## model-based definition

Model based definition (MBD), also known as digital product definition (DPD), is the practice of using 3D digital data (such as solid models and associated metadata) within 3D CAD software to provide specifications for individual components and product assemblies. The types of information included are geometric dimensioning and tolerancing (GD&T), component level materials, assembly level bills of materials, engineering configurations, design intent, etc. By contrast, other methodologies have historically required accompanying use of 2D drawings to provide such details.

## Use of the 3D digital data set

Modern 3D CAD applications allow for the insertion of engineering information such as dimensions, GD&T, notes and other product details within the 3D digital data set for components and assemblies. MBD uses such capabilities to establish the 3D digital data set as the source of these specifications and design authority for the product. The 3D digital data set may contain enough information to manufacture and inspect product without the need for engineering drawings. Engineering drawings have traditionally contained such information.

In many instances, use of some information from 3D digital data set (e.g., the solid model) allows for rapid prototyping of product via various processes, such as 3D printing. A manufacturer may be able to feed 3D digital data directly to manufacturing devices such as CNC machines to manufacture final product.

## Standardization

In 2003, ASME published the ASME Y14.41-2003 Digital Product Definition Data Practices. The standard provides for the use of some MBD aspects, such as GD&T within the solid model. Other standards, such as ISO 1101:2004 and of AS9100 also make use of MBD.

## 

Example of pad printing on a keyboard.

Pad printing is a printing process that can transfer a 2-D image onto a 3-D object. This is accomplished using an indirect offset (gravure) printing process that involves an image being transferred from the cliché via a silicone pad onto a substrate. Pad printing is used for printing on otherwise impossible products in many industries including medical, automotive, promotional, apparel, and electronic objects, as well as appliances, sports equipment and toys. It can also be used to deposit functional materials such as conductive inks, adhesives, dyes and lubricants.

Physical changes within the ink film both on the cliché and on the pad allow it to leave the etched image area in favor of adhering to the pad, and to subsequently release from the pad in favor of adhering to the substrate.

The unique properties of the silicone pad enable it to pick the image up from a flat plane and transfer it to a variety of surfaces, such as flat, cylindrical, spherical, compound angles, textures, concave, or convex surfaces.

## History

While crude forms of pad printing have existed for centuries, it was not until the twentieth century that the technology became suitable for widespread use. First gaining a foothold in the watch-making industry following World War II, developments in the late 60s and early 70s, such as silicone pads and more advanced equipment, made the printing method far more practical. The ability to print on formerly unprintable surfaces caught the imaginations of engineers and designers, and as a result pad printing exploded into the mass production marketplace.

Today, pad printing is a well established technology covering a wide spectrum of industries and applications.

## Process

1. From the home position, the sealed ink cup (an inverted cup containing ink) sits over the etched artwork area of the printing plate, covering the image and filling it with ink.
2. The sealed ink cup moves away from the etched artwork area, taking all excess ink and exposing the etched image, which is filled with ink. The top layer of ink becomes tacky as soon as it is exposed to the air; that is how the ink adheres to the transfer pad and later to the substrate.
3. The transfer pad presses down onto the printing plate momentarily. As the pad is compressed, it pushes air outward and causes the ink to lift (transfer) from the etched artwork area onto the pad.
4. As the transfer pad lifts away, the tacky ink film inside the etched artwork area is picked up on the pad. A small amount of ink remains in the printing plate.
5. As the transfer pad moves forward, the ink cup also moves to cover the etched artwork area on the printing plate. The ink cup again fills the etched artwork image on the plate with ink in preparation for the next cycle.
6. The transfer pad compresses down onto the substrate, transferring the ink layer picked up from the printing plate to the substrate surface. Then, it lifts off the substrate and returns to the home position, thus completing one print cycle.

### Plate and ink interface technologies

#### Open inkwell system

Open ink well systems, the older method of pad printing, used an ink trough for the ink supply, which was located behind the printing plate. A flood bar pushed a pool of ink over the plate, and a doctor blade removes the ink from the plate surface, leaving ink on the etched artwork area ready for the pad to pick up.

#### Sealed ink cup system

Sealed ink cup systems employ a sealed container which acts as the ink supply, flood bar and doctor blade all at the same time. A ceramic ring with a highly polished working edge provides the seal against the printing plate.

Pads are three dimensional objects typically moulded of silicone rubber. They function as a transfer vehicle, picking up ink from the printing plate, and transferring it to the part (substrate). They vary in shape and diameter depending on the application.

There are two main shape groups: “round pads” and long narrow pads called “bar pads”. Pads are also made in other shapes, called “loaf pads”. Within each group there are three size categories: small, medium, and large size pads. It is also possible to engineer custom-shaped pads to meet special application requirements.

### Image plate

Image plates are used to contain the desired artwork “image” etched in its surface. Their function is to hold ink in this etched cavity, allowing the pad to pick up this ink as a film in the shape of the artwork, which is then transferred to the substrate.

There are two main types of printing plate materials: photopolymer and steel. Photopolymer plates are the most popular, as they are easy to use. These are typically used in short to medium production runs. Steel plates come in two forms: thin steel for medium to long runs, and thick steel for very long runs. Both steel plate types are generally processed by the plate supplier as it involves the use of specialized equipment.

### Printing ink

Ink is used to mark or decorate parts. It comes in different chemical families to match the type of material to be printed (please consult the substrate compatibility chart for selection).

Pad printing inks are “solvent-based” and require mixing with additives before use. They typically seem dry to the touch within seconds although complete drying (cure) might take a substantially longer period of time. There are many more options. Inks that cure via the use of Ultra Violet light are convenient for certain applications. UV inks will not fully cure until UV light hits the ink. UV curable ink can be wiped off many substrates when mistakes are made. They can be cured with UV light in as fast as 1 second of light exposure. This depends on the ink, substrate and the light power and spectrum. UV inks can be reused as the pot life can be high as long as the ink stays clean, blocked from UV light and hasn’t broken down from sitting. This same feature makes it easier to clean than some solvent and epoxy like two part component inks. Also there are heat curable inks, which work in much the same way as UV in the sense that there is a “trigger” that cures the ink when pulled. Two part inks usually have a pot life of only a few hours or so. They must be disposed of when they cannot be revived (by means of retarders etc.)

Climatic conditions will significantly affect the performance of any pad printing ink, especially the open ink well style printers. Too dry conditions can lead to faster evaporation of solvents causing the ink to thicken prematurely and too much moisture can lead to ink issues of “clumping” or something alike. Also the climate can affect other aspects of the printing process such as ink pick up and release from the plate to the pad to the substrate, as well as polymer plate to blade chattering or binding due to humidity.

### Substrate

Substrate is the technical term used to address any parts or materials to be printed. Fixtures vary in materials and complexity depending on the application. Substrates need to be clean and free from surface contamination to allow proper ink adhesion.

## Making of printing plates

There are two main techniques used to create a printing plate. The traditional technique requires a UV exposure unit and involves photo exposure with film positives and chemical etching of a photopolymer plate. A second technique known as “computer to plate” requires a laser engraver and involves laser etching of a specialized polymer plate. Although the latter technique is convenient for short run printing it does have several disadvantages over the former.

Laser plate making is a process that requires the use of a very soft, low quality polymer coated plate. Thus, the standard cycle life that can be expected out of a laser etched plate is quite low (10,000 impressions on the high end). By comparison, a hardened steel plate can easily last for over 1 million impressions.

## Printing application examples

• Medical devices (surgical instruments, etc.)
• Implantable & in body medical items (catheter tubes, contact lenses, etc.)
• Golf ball logos/graphics
• Hockey Pucks[1]
• Decorative designs/graphics appearing on Hot Wheels or Matchbox toy cars
• Automotive parts (turn signal indicators, panel controls, etc.)
• Letters on computer keyboards and calculator keys
• TV and computer monitors
• Identification labels and serial numbers for many applications

## References

1. ^ “Custom Logo Hockey Pucks”. NYCO Sports. Retrieved 23 January 2013.

## 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
ClassPlatonic solidsKepler-Poinsot polyhedra
SymmetryTdOhIh
Coxeter groupA3BC3H3
Order2448120
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

## 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]

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