The Science of Lenticular Optics

The Science of Lenticular Optics

Lenticular sheets are amazing; covered in hundreds of tiny lenticular lenses, they can grant partial invisibility, create 3D pictures, and animate still images. That’s a lot of heavy lifting for lenses just half a millimeter thick. What’s the secret? The power of refraction: the ability of the lenses to bend light. But it works a little differently in each case; let’s investigate how.

We’ll start with the 3D effect, which is sometimes called “autostereoscopic display,” because it doesn’t require 3D glasses or outside elements to make it work. So what’s going on? Just as with other printed 3D effects (like the stereoviewer from your Fall 2021 box!), lenticular 3D operates by presenting each eye with a slightly different image. While most 3D systems show the images side by slide, or slightly overlapping, for lenticular 3D, the image is interlaced: the picture is sliced into strips that alternate next to each other. When the lenticular sheet is put on top, the lenses adjust the view of each little sliver of the image so that it enters one eye. Your brain adds the slivers together and delivers two complete, slightly different, images that take advantage of the stereoscopic effect to appear 3D.

Each R and L is a tiny slice of the right-eye and left-eye images. Illustration by The Electronic Visualization Lab at the University of Chicago.

Lenticular animation works the same way, but instead of two stereo images, the interlaced picture is essentially of two animation cells - the same picture, each slightly changed to show motion. So lenticular animation is essentially combining two (or more) pages of a flipbook into one image, then letting the lenses show you a different “page” as you change your viewing angle. 

An illustration how lenticular animation works, courtesy of The Smithsonian

Lenticular 3D and animation have been around for years, but it’s a newer application that’s extra fascinating: lenticular invisibility. Recently, people have become aware of this cool invisibility effect, which you’ll sometimes see referred to with the grandiose phrase “quantum stealth technology.” If you’ve played around with the sheet, you’ll note that it can turn things - especially straight lines or relatively long, thin objects - invisible. And unlike with the 3D effect, the invisibility doesn’t change if you move your head up, down, or sideways. But it only works in one direction - either horizontal objects are invisible, or if you rotate the sheet 90 degrees, vertical ones. How does it work?

As mentioned above, the effect is due to refraction. Hundreds of rows of tiny lenticular lenses refract (bend) the light that runs parallel to the orientation of the sheet’s lenses. In effect, when you look directly at the sheet, the lenticular lenses are bending the light so that you’re seeing around it: so instead of looking directly at an object, you’re actually seeing the background on the other side of it (that’s why the effect works best against a uniform background). 


Try experimenting with your sheet around the house, playing with different household items and locations to test the invisibility. The sheet works best when the item you’re making invisible has strong lines, and is oriented in the opposite direction of nearby objects. For example, you can hold a pen or pencil in your hand, and see it disappear while your fingers remain visible; make the stems of wine glasses disappear, while the bowl stays intact, hovering in mid-air. 



The directional orientation of the invisibility - why the pencil in your hand disappears but your fingers remain visible (then vanish in the other direction when you rotate the sheet 90 degrees) is because of the structure of the lenticular lenses, which affects the direction in which they refract the background light. Basically, things become invisible when they’re lined up in the same direction as the tiny lenses that make up the sheet. In a sense, the sheet is only an invisibility-producing refractive lens perpendicular to the direction of the bumps.

You can see a large-scale version of how the lenticular invisibility works - as a lenticular invisibility shield! - in the Harry Potter episode of Jake’s Emmy- and Streamy-award winning series Could You Survive the Movies? 

3D without glasses, animation without cels, and directional invisibility: we’re continually amazed at the flexibility (no pun intended) of lenticular sheets. Try the sheet on shapes, objects, and text around your house. Amaze your friends, surprise yourself - and have fun!

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