Reading a Time of Flight as a Distance
A ranging sensor does not measure distance. It measures an interval — the gap between a laser pulse leaving the emitter and its echo landing on the detector — and everything else is arithmetic. Timing hardware reports that interval in nanoseconds, while the physical constants, integration windows and datasheet specifications around it are written in seconds. Moving between the two is the first step in every range calculation, every error budget and every argument about whether a sensor can really resolve what the brochure claims.
The Constants Behind Every Range Reading
A metre costs 6.671 ns
Timing resolution is range resolution
Pulse width sets the near limit
Repetition rate caps the far limit
Working a Captured Interval Through the Page
Whether the number came off a time-to-digital converter, an oscilloscope cursor or a simulation log, the sequence is the same.
Enter the measured round trip
Type the interval in the left field — 667.1 for a target near a hundred metres. The seconds value updates as you type, and spaces inside long figures are ignored so 1 334 is read as one thousand three hundred and thirty-four.
Read the exponent, not a row of zeros
Anything under a microsecond is shown with an exponent, so 667.1 ns comes back as 6.671000e-7 s rather than a string of leading zeros you would have to count. That is the form the range equation wants anyway.
Reverse it when the datasheet is in seconds
The swap button (↔) gives s → ns, which is what you need when a specification lists a dead time or a gate width as 2.5e-8 s and the bench instrument only accepts nanoseconds.
Copy the digits into the range equation
Each field carries its own copy control and passes the plain number across with no unit attached, ready to be multiplied by the speed of light and halved in a sheet or a notebook. Ctrl + C in a field does the same.
Round-Trip Time Against Measured Range
Every row is the same multiplication by 6.671 ns per metre, shown in nanoseconds as the timing chain reports it and in seconds as the maths uses it. The last column is the shortest interval between shots that keeps the return unambiguous at that range.
| Target range | Typical use | Round trip (ns) | Round trip (s) | Unambiguous rate ceiling |
|---|---|---|---|---|
| 0.5 m | Depth camera near field | 3.336 ns | 3.336e-9 s | 300 MHz |
| 1 m | Reference distance | 6.671 ns | 6.671e-9 s | 150 MHz |
| 5 m | Indoor time-of-flight sensing | 33.36 ns | 3.336e-8 s | 30 MHz |
| 30 m | Parking and low-speed assist | 200.1 ns | 2.001e-7 s | 5 MHz |
| 100 m | Mid-range scanning | 667.1 ns | 6.671e-7 s | 1.5 MHz |
| 200 m | Highway-speed detection | 1 334 ns | 1.334e-6 s | 749 kHz |
| 300 m | Long-range automotive claim | 2 001 ns | 2.001e-6 s | 500 kHz |
| 1 000 m | Survey and corridor mapping | 6 671 ns | 6.671e-6 s | 150 kHz |
Two things fall out of the table. First, everything a car-mounted sensor cares about happens inside two microseconds, which is why the whole discipline lives in nanoseconds and only converts to seconds when the physics is written down. Second, the rate ceiling and the range pull in opposite directions: doubling the reach halves the shots per second available for building up a point cloud, and that trade is why long-range units interleave pulse patterns instead of simply firing faster.
What Is Useful at the Ranging Bench
Exponent form arrives on its own
Below one millionth of a second the result switches to an exponent with six decimals, which is exactly how a ranging interval belongs in a calculation sheet.
Step through a range sweep live
Both fields accept input and answer each other immediately, so a sweep of intervals from a few nanoseconds to several thousand takes one pass with no clearing between entries.
Flip when the spec is written in seconds
Gate widths, dead times and integration windows are often published in seconds or exponent form; swapping the direction turns them back into the nanoseconds a bench instrument expects.
Microseconds sit one dropdown away
Long returns read more naturally in microseconds, and the searchable unit lists on both sides let you change either end without leaving the page.
Questions From the Ranging Bench
What distance does a 100 ns round trip represent?
14.99 m, near enough 15. Divide 100 by 6.671 ns per metre, or take the seconds value of 1e-7, multiply by the speed of light and halve it. The tidy coincidence that 100 ns lands almost exactly on 15 m is worth memorising: it makes 1 ns roughly 15 cm and gives you a sanity check for any figure a timing chain hands over.
What timing resolution do I need for one-centimetre accuracy?
66.7 ps, which is 0.0667 ns or 6.67e-11 s. That is the round-trip interval a single centimetre of range adds, so a time-to-digital converter has to resolve at least that finely before a centimetre claim means anything. Resolution is not the whole story, though — walk error, jitter and how the timing circuit decides where an echo starts all add their own millimetres, and averaging many shots is how most sensors buy back what the electronics cannot resolve in one.
Why does pulse width limit the shortest range I can measure?
Because the pulse occupies space as well as time. A 5 ns pulse stretches 1.5 m through the air, so its tail is still leaving the aperture while its head is coming back from anything closer than about 0.75 m. The receiver is either saturated by the outgoing light or unable to tell the two edges apart. Shortening the pulse is the direct fix — a 1 ns pulse brings the blind zone down near 15 cm — and range gating, which simply ignores the detector for a set number of nanoseconds after firing, handles the rest.
What does a one-nanosecond timing error cost me in metres?
About 0.15 m of range, since the error is shared between the outbound and return legs. That number is unforgiving in context: a car at 30 m/s covers 15 cm in 5 ms, so a sensor with a nanosecond of timing uncertainty is reporting a position roughly as stale as one that is 5 ms late. Errors of a few nanoseconds are the difference between resolving a kerb and missing it.
When is a phase-shift sensor a better choice than a pulsed one?
Indoors and up close. A continuous-wave sensor modulates the beam and measures the phase of the returning light instead of timing an edge, which sidesteps the need for picosecond electronics and gives excellent precision over a few metres. The catch is ambiguity: phase repeats every half wavelength of the modulation, so 100 MHz wraps around at 1.5 m and 20 MHz at 7.5 m, and beyond that the sensor cannot tell one cycle from the next without a second frequency to disentangle it. Pulsed ranging carries no such wrap, tolerates sunlight better and is what long-range instruments use.
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