result. Ghosting also occurs on choosing the wrong set of images for flip.[2]

The combined lenticular print will show two or more different images simply by changing the angle from which the print is viewed. If more (30+) images are used, taken in a sequence, one can even show a short video of about one second. Though normally produced in sheet form, by interlacing simple images or different colors throughout the artwork, lenticular images can also be created in roll form with 3D effects or multi-color changes. Alternatively, one can use several images of the same object, taken from slightly different angles, and then create a lenticular print which shows a stereoscopic 3D effect. 3D effects can only be achieved in a side to side (left to right) direction, as the viewer’s left eye needs to be seeing from a slightly different angle than the right to achieve the stereoscopic effect. Other effects, like morphs, motion, and zooms work better (less ghosting or latent effects) as top-to-bottom effects, but can be achieved in both directions.

There are several film processors that will take two or more pictures and create lenticular prints for hobbyists, at a reasonable cost. For slightly more money one can buy the equipment to make lenticular prints at home. This is in addition to the many corporate services that provide high volume lenticular printing.

There are many commercial end uses for lenticular images, which can be made from PVC, APET, acrylic, and PETG, as well as other materials. While PETG and APET are the most common, other materials are becoming popular to accommodate outdoor use and special forming due to the increasing use of lenticular images on cups and gift cards. Lithographic lenticular printing allows for the flat side of the lenticular sheet to have ink placed directly onto the lens, while high-resolution photographic lenticulars typically have the image laminated to the lens.

Recently, large format (over 2m) lenticular images have been used in bus shelters and movie theaters. These are printed using an oversized lithographic press. Many advances have been made to the extrusion of lenticular lens and the way it is printed which has led to a decrease in cost and an increase in quality. Lenticular images have recently seen a surge in activity, from gracing the cover of the May 2006 issue of Rolling Stone to trading cards, sports posters and signs in stores that help to attract buyers.

The newest lenticular technology is manufacturing lenses with flexo, inkjet and screen-printing techniques. The lens material comes in a roll or sheet which is fed through flexo or offset printing systems at high speed, or printed with UV inkjet machines (usually flat-beds that enable a precise registration). This technology allows high volume 3D lenticular production at low cost.

## Construction

Images are interlaced on the substrate

How a lenticular lens works

Each image is arranged (slicing) into strips, which are then interlaced with one or more similarly arranged images (splicing). These are printed on the back of a piece of plastic, with a series of thin lenses molded into the opposite side. Alternatively, the images can be printed on paper, which is then bonded to the plastic. With the new technology, lenses are printed in the same printing operation as the interlaced image, either on both sides of a flat sheet of transparent material, or on the same side of a sheet of paper, the image being covered with a transparent sheet of plastic or with a layer of transparent, which in turn is printed with several layers of varnish to create the lenses.

The lenses are accurately aligned with the interlaces of the image, so that light reflected off each strip is refracted in a slightly different direction, but the light from all pixels originating from the same original image is sent in the same direction. The end result is that a single eye looking at the print sees a single whole image, but two eyes will see different images, which leads to stereoscopic 3D perception.

## Types of lenticular prints

There are three distinct types of lenticular prints, distinguished by how great a change in angle of view is required to change the image:

Transforming prints
Here two or more very different pictures are used, and the lenses are designed to require a relatively large change in angle of view to switch from one image to another. This allows viewers to easily see the original images, since small movements cause no change. Larger movement of the viewer or the print causes the image to flip from one image to another. (The “flip effect”.)
Animated prints
Here the distance between different angles of view is “medium”, so that while both eyes usually see the same picture, moving a little bit switches to the next picture in the series. Usually many sequential images would be used, with only small differences between each image and the next. This can be used to create an image that moves (“motion effect”), or can create a “zoom” or “morph” effect, in which part of the image expands in size or changes shape as the angle of view changes. The movie poster of the film Species II, shown in this article, is an example of this technique.
Stereoscopic effects
Here the change in viewing angle needed to change images is small, so that each eye sees a slightly different view. This creates a 3D effect without requiring special glasses.

## Motorized lenticular

The basic idea of motorized lenticular displays is simple. With static (non-motorized) lenticular, the viewer either moves the piece or moves past the piece in order to see the graphic effects. With motorized lenticular, a motor moves the graphics behind the lens, enabling the graphic effects while both the viewer and the display remain stationary.

## History of lenticular image technology

Images that change when viewed from different angles predate the development of lenticular lenses. In 1692 G. A. Bois-Clair, a French painter, created paintings containing two distinct images, with a grid of vertical laths in front.[3] Different images were visible when the work was viewed from the left and right sides.

Saturnalia record with lenticular label that switches from “Magical love” to a logo.

Han-O-Disc record with diffraction grating ‘Rainbow’ film (outside ring), color shifting Rowlux (middle ring) and “silver balls” Rowlux film (center of record).

Han-O-Disc manufactured for Light Fantastic with metal flake outside and Dufex process print within.

Lenticular images were popularized from the late 1940s to the mid-1980s by the Vari-Vue company.[4] Early products included animated political campaign badges with the slogan “I Like Ike!” and animated cards that were stuck on boxes of Cheerios.[4] By the late sixties the company marketed about two thousand stock products including twelve inch square moving pattern and color sheets, large images (many religious), and a huge range of novelties including badges. The badge products included the Rolling Stones’ tongue logo and an early Beatles badge with pictures of the ‘fab four’ on a red background.

Some notable lenticular prints from this time include the limited-edition cover of the Rolling Stones’ Their Satanic Majesties Request, and Saturnalia‘s Magical Love, a picture disk with a lenticular center. Several magazines including Look and Venture published issues in the 1960s that contained lenticular images. Many of the magazine images were produced by Crowle Communications (also known as Visual Panographics). Images produced by the company ranged from just a few millimeters to 28 by 19.5 inches.

The panoramic cameras used for most of the early lenticular prints were French-made and weighed about 300 pounds. In the 1930s they were known as “auto-stereo cameras”. These wood and brass cameras had a motorized lens that moved in a semicircle around the lens’ nodal point. Sheet transparency film with the lenticular lens overlay was loaded into special dark slides (about 10×15 inches) and these were then inserted into the camera. The exposure time was several seconds long, giving time for the motor drive to power the lens around in an arc.[citation needed“>citation needed]

A related product produced by a small company in New Jersey was Rowlux. Unlike the Vari-Vue product, Rowlux used a microprismatic lens structure made by a process they patented in 1972,[5] and no paper print. Instead, the plastic (Polycarbonate, flexible PVC and later PETG) was dyed with translucent colors and the film was usually thin and flexible (from 0.002″ in thickness).

Lenticular arrays are also used for 3D television (autostereoscopic, enabling the 3D perception without glasses), and number of prototypes have been shown in 2009 2010 by major companies such as Philips and LG. They are using cylindrical lenses slanted to the vertical, or spherical lenses arranged as a honeycomb which provides a better resolution.

While not a true lenticular, the Dufex Process (Manufactured by F.J. Warren Ltd.)[6] does use a form of lens structure to animate the image. The process consists of a metallic foil imprinted by litho printing with the image. The foil is than laminated to a thin sheet of card stock that has had a thick layer of wax coated upon it. The heated lamination press has the Dufex embossing plate on its upper platen. The plate has been engraved with angled ‘lenses’ at different angles so designed as to match the artwork and reflect light at different intensities depending on angle of view.

## Manufacturing process

Designing and manufacturing a lenticular product requires a sound knowledge of optics, binocular vision, computing, the graphic chain, and also stringency in work and precision throughout the manufacturing process.

### Printing

Creation of lenticular images in volume requires printing presses that are adapted to print on sensitive thermoplastic materials. Lithographic offset printing is typically used, to ensure the images are good quality. Printing presses for lenticulars must be capable of adjusting image placement in 10 µm steps, to allow good alignment of the image to the lens array.

Typically, ultravioletcured inks are used. These dry very quickly by direct conversion of the liquid ink to a solid form, rather than by evaporation of liquid solvents from a mixture. Powerful (400W per sq. in) ultraviolet (UV) lamps are used to rapidly cure the ink. This allows lenticular images to be printed at high speed.

In some cases, electron beam lithography is used instead. The curing of the ink is then initiated directly by an electron beam scanned across the surface.

### Defects

#### Design defects

Double images on the relief and in depth

Double images are usually caused by an exaggeration of the 3-D effect from angles of view or an insufficient number of frames. Poor design can lead to doubling, small jumps, or a fuzzy image, especially on objects in relief or in depth. For some visuals, where the foreground and background are fuzzy or shaded, this exaggeration can prove to be an advantage. In most cases, the detail and precision required do not allow this.

Image ghosting

Ghosting occurs due to poor treatment of the source images, and also due to transitions where demand for an effect goes beyond the limits and technical possibilities of the system. This causes some of the images to remain visible when they should disappear. These effects can depend on the lighting of the lenticular print.

#### Prepress defects

Synchronisation of the print (master) with the pitch

Also known as “Banding”. Poor calibration of the material can cause the passage from one image to another to not be simultaneous over the entire print. The image transition progresses from one side of the print to the other, giving the impression of a veil or curtain crossing the visual. This phenomenon is felt less for the 3-D effects, but is manifested by a jump of the transverse image. In some cases, the transition starts in several places and progresses from each starting point towards the next, giving the impression of several curtains crossing the visual, as described above.

Discordant harmonics

This phenomenon is unfortunately very common, and is explained either by incorrect calibration of the support or by incorrect parametrisation of the prepress operations. It is manifested in particular by streaks that appear parallel to the lenticules during transitions from one visual to the other.

#### Printing defects

Colour synchronisation

One of the main difficulties in lenticular printing is colour synchronisation. The causes are varied, they may come from a malleable material, incorrect printing conditions and adjustments, or again a dimensional differential of the engraving of the offset plates in each colour.

This poor marking is shown by doubling of the visual; a lack of clarity; a streak of colour or wavy colours (especially for four-colour shades) during a change of phase by inclination of the visual.

Synchronisation of parallelism of the printing to the lenticules

The origin of this problem is a fault in the printing and forcibly generates a phase defect. The passage from one visual to another must be simultaneous over the entire format. But when this problem occurs, there is a lag in the effects on the diagonals. At the end of one diagonal of the visual, we have one effect, and at the other end we have another.

Phasing

In most cases, the problem comes from imprecise cutting of the material, as explained below. Nevertheless, poor printing and rectification conditions may also be behind it.

In theory, for a given angle of observation, one and the same visual must appear, for the entire batch. As a general rule, the angle of vision is around 45°, and this angle must be in agreement with the sequence provided by the master. If the images have a tendency to double perpendicularly (for 3-D) or if the images provided for observation to the left appear to the right (top/bottom), there is a phasing problem.

#### Cutting defects

Defects in the way the lenticular lens is cut lead to phase errors between the lens and the image.

Two examples, taken from the same production batch:

 First image Second image

The first image shows a cut which removed about 150 µm of the first lens, and which shows irregular cutting of the lenticular lenses. The second image shows a cut which removed about 30 µm of the first lens. Defects in cutting such as these lead to a serious phase problem. In the printing press the image being printed is aligned relative to the edges of the sheet of material. If the sheet is not always cut in the same place relative to the first lenticule, a phase error is introduced between the lenses and the image slices.

• Lenticular lens, the technology used in lenticular printing and for 3D displays
• Integral imaging, a broader concept that includes lenticular printing
• Autostereoscopy, any method of displaying stereoscopic images without the use of glasses
• Parallax barrier, another technology for displaying stereoscopic images without the use of glasses

## Notes and references

1. ^ O’Brien, Katherine (2006). “As big as all outdoors”. American Printer (August 1, 2006). Retrieved 2008-06-04.
2. ^ How to Prevent Ghosting in Lenticular Printing
3. ^ Oster, Gerald (1965). “Optical Art” (subscription required). Applied Optics 4 (11): 1359–69. doi:10.1364/AO.4.001359.
4. ^ a b Lake, Matt (1999-05-20). “An art form that’s precise but friendly enough to wink”. New York Times. Retrieved 2008-06-04.
5. ^ US patent 3689346, Rowland, William P., “Method for producing retroreflective material”, issued 1972-09-05, assigned to Rowland Development Corp.
6. ^ “F.J. Warren Ltd”. Kompass UK. Retrieved 2008-06-04.
• Bordas Encyclopedia: Organic Chemistry (French).
• Sirost, Jean-Claude (2007). L’Offset : Principes, Technologies, Pratiques (in French) (2nd ed.). Dunod. ISBN 2-10-051366-4.
• Okoshi, Takanori Three-Dimensional Imaging Techniques Atara Press (2011), ISBN 978-0-9822251-4-1

## 3D Printing

An ORDbot Quantum 3D printer

Timelapse video of a hyperboloid object print (made of PLA) using a RepRap “Prusa Mendel” 3D printer for molten polymer deposition

Additive manufacturing or 3D printing[1] is a process of making a three-dimensional solid object of virtually any shape from a digital model. 3D printing is achieved using an additive process, where successive layers of material are laid down in different shapes.[2] 3D printing is considered distinct from traditional machining techniques, which mostly rely on the removal of material by methods such as cutting or drilling (subtractive processes).

A materials printer usually performs 3D printing processes using digital technology. Since the start of the twenty-first century there has been a large growth in the sales of these machines, and their price has dropped substantially.[3]

The technology is used in jewelry, footwear, industrial design, architecture, engineering and construction (AEC), automotive, aerospace, dental and medical industries, education, geographic information systems, civil engineering, and many other fields.

## Terminology

The term additive manufacturing refers to technologies that create objects through a sequential layering process. Objects that are manufactured additively can be used anywhere throughout the product life cycle, from pre-production (i.e. rapid prototyping) to full-scale production (i.e. rapid manufacturing), in addition to tooling applications and post-production customization.

In manufacturing, and machining in particular, subtractive methods are typically coined as traditional methods. The very term subtractive manufacturing is a retronym developed in recent years to distinguish it from newer additive manufacturing techniques. Although fabrication has included methods that are essentially “additive” for centuries (such as joining plates, sheets, forgings, and rolled work via riveting, screwing, forge welding, or newer kinds of welding), it did not include the information technology component of model-based definition. Machining (generating exact shapes with high precision) has typically been subtractive, from filing and turning to milling and grinding.

## General principles

3D model slicing

### Modeling

Additive manufacturing takes virtual blueprints from computer aided design (CAD) or animation modeling software and “slices” them into digital cross-sections for the machine to successively use as a guideline for printing. Depending on the machine used, material or a binding material is deposited on the build bed or platform until material/binder layering is complete and the final 3D model has been “printed.” It is a WYSIWYG process where the virtual model and the physical model are almost identical.

A standard data interface between CAD software and the machines is the STL file format. An STL file approximates the shape of a part or assembly using triangular facets. Smaller facets produce a higher quality surface. PLY is a scanner generated input file format, and VRML (or WRL) files are often used as input for 3D printing technologies that are able to print in full color.

### Printing

To perform a print, the machine reads the design from an .stl file and lays down successive layers of liquid, powder, paper or sheet material to build the model from a series of cross sections. These layers, which correspond to the virtual cross sections from the CAD model, are joined together or automatically fused to create the final shape. The primary advantage of this technique is its ability to create almost any shape or geometric feature.

Printer resolution describes layer thickness and X-Y resolution in dpi (dots per inch),[citation needed“>citation needed] or micrometres. Typical layer thickness is around 100 micrometres (0.1 mm), although some machines such as the Objet Connex series and 3D Systems’ ProJet series can print layers as thin as 16 micrometres.[4] X-Y resolution is comparable to that of laser printers. The particles (3D dots) are around 50 to 100 micrometres (0.05–0.1 mm) in diameter.

Construction of a model with contemporary methods can take anywhere from several hours to several days, depending on the method used and the size and complexity of the model. Additive systems can typically reduce this time to a few hours, although it varies widely depending on the type of machine used and the size and number of models being produced simultaneously.

Traditional techniques like injection moulding can be less expensive for manufacturing polymer products in high quantities, but additive manufacturing can be faster, more flexible and less expensive when producing relatively small quantities of parts. 3D printers give designers and concept development teams the ability to produce parts and concept models using a desktop size printer.

### Finishing

Though the printer-produced resolution is sufficient for many applications, printing a slightly over sized version of the desired object in standard resolution, and then removing material with a higher-resolution subtractive process can achieve greater precision.

Some additive manufacturing techniques are capable of using multiple materials in the course of constructing parts. Some are able to print in multiple colors and color combinations simultaneously. Some also utilize supports when building. Supports are removable or dissolvable upon completion of the print, and are used to support overhanging features during construction.

Rapid prototyping worldwide[5]

The Audi RSQ was made with rapid prototyping industrial KUKA robots

Several different 3D printing processes have been invented since the late 1970s. The printers were originally large, expensive, and highly limited in what they could produce.[6]

A number of additive processes are now available. They differ in the way layers are deposited to create parts and in the materials that can be used. Some methods melt or soften material to produce the layers, e.g. selective laser sintering (SLS) and fused deposition modeling (FDM), while others cure liquid materials using different sophisticated technologies, e.g. stereolithography (SLA). With laminated object manufacturing (LOM), thin layers are cut to shape and joined together (e.g. paper, polymer, metal). Each method has its own advantages and drawbacks, and some companies consequently offer a choice between powder and polymer for the material from which the object is built.[7] Some companies use standard, off-the-shelf business paper as the build material to produce a durable prototype. The main considerations in choosing a machine are generally speed, cost of the 3D printer, cost of the printed prototype, and cost and choice of materials and color capabilities.[8]

Printers that work directly with metals are expensive. In some cases, however, less expensive printers can be used to make a mould, which is then used to make metal parts.[9]

Type Technologies Materials
Extrusion Fused deposition modeling (FDM) Thermoplastics (e.g. PLA, ABS), eutectic metals, edible materials
Wire Electron Beam Freeform Fabrication (EBF3) Almost any metal alloy
Granular Direct metal laser sintering (DMLS) Almost any metal alloy
Electron beam melting (EBM) Titanium alloys
Selective heat sintering (SHS)[citation needed“>citation needed] Thermoplastic powder
Selective laser sintering (SLS) Thermoplastics, metal powders, ceramic powders
Powder bed and inkjet head 3d printing, Plaster-based 3D printing (PP) Plaster
Laminated Laminated object manufacturing (LOM) Paper, metal foil, plastic film
Light polymerised Stereolithography (SLA) photopolymer
Digital Light Processing (DLP) photopolymer

### Extrusion deposition

Fused deposition modeling: 1 – nozzle ejecting molten plastic, 2 – deposited material (modeled part), 3 – controlled movable table

Fused deposition modeling (FDM) was developed by S. Scott Crump in the late 1980s and was commercialized in 1990 by Stratasys.[10]

Fused deposition modeling uses a plastic filament or metal wire that is wound on a coil and unreeled to supply material to an extrusion nozzle, which turns the flow on and off. The nozzle heats to melt the material and can be moved in both horizontal and vertical directions by a numerically controlled mechanism that is directly controlled by a computer-aided manufacturing (CAM) software package. The model or part is produced by extruding small beads of thermoplastic material to form layers as the material hardens immediately after extrusion from the nozzle. Stepper motors or servo motors are typically employed to move the extrusion head.

Various polymers are used, including acrylonitrile butadiene styrene (ABS), polycarbonate (PC), polylactic acid (PLA), PC/ABS, and polyphenylsulfone (PPSU).

FDM has some restrictions on the shapes that may be fabricated. For example, FDM usually cannot produce stalactite-like structures, since they would be unsupported during the build. These have to be avoided or a thin support may be designed into the structure which can be broken away during finishing processes.

### Granular materials binding

The CandyFab granular printing system uses heated air and granulated sugar to produce food-grade art objects.

Another 3D printing approach is the selective fusing of materials in a granular bed. The technique fuses parts of the layer, and then moves the working area downwards, adding another layer of granules and repeating the process until the piece has built up. This process uses the unfused media to support overhangs and thin walls in the part being produced, which reduces the need for temporary auxiliary supports for the piece. A laser is typically used to sinter the media into a solid. Examples include selective laser sintering (SLS), with both metals and polymers (e.g. PA, PA-GF, Rigid GF, PEEK, PS, Alumide, Carbonmide, elastomers), and direct metal laser sintering (DMLS).

Selective Laser Sintering (SLS) was developed and patented by Dr. Carl Deckard and Dr. Joseph Beaman at the University of Texas at Austin in the mid-1980s, under sponsorship of DARPA.[11] A similar process was patented without being commercialized by R. F. Housholder in 1979.[12]

Electron beam melting (EBM) is a similar type of additive manufacturing technology for metal parts (e.g. titanium alloys). EBM manufactures parts by melting metal powder layer by layer with an electron beam in a high vacuum. Unlike metal sintering techniques that operate below melting point, EBM parts are fully dense, void-free, and very strong.[13][14]

Another method consists of an inkjet 3D printing system. The printer creates the model one layer at a time by spreading a layer of powder (plaster, or resins) and printing a binder in the cross-section of the part using an inkjet-like process. This is repeated until every layer has been printed. This technology allows the printing of full color prototypes, overhangs, and elastomer parts. The strength of bonded powder prints can be enhanced with wax or thermoset polymer impregnation.

### Lamination

In some printers, paper can be used as the build material, resulting in a lower cost to print. During the 1990s some companies marketed printers that cut cross sections out of special adhesive coated paper using a carbon dioxide laser, and then laminated them together.

In 2005, Mcor Technologies Ltd developed a different process using ordinary sheets of office paper, a Tungsten carbide blade to cut the shape, and selective deposition of adhesive and pressure to bond the prototype.[15]

There are also a number of companies selling printers that print laminated objects using thin plastic and metal sheets.

### Photopolymerization

Stereolithography apparatus

Stereolithography was patented in 1987 by Chuck Hull. Photopolymerization is primarily used in stereolithography (STL) to produce a solid part from a liquid.

In digital light processing (DLP), a vat of liquid polymer is exposed to light from a DLP projector under safelight conditions. The exposed liquid polymer hardens. The build plate then moves down in small increments and the liquid polymer is again exposed to light. The process repeats until the model has been built. The liquid polymer is then drained from the vat, leaving the solid model. The EnvisionTec Ultra[16] is an example of a DLP rapid prototyping system.

Inkjet printer systems like the Objet PolyJet system spray photopolymer materials onto a build tray in ultra-thin layers (between 16 and 30 microns) until the part is completed. Each photopolymer layer is cured with UV light after it is jetted, producing fully cured models that can be handled and used immediately, without post-curing. The gel-like support material, which is designed to support complicated geometries, is removed by hand and water jetting. It is also suitable for elastomers.

Ultra-small features can be made with the 3D microfabrication technique used in multiphoton photopolymerization. This approach traces the desired 3D object in a block of gel using a focused laser. Due to the nonlinear nature of photoexcitation, the gel is cured to a solid only in the places where the laser was focused and the remaining gel is then washed away. Feature sizes of under 100 nm are easily produced, as well as complex structures with moving and interlocked parts.[17]

Yet another approach uses a synthetic resin that is solidified using LEDs.[18]

## Printers

### Printers for domestic use

RepRap version 2.0 (Mendel)

MakerBot Cupcake CNC

Airwolf 3D AW3D v.4 (Prusa)

There are several projects and companies making efforts to develop affordable 3D printers for home desktop use. Much of this work has been driven by and targeted at DIY/enthusiast/early adopter communities, with additional ties to the academic and hacker communities.[19]

RepRap is one of the longest running projects in the desktop category. The RepRap project aims to produce a free and open source software (FOSS) 3D printer, whose full specifications are released under the GNU General Public License, and which is capable of replicating itself by printing many of its own (plastic) parts to create more machines.[20] Research is under way to enable the device to print circuit boards, as well as metal parts.

Because of the FOSS aims of RepRap, many related projects have used their design for inspiration, creating an ecosystem of related or derivative 3D printers, most of which are also open source designs. The availability of these open source designs means that variants of 3D printers are easy to invent. The quality and complexity of printer designs, however, as well as the quality of kit or finished products, varies greatly from project to project. This rapid development of open source 3D printers is gaining interest in many spheres as it enables hyper-customization and the use of public domain designs to fabricate open source appropriate technology through conduits such as Thingiverse and Cubify. This technology can also assist initiatives in sustainable development since technologies are easily and economically made from resources available to local communities.[21]

The cost of 3-D printers has decreased dramatically between about 2010 and 2012, with machines that used to cost \$20,000 costing less than \$1,000.[22] For instance, as of 2012, several companies and individuals are selling parts to build various RepRap designs, with prices starting at about €400 / US\$500.[23] The price of printer kits vary from US\$400 for the open source SeeMeCNC H-1 and US\$500 for the Printrbot (both derived from the previous RepRap models), to over US\$2000 for the Fab@Home 2.0 two-syringe system.[23] The Shark 3D printer comes fully assembled for less than 2k . The open source Fab@Home project[24] has developed printers for general use with anything that can be squirted through a nozzle, from chocolate to silicone sealant and chemical reactants. Printers following the project’s designs have been available from suppliers in kits or in pre-assembled form since 2012 at prices in the US\$2000 range.[23]

### Printers for commercial and domestic use

The development and hyper-customization of the RepRap-based 3D printers has produced a new category of printers suitable for both domestic and commercial use. The least expensive assembled machine available is the Solidoodle 2, while the RepRapPro’s Huxley DIY kit is reputedly one of the more reliable of the lower-priced machines, at around US\$680. There are other RepRap-based high-end kits and fully assembled machines that have been enhanced to print at high speed and high definition. Depending on the application, the print resolution and speed of manufacturing lies somewhere between a personal printer and an industrial printer. A list of printers with pricing and other information is maintained.[23] Most recently delta robots have been utilized for 3D printing to increase fabrication speed further.[25]

## Applications

 “ Three-dimensional printing makes it as cheap to create single items as it is to produce thousands and thus undermines economies of scale. It may have as profound an impact on the world as the coming of the factory did….Just as nobody could have predicted the impact of the steam engine in 1750—or the printing press in 1450, or the transistor in 1950—it is impossible to foresee the long-term impact of 3D printing. But the technology is coming, and it is likely to disrupt every field it touches. ” — The Economist, in a February 10, 2011 leader[26]

A model (left) was digitally acquired by using a 3D scanner, the scanned data processed using MeshLab, and the resulting 3D model used by a rapid prototyping machine to create a resin replica (right)

An example of 3D printed limited edition jewellery. This necklace is made of glassfiber-filled dyed nylon. It has rotating linkages that were produced in the same manufacturing step as the other parts.

Additive manufacturing’s earliest applications have been on the toolroom end of the manufacturing spectrum. For example, rapid prototyping was one of the earliest additive variants, and its mission was to reduce the lead time and cost of developing prototypes of new parts and devices, which was earlier only done with subtractive toolroom methods (typically slowly and expensively).[27] With technological advances in additive manufacturing, however, and the dissemination of those advances into the business world, additive methods are moving ever further into the production end of manufacturing in creative and sometimes unexpected ways.[27] Parts that were formerly the sole province of subtractive methods can now in some cases be made more profitably via additive ones.

Standard applications include design visualization, prototyping/CAD, metal casting, architecture, education, geospatial, healthcare, and entertainment/retail.

### Industrial uses

#### Rapid prototyping

Full color miniature face models produced on a Spectrum Z510 3D Printer

Industrial 3D printers have existed since the early 1980s and have been used extensively for rapid prototyping and research purposes. These are generally larger machines that use proprietary powdered metals, casting media (e.g. sand), plastics, paper or cartridges, and are used for rapid prototyping by universities and commercial companies. Industrial 3D printers are made by companies including Mcor Technologies Ltd, 3D Systems, Objet Geometries, and Stratasys.

#### Rapid manufacturing

Advances in RP technology have introduced materials that are appropriate for final manufacture, which has in turn introduced the possibility of directly manufacturing finished components. One advantage of 3D printing for rapid manufacturing lies in the relatively inexpensive production of small numbers of parts.

Rapid manufacturing is a new method of manufacturing and many of its processes remain unproven. 3D printing is now entering the field of rapid manufacturing and was identified as a “next level” technology by many experts in a 2009 report.[28] One of the most promising processes looks to be the adaptation of laser sintering (LS), one of the better-established rapid prototyping methods. As of 2006, however, these techniques were still very much in their infancy, with many obstacles to be overcome before RM could be considered a realistic manufacturing method.[29]

#### Mass customization

Companies have created services where consumers can customize objects using simplified web based customization software, and order the resulting items as 3D printed unique objects.[30][31] This now allows consumers to create custom cases for their mobile phones.[32] Nokia has released the 3D designs for its case so that owners can customize their own case and have it 3D printed.[33]

#### Mass production

The current slow print speed of 3D printers limits their use for mass production. To reduce this overhead, several fused filament machines now offer multiple extruder heads. These can be used to print in multiple colors, with different polymers, or to make multiple prints simultaneously. This increases their overall print speed during multiple instance production, while requiring less capital cost than duplicate machines since they can share a single controller. Distinct from the use of multiple machines, multi-material machines are restricted to making identical copies of the same part, but can offer multi-color and multi-material features when needed. The print speed increases proportionately to the number of heads. Furthermore, the energy cost is reduced due to the fact that they share the same heated print volume. Together, these two features reduce overhead costs, yet the main cost continues to be the raw filament, which is unchanged.

Many printers now offer twin print heads. However, these are used to manufacture single (sets of) parts in multiple colors/materials.

Few studies have yet been done in this field to see if conventional subtractive methods are comparable to additive methods.

### Domestic and hobbyist uses

As of 2012, domestic 3D printing has mainly captivated hobbyists and enthusiasts and has not quite gained recognition for practical household applications. A working clock has been made[34] and gears have been printed for home woodworking machines[35] among other purposes.[36] 3D printing is also used for ornamental objects. One printer (the Fab@Home) includes chocolate in the materials that can be printed. Web sites associated with home 3D printing tend to include backscratchers, coathooks, etc. among their offered prints. The Fab@Home gallery includes many objects that lack practical application, but includes examples of practical possibilities, including a flashlight/torch using conductive ink for the electrical circuit, a battery-powered motor, an iPod case, a silicone watch band, and somewhat miscellaneously, a translucent cylinder completely enclosing a brown box, a construct difficult to fabricate any other way.[37]

The open source Fab@Home project[24] has developed printers for general use. They have been used in research environments to produce chemical compounds with 3D printing technology, including new ones, initially without immediate application as proof of principle.[38] The printer can print with anything that can be dispensed from a syringe as liquid or paste. The developers of the chemical application envisage that this technology could be used for both in industrial and domestic use. Including, for example, enabling users in remote locations to be able to produce their own medicine or household chemicals.[39][40]

### 3D printing services

Some companies offer on-line 3D printing services open to both consumers and industries.[41] Such services require people to upload their 3D designs to the company website. Designs are then 3D printed using industrial 3D printers and either shipped to the customer or in some cases, the consumer can pick the object up at the store.[42] Some examples of 3D printing services companies are Staples Inc.,[43] Shapeways,[44] Kraftwurx,[45] i.materialise[46], Solid Concepts[47], and Freedom of Creation[48]

### Research into new applications

Future applications for 3D printing might include creating open-source scientific equipment[49] or other science-based applications like reconstructing fossils in paleontology, replicating ancient and priceless artifacts in archaeology, reconstructing bones and body parts in forensic pathology, and reconstructing heavily damaged evidence acquired from crime scene investigations. The technology is even being explored for building construction.

In 2005, academic journals had begun to report on the possible artistic applications of 3D printing technology.[50] By 2007 the mass media followed with an article in the Wall Street Journal[51] and Time Magazine, listing a 3D printed design among their 100 most influential designs of the year.[52] During the 2011 London Design Festival, an installation, curated by Murray Moss and focused on 3D Printing, was held in the Victoria and Albert Museum (the V&A). The installation was called Industrial Revolution 2.0: How the Material World will Newly Materialise.[53]

As of 2012, 3D printing technology has been studied by biotechnology firms and academia for possible use in tissue engineering applications in which organs and body parts are built using inkjet techniques. In this process, layers of living cells are deposited onto a gel medium or sugar matrix and slowly built up to form three-dimensional structures including vascular systems.[54] Several terms have been used to refer to this field of research: organ printing, bio-printing, body part printing,[55] and computer-aided tissue engineering, among others.[56] 3D printing can produce a personalized hip replacement in one pass, with the ball permanently inside the socket and is available in printing resolutions that don’t require polishing.[citation needed“>citation needed]

A proof-of-principle project at the University of Glasgow, UK, in 2012 showed that it is possible to use 3D printing techniques to create chemical compounds, including new ones. They first concept printed chemical reaction vessels, then use the printer to squirt reactants into them as “chemical inks” which would then react.[38] They have produced new compounds to verify the validity of the process, but have not pursued anything with a particular application.[38] They used the Fab@Home open source printer, at a reported cost of US\$2,000. Cornell Creative Machines Lab has confirmed that it is possible to produce customized food with 3D Hydrocolloid Printing.[57]

The use of 3D scanning technologies allows the replication of real objects without the use of moulding techniques that in many cases can be more expensive, more difficult, or too invasive to be performed, particularly for precious or delicate cultural heritage artifacts[58] where direct contact with the molding substances could harm the original object’s surface. Objects as ubiquitous as smartphones can be used as 3D scanners: Sculpteo unveiled a mobile app at the 2012 Consumer Electronics Show that allows a 3D file to be generated directly via smartphone.[59]

As an example of possible future applications, an open source group emerged in the US in 2012 that was attempting to design a firearm that was downloadable and printable from the Internet.[60] The weapon would still require bullets produced by traditional methods. Calling itself Defense Distributed, the group wants to facilitate “a working plastic gun that could be downloaded and reproduced by anybody with a 3D printer”.[61]

An additional use being developed is building printing, or using 3d printing to build buildings. This could allow faster construction for lower costs, and has been investigated for construction of off-Earth habitats.[62][63]

## Intellectual property

Three different sorts of intellectual property are commonly defined, patent, copyright and trademark. Patents are to do with protecting how something works, and lasts up to about 25 years, depending on the jurisdiction. Copyrights protect artistic works, and generally last the artists life plus 70 years.[64]

Usually, purely functional items, and plans and documents for these items, older than 25 years are usually no longer patented and can be freely copied, scanned and 3D printed.[64]

However, if an item has artistic features, those artistic features are generally considered copyrighted.[64][65] When a feature has both artistic and functional merits, when the question has appeared in US court, the courts have often held the feature is not copyrightable unless it can be separated from the functional aspects of the item.[64]

## Effects of 3D printing

Predictions for future commercial additive manufacturing, starting with today’s infancy period, require manufacturing firms to be flexible, ever-improving users of all available technologies in order to remain competitive. Advocates of additive manufacturing also predict that this arc of technological development will counter globalisation, as end users will do much of their own manufacturing rather than engage in trade to buy products from other people and corporations.[6] The real integration of the newer additive technologies into commercial production, however, is more a matter of complementing traditional subtractive methods rather than displacing them entirely.[66]

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