The Era of Yocto-Second Resolution

The Era of Yocto-Second Resolution

Today, as a proof of concept, I built a timestamping device with yoctosecond resolution. The device is not for sale yet – and it will not be any time soon. I explain.

Yocto is a metric system prefix adopted in 1991 to signify one septillionth. Applied to time, one yoctosecond means 1/1,000,000,000,000,000,000,000,000s. Just as comparison, one nanosecond means 1/1,000,000,000s. A very small time.

Notwithstanding such unbelievably small scale, we succeeded to create the yoctosecond device, but it needed a small smart trick that I’ll share with you for free. Later. Before that, let me dive in three important (but distinct!) concepts when it comes to the science of measuring things: resolution, precision and accuracy.

Let us dive into a practical example. When you get in the Army’s boot camp, invariably you are assigned a rifle as your companion for the entire duration of the course. I had the bad luck to be assigned a bad gun. It will shoot well, meaning the shots will be grouped all together in a group but far from the bull’s eye. It would require a quick adjustment in the horizontal and vertical controls such that the shots zero in the bull’s eye. However, after a day or two of use, which means running, jumping, wading through mud pits, and eating with it, my gun would lose the adjustment and drift away. The shots will still be grouped but far from the center.

 Bad precision, bad accuracy.
 Bad precision, better accuracy.

 Good precision, bad accuracy.

 Good precision, good accuracy.

In scientific terms, my gun had good precision but very bad accuracy! Precision is the term that (usually) describes the dispersion around the center. For statisticians, it relates to the standard deviation around the mean. Accuracy means the distance between the sample’s mean to the reference (aka true) value.

The third term, resolution, has nothing to do with the actual precision or accuracy of the physical phenomena being measured. Resolution is a characteristic of the measuring equipment. Rulers have resolution in millimeters or 1/8th of an inch, usually. Urban vehicles measure speed with 5-mph resolution displays.

The relationship between resolution and precision is one of practical purposes – ideally you want the resolution of your measuring equipment to be twice to one order of magnitude smaller than the precision of the quantity being measured. For example, a popular electronic digital caliper sold at Amazon has a resolution of 0.01mm and maximum accuracy of 0.02mm.

I bet the producers of this equipment would be glad to put on a bigger display, lower the resolution to 0.0001mm and market the hell out of it. In fact, it just requires a software change. But wouldn’t claim having a 0.0001mm resolution equipment when the actual accuracy never smaller than 0.02mm? Yep that sounds like cheating.

By this time you’d have realized that what we did to create the yoctosecond measuring device was just increase the size of the timestamp from 64 to 128 bits. Which actually reaches beyond yoctosecond into metric prefixes not yet officially defined.

Such device actually exists, it’s an FPGA board with PPS inputs and all that jazz with an output resolution of 128 bits (or yoctosecond resolution) sitting in my office’s desktop. Will we ever commercialize it? No, because bragging resolution in hope to lure decision makers unaware of the distinction between resolution, precision and accuracy is despicable sales tactics and reputation is everything for a consulting company.

So, next time you hear a vendor boosting “one nanosecond resolution”, feel free to give my office a call and ask our opinion on it. It will be free, polite and I promise, elucidating.