Timing Properties of SPADs

I've gotten requests for more technical material, so here ya go:

Today I'm going to talk about some applications of SPADs. If you want a reminder of the basics of SPADs, you can read my introductory post or my post on noise. SPADs are single-photon detectors that use feedback systems in conjunction with one another to accurately time the arrival of single-photons. Accurately timing a photon's arrival time is important in many applications, but today I'll be talking about rangefinding.

In rangefinding applications, such as laser-based rangefinding for land surveying, a laser fires a pulse of photons and a detector times the difference between the pulse and the photon detection time. Photons, being light, travel at the speed of light. You'll usually here the speed of light quoted as 300,000,000 meters per second, but optics people prefer to quote the speed of light as
  • 30 centimeters per nanosecond
  • 300 millimeters per nanosecond
  • 300 micrometers (microns) per picosecond
  • 30 millimeters per 100 picoseconds
We use these values because modern electronics usually have around 100 picoseconds of accuracy. In the future, I think the 300 microns per picosecond value will become more common.

Anyways, we have to accurately time this photon arrival so we can determine the time of flight. The timing inaccuracy is termed jitter; we use various metrics to quantify the jitter, but most of these metrics just capture the usual case. For SPADs, the jitter depends on a few things.

First, the temperature is very important. In a silicon integrated circuit, increasing the temperature increases the ambient energy available to electrons, the main information carriers in the circuit. The introduction of additional energy modifies a carrier's behavior, and thus changing the temperature will change the characteristics of both the fast and slow feedback loops in SPADs.

Next, the color of the light is also important. Different colors of light have different wavelengths. The wavelength describes how frequently the energy moves around in space. Since silicon has a repeating structure, the wavelengths will help determine how likely it is that the light interacts with the crystal, producing the primary electron that could cause an avalanche. It turns out that blue light is optimal for the current generation of SPADs - the optimal wavelength is a balance between how far light usually penetrates into the silicon and where the avalanche region is (remember that we moved the region away from the surface to avoid the noise-causing irregularities at the surface).

Within the avalanche region, the build-up time of the avalanche is obviously important. During the initial portion of the positive feed-back loop, when there are very few carriers active, the variation in each carrier can change the build-up time. Current understanding is that it takes between 0 and 15 picoseconds to generate enough carriers to average out these variations, though this build-up process depends on characteristics like the temperature and strength of the applied force (the electric field).

So what is the end result? Well it depends on what you need and what you have available. If you have a lot of area available on a silicon chip, you can use more complex current detectors to get the jitter as low as 15 or 20 picoseconds. On the other hand, if you're short on area you can raise the jitter as much as you like, but you'd be hard-pressed to raise it above nanoseconds and still have a viable application. Keep in mind that you'll be changing how close the SPADs are, so the cross-talk will change.

When you're making a range-finder, you might care only about one specific range, or you might be trying to acquire a bunch of ranges to get a 3D pictures. If you only care about one range, you can use a lot of area to achieve the 20 picosecond resolution. This corresponds to an uncertainty in space around 6 millimeters. If you have an array of SPADs and timing circuitry, you're more likely to have an error in the 100 picosecond range. 100 picoseconds corresponds to an error of 3 cm in space. You can lower this uncertainty by taking multiple measurements, and since the measurements are so fast the accuracy can easily be one millimeter or less.

Anyways, I hope this post helped you understand about the timing uncertainty in SPADs. The uncertainty affects other applications besides rangefinding, things like quantum-based encryption algorithms, biological imaging, and cancer detection, but those applications are a bit more complicated to explain! I'll be attempting in future posts, and we'll see how it goes.

Another Airbrushing Site

I stumbled across a really interesting airbrushing site today...I can never click through enough of these to remind me how much people are mis-represented in print and online media. (earlier post)



Why are TVs and computer monitors horizontally long, but paper is vertically long? I suppose it makes sense that monitors and TVs are horizontal, as this matches our visual field, but then why is paper tall, rather than wide?



It has been a year! Here are some of the things I've done in the past year:

1) Forgot / lost passport, had to travel 3 hours to get it back
2) Setup an experiment using somewhat dangerous radiation while I was suffering a headache from lack of sleep
3) Was the last person on a plane, having nearly missed it (this experience is over-rated)
4) Laid out a portion of an integrated ciricuit that (if it works, crosses fingers!) will have 5.12 GBps going through it
5) Lost PhD topic
5.5) Lost PhD topic
6) Found PhD topic (errrr.....I think?)
7) Went all-in and won a poker pot, went all-in and lost a poker pot, successfully spotted a bluff at a poker table, successfully set a trap at a poker table
8) Gone to one of those fancy European clubs in Paris (it was worse than I thought and I will not be returning)
9) Bought plane tickets, booked a hotel, flew on plane and checked into hotel within 5 hours of one another
10) Successfully found apartment in a foreign country and moved into it from another apartment
11) Gotten a first-hand view of how difficult it is to be an immigrant
12) Earned the title Expatriate

Things I haven't done:

1) Successfully had a conversation in Dutch (I haven't had many successful ones in English over here, either)
2) Joined a choir
3) Written a paper (I'm working on one right now, and I have two in various stages of the paper pipeline)
4) Used tools to go from VHDL to ASIC

By the numbers:

Guitars purchased - 1
Bicycles purchased - 1
Haircuts - 2
"Original" research ideas that someone else had actually tried but adviser didn't know about - 3
Canned hot dogs consumed - 4
Moose seen - 4 (two real, two mascots)
Shoes purchased - 6
Countries book was purchased in - 5 (6 if you separate England and Scotland, 7 if you include online purchases)
Countries "visited" - 7 (Scotland, US, Canada, Switzerland, Ghana, France, Belgium)
Passport resources used - 27 boxes from stamps, 2 pages from visas
Train tickets purchased - ~100 (I go through about 8 a month)
PB&J Sandwichs consumed - ~150 (they have this awesome sour cherry jam over here)
Emails sent - 2,088 (more than I thought, 25 were to myself)
Emails received - 2,698 (fewer than I thought)
Most lines of code written in a single day - ~3,200 (most of it was test code...firmware test code can be pretty massive to go through the appropriate states)
Lines of code written overall - ~16,000 (again, around 14,000 lines are test code)
Heartbeats - ~37,000,000 (the heart is a work of art)

And finally:

Dutch postcards sent - 0 (yeeeeeeeah...I still owe a lot of people postcards.....)

$500 for a Bicycle

The Freakonomics blog has a great post on the cost of bicycles in bicycle-crazy Portland:
Yeah, the bike guy answered, he had something super-cheap for me ... I could have it, he said, for $475.

So I went to another store. Same deal, more or less. There was one bike for $275, but it was a girl’s Raleigh from the 1960’s with a wicker basket.


At Portland’s Costco, meanwhile — on the outskirts of the city — you can buy a brand-new Schwinn Midtown city bike with Shimano shifters for around $200. But, according to the clerk there, those Schwinns aren’t moving.

I bought an inexpensive, new bicycle in Delft for just over $500, though the university reimbursed most of the cost through a travel program. I was expecting to find a nice, new one for around $250.

We don't have CostCo here, and sadly Ikea doesn't sell bicycles. I'll just keep dreaming.