How Hologram Pyramids Work: The Optics Behind a Phone Projector
A clear plastic pyramid stood on a phone screen makes a glowing figure appear to float inside it, visible from all four sides. It is not a hologram in the physicist's sense, because nothing records or rebuilds a light wave. It is a reflection, the same trick as the Victorian stage illusion Pepper's Ghost, run four times at once. Working through the optics explains every rule for making content for one.
A window that is also a faint mirror
Every clear surface reflects a little of the light that reaches it and lets the rest through. How much depends on the material and the angle. At the 45° of a pyramid face, acrylic reflects about 4.9% of the light at its front surface, and PET film, the material of overhead transparencies, about 7%. The rest passes straight through.
That is why the effect needs the dark. The reflected image is roughly a twentieth as bright as the screen, and the face itself is nearly invisible because almost all light goes through it. Your eye picks out the faint reflection only when nothing brighter competes with it.
A sheet has two surfaces, and both reflect. That is the faint second image, slightly offset, that thick plastic produces. A thinner sheet brings the two images closer together until they merge.
Why 45°, and where the image appears
Light leaves the screen travelling straight up. A face tilted at 45° turns it through a right angle, so it travels horizontally, toward a viewer whose eyes are level with the pyramid.
Treat the face as a mirror and the floating image's position follows. A pixel on the screen appears above the centre of the pyramid, at a height that grows one for one with its distance from the centre: a pixel 1 cm further out floats 1 cm higher. The flat picture on the screen is, in effect, stood on its end in the middle of the pyramid.
Two layout rules come straight from this:
- The top of each copy points at the edge of the screen. The further from the centre, the higher it floats, so the edge end of the picture becomes the top of the hologram. HoloPath's pyramid layouts draw every copy this way.
- Each copy must be mirrored. A reflection swaps left and right, which is why teleprompters display their text backwards. HoloPath mirrors every copy in its pyramid layouts, so text and logos read correctly in the plastic.
Why four copies
Each face reflects only the part of the screen beneath it, toward the viewer on its side. Four faces need four copies, one under each, turned so its top points outward. Walk around the pyramid and each face hands over to the next; from a corner you see parts of two copies at once.
The copies are identical, so this is one flat image seen from four directions, not an object with four sides. The back of your subject never appears.
Why the background must be pure black
Everything lit on the screen reflects, not only the subject. A dark grey background reflects as a dim grey sheet in every face, and because the subject's reflection is so faint, even a dim sheet washes it out. HoloPath colours each pixel by its brightness, so anything short of true black in your source becomes coloured light on the screen.
The screen type matters as well. An OLED screen switches black pixels off entirely. An LCD shines its backlight through them, so even pure black leaks a little light, which shows as a faint glow behind the image. On an LCD phone, the darker the room the better.
Why one pair of faces can look dimmer
Screens send out polarised light: LCDs always, and many OLEDs through the polarising layer that keeps their blacks deep. A face reflects polarised light very unevenly. For acrylic at 45°, light polarised along the face's surface reflects about 9%, and light polarised across it under 1%.
So on some phones two opposite faces look far dimmer than the other two, and turning the phone through 90° swaps the dim pair. Phones whose light is polarised diagonally, or circularly, light all four faces evenly, which is why many never show the effect.
How big the image can be
With 45° faces, the floating image can be up to half the difference between the pyramid's base and its top. A pyramid with a 60 mm base and a 10 mm top shows an image up to 25 mm tall. The base can be no wider than the screen's short side, which is why phone pyramids make small holograms and tablet pyramids larger ones. The DIY guide turns this into cutting dimensions sized to HoloPath's layout.
Viewing
Look straight in at the height of the pyramid's middle, from a little way back, in a dark room with the screen at full brightness. Looking down from above shows you the screen through the plastic instead of the reflection.