How to draw holograms with a pen plotter, a CD case, and greasy fingers

A hobbyist walks through using a secondhand pen plotter to etch scratch holograms — the same trick behind the moving ‘glare’ streaks you see on a CD or a smudged phone screen. The core insight is intuitive rather than mathematical: a curved scratch reflects a point-source light into your eye at a spot that shifts as you move your head, and the speed of that shift is inversely proportional to the ridge’s radius of curvature. Because far-away objects also appear to move more slowly as you shift your viewpoint, mapping each point in a 3D scene to a scratch of the right curvature reproduces real depth cues. The plotter automates the tedious work of drawing thousands of precisely curved arcs.

Getting it to work took trial and error on materials and tooling. Lamination sheets flexed too much and waxed craft paper tore under the density of curves; an old CD jewel case, scored with a sharp straight pick, finally held up. The effect depends on a genuine point-source light — a flashlight in a dark room — since any wider source blurs the virtual image points and washes out the depth. Over-etching eventually roughens the plastic into a matte blob, so the author is eyeing a diamond-tipped stylus.

The appeal is that it reproduces a real optical phenomenon with no lasers or optical tables — even small fragments of the etched scene retain the whole image, the property the author cares about most in calling these holograms. The rendering code is posted on GitHub, and the piece closes on a fun speculation, borrowed from William Beaty’s foundational writeup: ancient geometry-minded cultures had all the tools to scratch such images by accident, so the effect may be hiding on polished artifacts in some museum’s storage.