Making holograms with a pen plotter

I person a pen-plotter! It’s great. It’s for illustration having a printer but slow and it breaks much often. I sewage it connected eBay and it came sorta surgery and I instantly spent the quality betwixt what I paid and the value of caller 1 fixing it. Now it’s fixed!

My favourite point to do pinch the pen plotter is to create things that I wouldn’t beryllium capable to create on, say, a printer, aliases by hand.1 Sometimes that’s because the mean is different; for example, these golden ink postcards I made of an Iguanodon fossil:

But recently, I’ve gotten excited astir utilizing the pen plotter to make holograms.

You could deduce hand-drawn holograms from scratch

William Beaty has an astonishing page2 astir really to make holograms by manus and it includes intuitive explanations of the optics down them. You tin publication this page for an awesome mentation of why hand-drawn holograms activity and what makes them truthful effective.3

But instead, I want to show you really you could understand hand-drawn etch-holograms wholly intuitively and de novo, without immoderate anterior knowledge of holography, and without immoderate math. It each starts pinch greasy fingers.

1. Greasing your fingers

I selected a bully other virgin oliva lipid for this, but you tin substitute for rootlike aliases coconut, to taste.

It was a genuinely bizarre acquisition deliberately smearing my fingers pinch lipid and past rubbing my telephone screen. Try it! Rules are made up!

You’ve astir apt seen a akin smudge earlier connected your ain phone. You get these small “highlights” wherever the ray reflects disconnected a peculiar portion of the smudge. On the correct broadside I’ve drawn a schematic of what’s happening: the ray finds a way from the ray root to your oculus that bounces disconnected somewhere on the ridges near by your fingerprint.

Now I’m going to tie a different pattern:

As I move the camera astir the phone, the item of the streak moves.

We tin steer that! That’s the cardinal penetration of hand-etched holography: the curvature of the reflective ridges determines the direction and velocity of movement of this “virtual image” highlight.

This is the aforesaid arena arsenic the rainbow pizza-slice connected CDs, and what windshield-wiper “streaking” is: the ray is bouncing disconnected a peculiar portion of the smudge and into your eye, and arsenic you move your head, the ray bounces disconnected a different portion of the smudge. Thanks to 2 random Facebook users for posting these.

2. Applying the penetration to holography

The logic we tin power the guidance and velocity of the item is that the item moves less comparative to your caput erstwhile the radius of curvature of the ridge is steep, and it moves more erstwhile the radius of curvature is shallow:

In this video, I first move the ray root astir shiny rings (a low-fi hologram!) and the glare connected the rings moves astatine different speeds. And past I move the camera astir a group of spheres; the “virtual image” points of the hologram person the aforesaid evident mobility arsenic the existent spheres!

In different words, our reflective ridges person a item glare that moves astatine a velocity that is inversely proportional to the radius of curvature of the ridge — conscionable for illustration really objects successful the existent world look to move slower erstwhile they’re further away.

3. Pen-plotting

This intends we now person a measurement to tie a 3D segment that really communicates extent accusation to the viewer. To put this into practice, we will “render” a segment specified that each constituent becomes a reflective ridge pinch a radius of curvature that is inversely proportional to the region of the constituent from the camera.

Math, briefly. You person my support to skip this box. I’m glossing complete a ton of mathematics and debugging present — code’s connected my GitHub if you want to spot it — but the basal thought is that each constituent that we want to render becomes, roughly, a hyperboloid4 section:

Where \(d\) is the region of the constituent from the image plane, \(θ\) is spectator perspective crossed the horizontal, and \(α\) is the ray perspective comparative to the level normal.

If you didn’t for illustration that sentence, disregard it — I will not do mathematics again successful this post.

I’ll show a fewer grounded attempts below, but first, immoderate cool shots of this working:

Some Fails

I wasn’t judge what materials to usage to get started. My first effort was to usage a clear integrative “lamination” expanse from the agency proviso store, which was a total fail, chiefly because the integrative was excessively elastic and (1) moved erstwhile I was trying to etch it, and (2) it was excessively wavey to bespeak ray coplanar to the viewing angle.

Then I tried utilizing a woody stylus to etch those waxed sheets of colored insubstantial that we utilized to tie connected successful simple school; do you retrieve them? These were alright, but the measurement of curves I needed to tie was excessively overmuch for the insubstantial to handle, and it coiled up tearing and crumpling.

The worldly that yet worked was an aged CD jewel case. I coiled up going connected eBay and buying a bunch of them for a fewer dollars. I don’t cognize what I expected5, but I was benignant of assuming I was buying caller jewel cases. Instead I sewage a immense container of aged and soiled utilized ones. Weird! But also… Okay I guess!

Lessons Learned

The results truthful acold are a spot underwhelming connected camera, but to me, sitting pinch a flashlight successful my transportation achromatic closet and moving my caput astir for illustration a pigeon, the effect of the first moving hologram was magical. I still deliberation the Stanford Bunny illustration supra looks for illustration a genuinely cool portion of art!

There are a batch of lessons learned. For instance, I needed thing beautiful constrictive and beautiful crisp to get the etching to work. My dada gave maine a hooks/picks group from (I think) Harbor Freight, and the pokiest consecutive prime (seen pinch an orangish grip successful the videos above) worked awesome connected the CD jewel cases, but wholly annihilated the papers I tried.

The ray besides needs to beryllium a point-source; this is simply a awesome quality from “rainbow” holograms aliases white-light holograms, which activity good successful ambient light. Basically, the wider the root of light, the wider the virtual image points get, and the little extent accusation is communicated. Reflect a flashlight straight into your eyeballs! That’s what I did. The illusion useful champion erstwhile the main glare of the constituent root ray is conscionable above the apical of the etches.

I deliberation I’m still not rather retired of the woods connected worldly choice, either. The much etches I make connected the jewel cases, the amended the results look to be, but besides the rougher the aboveground becomes, and pinch precocious capable sampling, the etched region conscionable becomes a large matte blob. I person a back-of-mind conception that I should effort a diamond-tipped stylus, but I judge don’t want to walk that benignant of money connected a not-cool-yet project! Do you person 1 laying astir that you want to springiness me?

Are these really holographic?

As acold arsenic I’m concerned, they person the main characteristic of a hologram that I attraction about, which is that moreover comparatively mini cutouts of the hologram clasp a complete transcript of the scene. This isn’t a general meaning — it’s conscionable the truth astir holograms that I for illustration the most.

Beaty makes an fantabulous statement for why you should see these holograms and I surely won’t do a amended job. But if you consciousness powerfully that these are not holograms, past find for maine a better sanction and you tin telephone them that thing. I conscionable deliberation they’re neat!

Whatever they’re called, I deliberation it is simply a beautiful point that — for illustration Gabor who first described holography — we person each the instrumentality we request to research these physics phenomena without costly lasers aliases optical tables.

Finally — thing that gives maine (good! excited!) shivers. From Beaty’s page:

P.S. The required devices are truthful elemental that ancient peoples could person drawn these images successful hardened sooty resin pools pinch woody tools, had they but known the trick. Several ancient civilizations were heavy into geometry. I wonderment if immoderate artifacts beryllium successful retention location which look to person immoderate ‘sandpaper marks’ connected their polished surfaces… ;)

Now if that isn’t a cool thought, I don’t cognize what is.