Tin Foil
A sheet of kitchen foil on a table, lit by real lamps. Write a word under the foil and watch it show through the crinkles, or press letters into it. Rub the foil to pull it tight over what is underneath. Every lamp has a real spectrum (sodium street lamp, halogen, light bulb, LED, candle), and every foil has a real reflectance spectrum, so gold chocolate foil and silver foil can look the same under one lamp and nothing alike under another.
Things to try
- Hidden message. A word lies under loosely crumpled foil. Pick Burnish and rub: the foil pulls tight, the crinkles flatten, and the letters come up, as in a pencil rubbing.
- Gold and silver under sodium. The left half is gold chocolate foil, the right half plain aluminium. Under a low-pressure sodium street lamp they are the same colour, because the lamp sends out a single wavelength (589 nm) and a colour needs at least two to compare. Switch the lamp to halogen and the gold comes back.
- Red foil goes black. Pick red chocolate foil and a sodium lamp. Red lacquer passes light above about 600 nm, and sodium's 589 nm is just below that.
- A 450 nm laser. Real gold reflects less than half of blue light, so in blue laser light gold leaf turns dark while aluminium stays bright.
- Move a lamp low. Grazing light makes long shadows in the creases and shows the relief best; a lamp overhead hides it.
- White balance. Your eyes adapt to a light bulb within minutes and see it as white, and so does a camera on auto. Set white balance to None to see the bulb's real orange. With two different lamps no balance can make both white.
How it works
The foil is a height map 24 by 16 cm. Crumpled foil barely stretches, so instead of curving it folds: flat facets meet in sharp ridges and valleys. The page builds that from several sizes of random facets, each one a gently curved plane, and keeps the lowest at every point; alternating sizes are turned upside down so there are valleys as well as ridges. Things under the foil (letters, a chocolate bar, coins, string drawings) are a second height map. Loose foil only follows them in a wide blur. Tight or burnished foil follows them exactly, with its crinkles ironed out. Pressed letters push the foil down and flatten it, which is why they come out mirror-smooth.
Each pixel is lit by every lamp with a microfacet mirror model (anisotropic GGX), because rolled foil has fine streaks along the rolling direction. Crease shadows are traced through the height map. The lamps also light the room, and the foil reflects that room, darker straight overhead where the camera is.
Colour is spectral. A lamp's spectrum times the foil's reflectance spectrum, summed against the CIE 1931 colour-matching functions, gives the colour of that lamp's reflection in that foil. This is done once per lamp and foil on the CPU, so the picture follows from physics rather than from an RGB guess. The lamp spectra are the same models as on the spectroscopy playground and the optical bench. Gold and copper reflectance are rough fits to published optical constants; the coloured chocolate foils are aluminium under a transparent lacquer, which filters the light twice (in and out) and adds a faint clear reflection of its own.
Why "tin" foil?
Foil used to be tin. Aluminium foil took over in the early 1900s (chocolate makers in Switzerland were early users), and the old name stuck. Kitchen foil has a shiny and a matte side because the last rolling pass squeezes two sheets together: the sides that touched the polished steel rolls come out shiny, and the sides that touched each other come out matte. Both carry faint streaks along the rolling direction.