Making [etched] holograms with a pen plotter

使用绘图仪制作[蚀刻]全息图

I have a pen-plotter! It’s great. It’s like having a printer but slow and it breaks more often. 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. Now it’s fixed! 我有一台绘图仪！它很棒。它就像一台打印机，只不过速度更慢，而且更容易坏。我是在 eBay 上买的，到手时有点损坏，我立刻把买它的钱和买一台新机器的差价花在维修上。现在它修好了！

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. 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. 我最喜欢用绘图仪做的事情，就是创作一些我无法用打印机或手工完成的作品。有时是因为介质不同；例如，我用金墨水制作的禽龙化石明信片。但最近，我对使用绘图仪制作全息图产生了浓厚的兴趣。

You could derive hand-drawn holograms from scratch

你可以从零开始推导手绘全息图

William Beaty has an amazing page about how to make holograms by hand and it includes intuitive explanations of the optics behind them. You can read this page for an awesome explanation of why hand-drawn holograms work and what makes them so effective. 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. William Beaty 有一个很棒的页面，介绍了如何手工制作全息图，其中包含了对其背后光学原理的直观解释。你可以阅读该页面，了解为什么手绘全息图有效以及它们为何如此出色。但我想向你展示如何完全直观地、从零开始理解手绘蚀刻全息图，无需任何全息摄影的先验知识，也不需要任何数学计算。这一切都始于油腻的手指。

1. Greasing your fingers

1. 油腻的手指

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! 我为此选用了优质的特级初榨橄榄油，但你也可以根据喜好换成植物油或椰子油。故意把手指涂满油然后去触摸手机屏幕，这真是一种极其怪异的体验。试试看！规则都是人定的！

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. 你可能在自己的手机上见过类似的污迹。你会看到一些小小的“高光”，那是光线在污迹的特定部分反射形成的。在右侧，我画了一个示意图来解释发生了什么：光线从光源出发，经过指纹留下的纹路反射，最终进入你的眼睛。

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. 现在我要画一个不同的图案：当我移动手机周围的摄像头时，条纹的高光也会随之移动。我们可以控制它！这就是手绘蚀刻全息术的关键洞察：反射纹路的曲率决定了这种“虚像”高光的移动方向和速度。

2. Applying the insight to holography

2. 将这一洞察应用于全息术

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. 我们之所以能控制高光的方向和速度，是因为当纹路的曲率半径较陡时，高光相对于你头部的移动较小；而当曲率半径较平缓时，高光的移动则较大。

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. 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! 在这个视频中，我首先在闪亮的圆环（一个低保真全息图！）周围移动光源，圆环上的眩光以不同的速度移动。然后，我在一组球体周围移动摄像头；全息图的“虚像”点具有与真实球体相同的视运动！

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. 换句话说，我们的反射纹路产生的高光，其移动速度与纹路的曲率半径成反比——就像现实世界中物体越远看起来移动越慢一样。

3. Pen-plotting

3. 绘图仪绘图

This means we now have a way to draw a 3D scene that actually communicates depth information to the viewer. 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. 这意味着我们现在有一种方法可以绘制 3D 场景，并向观众传达深度信息。为了付诸实践，我们将“渲染”一个场景，使每个点都变成一个反射纹路，其曲率半径与该点到摄像头的距离成反比。

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 hyperboloid section. 简要说一下数学。你可以跳过这一段。我在这里略过了大量的数学计算和调试过程——如果你想看代码，可以在我的 GitHub 上找到——但基本思想是，我们要渲染的每个点大致上都变成了一个双曲面截面。

Lessons Learned

经验教训

The results so far are a bit underwhelming on camera, but to me, sitting with a flashlight in my pitch black closet and moving my head around like a pigeon, the effect of the first working hologram was magical. I still think the Stanford Bunny example above looks like a truly cool piece of art! 到目前为止，拍摄出来的效果在镜头下略显平淡，但对我来说，坐在漆黑的壁橱里，拿着手电筒像鸽子一样晃动脑袋，第一个成功全息图的效果简直太神奇了。我仍然认为上面的斯坦福兔子示例看起来是一件非常酷的艺术品！

There are a lot of lessons learned. For instance, I needed something pretty narrow and pretty sharp to get the etching to work. The light also needs to be a point-source; this is a major difference from “rainbow” holograms or white-light holograms, which work fine in ambient light. 我学到了很多经验。例如，我需要非常细且非常尖的工具才能完成蚀刻。此外，光源必须是点光源；这与在环境光下也能正常工作的“彩虹”全息图或白光全息图有很大不同。