A lenticular lens is an array of magnifying lenses, designed so that when viewed from slightly different angles, different images are magnified. The most common example is the lenses used in lenticular printing

Lenticular printing

Lenticular printing is a technology in which a lenticular lens is used to produce images with an illusion of depth, or the ability to change or move as the image is viewed from different angles...

, where the technology is used to give an illusion of depth, or to make images that appear to change or move as the image is viewed from different angles.

Lenticular printing

Lenticular printing is a multi-step process consisting of creating a lenticular image from at least two existing images, and combining it with a lenticular lens. This process can be used to create various frames of animation

Animation

Animation is the rapid display of a sequence of images of 2-D or 3-D artwork or model positions in order to create an illusion of movement. The effect is an optical illusion of motion due to the phenomenon of persistence of vision, and can be created and demonstrated in several ways...

 (for a motion effect), offsetting the various layers at different increments (for a 3d

Stereoscopy

Stereoscopy refers to a technique for creating or enhancing the illusion of depth in an image by presenting two offset images separately to the left and right eye of the viewer. Both of these 2-D offset images are then combined in the brain to give the perception of 3-D depth...

 effect), or simply to show a set of alternate images which may appear to transform into each other.

Corrective lenses

Lenticular lenses are sometimes used as corrective lens

Corrective lens

A corrective lens is a lens worn in front of the eye, mainly used to treat myopia, hyperopia, astigmatism, and presbyopia. Glasses or "spectacles" are worn on the face a short distance in front of the eye. Contact lenses are worn directly on the surface of the eye...

es for improving vision. A bifocal lens could be considered a simple example.

Lenticular eyeglass lenses have been employed to correct extreme hypermetropia (farsightedness), a condition often created by cataract

Cataract

A cataract is a clouding that develops in the crystalline lens of the eye or in its envelope, varying in degree from slight to complete opacity and obstructing the passage of light...

 surgery when lens implants are not possible. To limit the great thickness and weight that such high-power lenses would otherwise require, all the power

Optical power

Optical power is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device. The dioptre is the most common unit of measurement of optical power...

 of the lens is concentrated in a small area in the center. In appearance, such a lens is often described as resembling a fried egg

Fried egg

A fried egg is a food made from an egg fried whole with minimal accompaniment. They are traditionally eaten for breakfast in western countries, but may be eaten at other times of the day.-China:...

: a hemisphere atop a flat surface. The flat surface or "carrier lens" has little or no power and is there merely to fill up the rest of the eyeglass frame and to hold or "carry" the lenticular portion of the lens. This portion is typically 40 mm in diameter but may be smaller, as little as 20 mm, in sufficiently high powers. These lenses are generally used for plus (hyperopic) corrections at about 12 diopters or higher. A similar sort of eyeglass lens is the myodisc

Myodisc

A myodisc or myopic disk is a corrective lens with a steep concave curvature that is fitted on the posterior surface of a carrier lens, or a high power single-vision lens specially ordered with slab-off the edge, creating a central prescription disc. These are used for correction of extremely high...

, sometimes termed a minus lenticular lens, used for very high negative (myopic

Myopia

Myopia , "shortsightedness" ) is a refractive defect of the eye in which collimated light produces image focus in front of the retina under conditions of accommodation. In simpler terms, myopia is a condition of the eye where the light that comes in does not directly focus on the retina but in...

) corrections. More aesthetic aspheric lens

Aspheric lens

An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens....

 designs are sometimes fitted.

Lenticular screens

Screens with a molded lenticular surface are frequently used with projection television systems. In this case, the purpose of the lenses is to focus more of the light into a horizontal beam and allow less of the light to escape above and below the plane of the viewer. In this way, the apparent brightness of the image is increased.

Ordinary front-projection screens can also be described as lenticular. In this case, rather than transparent lenses, the shapes formed are tiny curved reflectors.

3D television

A number of manufacturers are developing auto-stereoscopic high definition 3D television

3D television

A 3D television is a television set that employs techniques of 3D presentation, such as stereoscopic capture, multi-view capture, or 2D-plus-depth, and a 3D display – a special viewing device to project a television program into a realistic three-dimensional field.- History :In the late-1890's,...

s, using lenticular lens systems to avoid the need for special spectacles. One of these, Chinese manufacturer TCL is selling a 42" LCD model - the TD-42F - in China for around $20,000.

Lenticular color motion picture processes

Lenticular lenses were used in early color motion picture processes of the 1920s such as the Keller-Dorian

Keller-dorian cinematography

Keller-Dorian cinematography was French technique from the 1920s for filming movies in color. It used a lenticular process to separate red, green and blue colors and record them on a single frame of black-and-white film...

 system and Kodacolor. This enabled color pictures with the use of merely monochrome film stock.

Angle of view of a lenticular print

The angle of view of a lenticular print is the range of angles within which the observer can see the entire image. This is determined by the maximum angle at which a ray

Ray (optics)

In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

 can leave the image through the correct lenticule.

Angle within the lens

The diagram at right shows in green the most extreme ray within the lenticular lens that will be refracted

Refraction

Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...

 correctly by the lens. This ray leaves one edge of an image strip (at the lower right) and exits through the opposite edge of the corresponding lenticule.

Definitions

• is the angle between the extreme ray and the normal
  Surface normal
  A surface normal, or simply normal, to a flat surface is a vector that is perpendicular to that surface. A normal to a non-flat surface at a point P on the surface is a vector perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a...
  
   at the point where it exits the lens,
• is the pitch, or width of each lenticular cell,
• is the radius of curvature
  Radius of curvature (optics)
  Radius of curvature has specific meaning and sign convention in optical design. A spherical lens or mirror surface has a center of curvature located in either along or decentered from the system local optical axis. The vertex of the lens surface is located on the local optical axis...
  
   of the lenticule,
• is the thickness of the lenticular lens
• is the thickness of the substrate below the curved surface of the lens, and
• is the lens's index of refraction.

Calculation

,
where, is the distance from the back of the grating to the edge of the lenticule, and.

Angle outside the lens

The angle outside the lens is given by refraction of the ray determined above. The full angle of observation is given by,
where is the angle between the extreme ray and the normal outside the lens. From Snell's Law

Snell's law

In optics and physics, Snell's law is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water and glass...

,,
where is the index of refraction of air.

Example

Consider a lenticular print that has lenses with 336.65 µm

Micrometre

A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

 pitch, 190.5 µm radius of curvature, 457 µm thickness, and an index of refraction of 1.557. The full angle of observation would be 64.6°.

Rear focal plane of a lenticular network

The focal length

Focal length

The focal length of an optical system is a measure of how strongly the system converges or diverges light. For an optical system in air, it is the distance over which initially collimated rays are brought to a focus...

 of the lens is calculated from the lensmaker's equation, which in this case simplifies to:,
where is the focal length of the lens.

The back focal plane is located at a distance from the back of the lens:
A negative BFD indicates that the focal plane lies inside the lens.

In most cases, lenticular lenses are designed to have the rear focal plane coincide with the back plane of the lens. The condition for this coincidence is , or
This equation imposes a relation between the lens thickness and its radius of curvature .

Example

The lenticular lens in the example above has focal length 342 µm and back focal distance 48 µm, indicating that the focal plane of the lens falls 48 micrometers behind the image printed on the back of the lens.

External links

• Lecture slides covering lenticular lenses (PowerPoint) by John Canny
  John Canny
  John F. Canny is an Australian computer scientist, and Paul and Stacy Jacobs Distinguished Professor of Engineering in the Computer Science Department of the University of California, Berkeley...
  
  
• Choosing the right lenticular sheet for inkjet printer

• http://www.microlens.com/pdfs/history_of_lenticular.pdf