Making holograms with a pen plotter – Jordan Matelsky – Code, Coffee, & Cortex

Making holograms with a pen plotter

18 July 2026

pen-plotter

art

holography

technology

science

optics

blender

I have a pen-plotter!<br>It’s great.<br>It’s like having a printer but slow and it breaks more often.<br>I got it on eBay and it came sorta broken and I immediately spent the difference between what I paid and the price of new one fixing it.<br>Now it’s fixed!

My favorite thing to do with the pen plotter is to create things that I wouldn’t be able to create on, say, a printer, or by hand.1<br>Sometimes that’s because the medium is different; for example, these gold ink postcards I made of an Iguanodon fossil:

But recently, I’ve gotten excited about using the pen plotter to make holograms.

You could derive hand-drawn holograms from scratch

William Beaty has an amazing page2 about how to make holograms by hand and it includes intuitive explanations of the optics behind them.<br>You can read this page for an awesome explanation of why hand-drawn holograms work and what makes them so effective.3

But instead, I want to show you how you could understand hand-drawn etch-holograms entirely intuitively and de novo, without any prior knowledge of holography, and without any math. It all starts with greasy fingers.

1. Greasing your fingers

I selected a nice extra virgin olive oil for this, but you can substitute for vegetable or coconut, to taste.

It was a truly bizarre experience deliberately smearing my fingers with oil and then touching my phone screen. Try it! Rules are made up!

You’ve probably seen a similar smudge before on your own phone. You get these little “highlights” where the light reflects off a particular part of the smudge. On the right side I’ve drawn a schematic of what’s happening: the light finds a path from the light source to your eye that bounces off somewhere along the ridges left by your fingerprint.

Now I’m going to draw a different pattern:

As I move the camera around the phone, the highlight of the streak moves.

We can steer that! That’s the key insight of hand-etched holography: the curvature of the reflective ridges determines the direction and speed of movement of this “virtual image” highlight.

This is the same phenomenon as the rainbow pizza-slice on CDs, and what windshield-wiper “streaking” is: the light is bouncing off a particular part of the smudge and into your eye, and as you move your head, the light bounces off a different part of the smudge. Thanks to two random Facebook users for posting these.

2. Applying the insight to holography

The reason we can control the direction and speed of the highlight is that the highlight moves less relative to your head when the radius of curvature of the ridge is steep, and it moves more when the radius of curvature is shallow:

In this video, I first move the light source around shiny rings (a low-fi hologram!) and the glare on the rings moves at different speeds.<br>And then I move the camera around a set of spheres; the “virtual image” points of the hologram have the same apparent motion as the real spheres!

In other words, our reflective ridges have a highlight glare that moves at a speed that is inversely proportional to the radius of curvature of the ridge — just like how objects in the real world appear to move slower when they’re further away.

3. Pen-plotting

This means we now have a way to draw a 3D scene that actually communicates depth information to the viewer.<br>To put this into practice, we will “render” a scene such that each point becomes a reflective ridge with a radius of curvature that is inversely proportional to the distance of the point from the camera.

Math, briefly. You have my permission to skip this box. I’m glossing over a ton of math and debugging here — code’s on my GitHub if you want to see it — but the basic idea is that each point that we want to render becomes, roughly, a hyperboloid4 section:

\[x = d · tan(θ)\]

\[y = d · sec(α) · (sec(θ) − 1)\]

Where \(d\) is the distance of the point from the image plane, \(θ\) is viewer angle across the horizontal, and \(α\) is the light angle relative to the plane normal.

If you didn’t like that sentence, ignore it — I will not do math again in this post.

I’ll show a few failed attempts below, but first, some cool shots of this working:

Some Fails

I wasn’t sure what materials to use to get started. My first try was to use a clear plastic “lamination” sheet from the office supply store, which was a total fail, mainly because the plastic was too flexible and (1) moved when I was trying to etch it, and (2) it was too wavey to reflect light coplanar to the viewing angle.

Then I tried using a wooden stylus to etch those waxed sheets of colored paper that we used to draw on in elementary school; do you remember them? These were alright, but the volume of curves I needed to draw was too much for the paper to handle, and it wound up tearing and crumpling.

The material that...