Alenticular lens is an array of lenses, designed so that when viewed from slightly different angles, different parts of the image underneath are shown.^{[1][2][failed verification –see discussion]} The most common example is the lenses used inlenticular printing, 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 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 ofanimation (for a motion effect), offsetting the various layers at different increments (for a3D effect), or simply to show a set of alternate images which may appear to transform into each other.

Lenticular lenses are sometimes used ascorrective lenses for improving vision. Abifocal lens could be considered a simple example.

Lenticulareyeglass lenses have been employed to correct extremehyperopia (farsightedness), a condition often created bycataract surgery whenlens implants are not possible. To limit the great thickness and weight that such high-power lenses would otherwise require, all thepower of the lens is concentrated in a small area in the center. In appearance, such a lens is often described as resembling afried egg: 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 (1.6 in) in diameter but may be smaller, as little as 20 mm (0.79 in), in sufficiently high powers. These lenses are generally used for plus (hyperopic) corrections at about 12diopters or higher. A similar sort of eyeglass lens is themyodisc, sometimes termed a minus lenticular lens, used for very high negative (myopic) corrections. More aestheticaspheric lens designs are sometimes fitted.^[3] A film made of cylindrical lenses molded in a plastic substrate as shown in above picture, can be applied to the inside of standard glasses to correct fordiplopia. The film is typically applied to the eye with the good muscle control of direction. Diplopia (also known as double vision) is typically caused by a sixth cranial nerve palsy that prevents full control of the muscles that control the direction the eye is pointed in. These films are defined in the number of degrees of correction that is needed where the higher the degree, the higher the directive correction that is needed.

Screens with a molded lenticular surface are frequently used withprojection 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 theplane 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. Lenticular screens are most often used for ambient light rejecting projector screens for ultra-short throw projectors.^[4] The lenticular structure of the surface reflects the light from the projector to the viewer without reflecting the light from sources above the screen.

As of 2010^[update], a number of manufacturers were developing auto-stereoscopic high definition3D televisions, using lenticular lens systems to avoid the need for specialspectacles. One of these, Chinese manufacturer TCL, was selling a 42-inch (110 cm) LCD model—the TD-42F—in China for around US$20,000.^[5]

In 2021 only specialist manufacturers are making these kinds of display.^[6]

Lenticular lenses were used in early color motion picture processes of the 1920s such as theKeller-Dorian system andKodacolor. This enabled color pictures with the use of merely monochrome film stock.^[7]

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 aray can leave the image through the correct lenticule.

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

• ${\displaystyle R}$ is the angle between the extreme ray and thenormal at the point where it exits the lens,
• ${\displaystyle p}$ is the pitch, or width of each lenticular cell,
• ${\displaystyle r}$ is theradius of curvature of the lenticule,
• ${\displaystyle e}$ is the thickness of the lenticular lens
• ${\displaystyle h}$ is the thickness of the substrate below the curved surface of the lens, and
• ${\displaystyle n}$ is the lens'sindex of refraction.

${\displaystyle R=A-\arctan \left(\frac{p}{h}\right)}$,

where

${\displaystyle A=\arcsin \left(\frac{p}{2r}\right)}$,

${\displaystyle h=e-f}$ is the distance from the back of the grating to the edge of the lenticule, and

${\displaystyle f=r-\sqrt{r^2-{\left(\frac{p}{2}\right)}^2}}$.

The angle outside the lens is given by refraction of the ray determined above. The full angle of observation${\displaystyle O}$ is given by

${\displaystyle O=2(A-I)}$,

where${\displaystyle I}$ is the angle between the extreme ray and the normaloutside the lens. FromSnell's Law,

${\displaystyle I=\arcsin \left(\frac{n\sin (R)}{n_a}\right)}$,

where${\displaystyle n_a\approx 1.0003}$ is the index of refraction ofair.

Consider a lenticular print that has lenses with 336.65μm pitch, 190.5 μm radius of curvature, 457 μm thickness, and an index of refraction of 1.557. The full angle of observation${\displaystyle O}$ would be 64.6°.

Thefocal length of the lens is calculated from thelensmaker's equation, which in this case simplifies to:

${\displaystyle F=\frac{r}{n-1}}$,

where${\displaystyle F}$ is the focal length of the lens.

The back focal plane is located at a distance${\displaystyle BFD}$ from the back of the lens:

${\displaystyle BFD=F-\frac{e}{n}.}$

A negative BFD indicates that the focal plane liesinside 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${\displaystyle BFD=0}$, or

${\displaystyle e=\frac{nr}{n-1}.}$

This equation imposes a relation between the lens thickness${\displaystyle e}$ and its radius of curvature${\displaystyle r}$.

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 micrometersbehind the image printed on the back of the lens.

• Fresnel lens, a different 'flat' lens technology
• Integral imaging
• Microlens

• Bartholdi, Paul (1997)."Quelques notions d'optique" (in French). Observatoire de Genève. Retrieved19 December 2007.
• Soulier, Bernard (2002)."Principe de fonctionnement de l'optique lenticulaire" (in French). Séquence 3d. Retrieved22 December 2007.
• Okoshi, TakanoriThree-Dimensional Imaging Techniques Atara Press (2011),ISBN 978-0-9822251-4-1.

• Lecture slides covering lenticular lenses (PowerPoint) byJohn Canny
• Choosing the right lenticular sheet for inkjet printer
• http://www.microlens.com/pdfs/history_of_lenticular.pdf

• Lenses

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• CS1 French-language sources (fr)