Lenticular lens
A lenticular 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 in lenticular 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.
Applications
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 (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.
Corrective lenses
Lenticular lenses are sometimes used as
Lenticular
Lenticular screens
Screens with a molded lenticular surface are frequently used with
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.
3D television
As of 2010[update], a number of manufacturers were developing auto-stereoscopic high definition 3D televisions, using lenticular lens systems to avoid the need for special spectacles. 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 color motion picture processes
Lenticular lenses were used in early color motion picture processes of the 1920s such as the
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 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 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 normalat the point where it exits the lens,
- is the pitch, or width of each lenticular cell,
- is the radius of curvature 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
- ,
where is the index of refraction of
Example
Consider a lenticular print that has lenses with 336.65 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
- ,
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.
See also
- Fresnel lens, a different 'flat' lens technology
- Integral imaging
- Microlens
References
- ^ "Lenticular, how it works". Lenstar.org. Archived from the original on 3 May 2016. Retrieved 25 May 2017.
- ^ DIY Printed Holographic Display (Lenticular Optics Explained), archived from the original on 21 December 2021, retrieved 8 May 2021
- ISBN 0-7506-5526-7.
- ^ "Lenticular projector screen vs. Fresnel projector screen for ultra short throws". ProjectorScreen.com. Retrieved 15 June 2022.
- ^ "Give Me 3D TV, Without The Glasses". Archived from the original on 13 February 2010. Retrieved 6 May 2010.
- ^ Factory, Looking Glass. "Looking Glass Factory · The World's Leading Holographic Display". Looking Glass Factory · The World's Leading Holographic Display. Retrieved 8 May 2021.
- ^ "Lenticular films on Timeline of Historical Film Colors". Archived from the original on 9 July 2014. Retrieved 29 June 2014.
- Bartholdi, Paul (1997). "Quelques notions d'optique" (in French). Observatoire de Genève. Retrieved 19 December 2007.
- Soulier, Bernard (2002). "Principe de fonctionnement de l'optique lenticulaire" (in French). Séquence 3d. Retrieved 22 December 2007.
- Okoshi, Takanori Three-Dimensional Imaging Techniques Atara Press (2011), ISBN 978-0-9822251-4-1.