Lidar: Time of Flight vs FMCW

Scope

Lidar measures distance by sending light to a target and timing or phase-comparing what comes back. This article compares the two approaches used in most current systems: direct time of flight (ToF), which times short pulses, and frequency-modulated continuous-wave (FMCW) lidar, which measures range as a beat frequency between a chirped laser and its echo. In short: ToF is simpler and cheaper and dominates today's products; FMCW measures velocity directly at every point and rejects sunlight and other lidars, at the cost of a narrow-linewidth laser and a coherent receiver. Scanning, wavelength and detector choices, which apply to both, are covered after the two methods.

Direct time of flight

A pulse leaves at time zero, reflects from a target at distance $d$, and returns after $t$:

$$d \;=\; \frac{c\,t}{2}.$$

Each metre of range adds 6.67 ns of round trip, and a target at 200 m returns after 1.33 μs. Two quantities follow from the timing:

• Range resolution, the separation at which two targets along the same line are told apart, is about $c\tau/2$ for pulse duration $\tau$: 15 cm for a 1 ns pulse.
• Range precision for a single target is set by how well the arrival time is found, usually much better than the pulse duration: a timing uncertainty of 100 ps corresponds to 1.5 cm.

The pulse rate limits the unambiguous range. A pulse must return before the next one leaves, so at a repetition rate $f$ the maximum range is $c/(2f)$: 150 m at 1 MHz. Faster point rates therefore use several lasers in parallel or codes that tell pulses apart.

The receiver is an avalanche photodiode with a timing circuit, or, increasingly, an array of single-photon avalanche diodes or a silicon photomultiplier that timestamps individual photons and builds a histogram over many pulses. Sunlight adds background counts that the timing gate must reject, and it limits range in daylight.

FMCW lidar

An FMCW lidar sweeps the laser frequency linearly (a chirp) by a bandwidth $B$ over a time $T$, splits off part of the light as a local oscillator, and mixes the returning light with it on a balanced detector. The echo is a delayed copy of the chirp, so at any instant it differs from the local oscillator by a constant beat frequency proportional to the delay:

$$f_R \;=\; \frac{2d}{c}\,\frac{B}{T}.$$

With $B$ = 1 GHz swept in $T$ = 10 μs, a target at 100 m gives a beat of 66.7 MHz. The range resolution is set by the sweep bandwidth, $c/(2B)$, which is 15 cm for 1 GHz, the same as a 1 ns pulse.

A moving target adds a Doppler shift $f_D = 2v/\lambda$ along the line of sight: 1.29 MHz per metre per second at 1550 nm, or 38.7 MHz at 30 m/s. On an up-chirp and a down-chirp the Doppler term enters with opposite signs relative to the range term, so measuring both beats and taking their mean and half-difference separates range from radial velocity. Each point in the cloud carries its own velocity, which a ToF system can only infer by comparing frames.

Because the receiver uses coherent detection, only light coherent with the transmitted chirp produces a beat in the measured band. The local oscillator amplifies the weak echo, which brings sensitivity to the shot-noise limit with milliwatt-class transmit power, and sunlight and other lidars appear as broadband background rather than false returns.

The costs are in the laser. Its coherence length must exceed the round trip: for a Lorentzian line, $c/(\pi\,\Delta\nu)$ gives 954 m at a 100 kHz linewidth, comfortably above the 400 m round trip to a 200 m target (see How to Measure Laser Linewidth). The chirp must also be linear, since any departure spreads the beat and blurs the range; systems correct it with drive predistortion, a phase-locked loop, or resampling against a reference interferometer.

Side by side

Wavelength: 905 nm or 1550 nm

Most ToF lidars use 905 nm (or nearby) pulsed diode lasers because silicon detectors, including SPAD arrays, work there and are inexpensive. Light at 905 nm reaches the retina, which limits the energy a pulse may carry within eye-safety limits. Light at 1550 nm is absorbed before it reaches the retina, so the permitted exposure is far higher, and telecom components (lasers, erbium amplifiers, fiber optics) are available; the detectors must be InGaAs, which costs more. FMCW lidars use 1550 nm almost universally, for the component base and the narrow-linewidth lasers developed for coherent communication.

Scanning

A single beam must be steered to build an image. Spinning assemblies rotate the whole optical head; MEMS mirrors and galvanometer scanners steer with a small moving mirror; flash lidar illuminates the whole field at once and images it onto a detector array, trading range for having no moving parts; and optical phased arrays steer by setting the phase of many emitters on a chip. A coherent receiver needs its own interferometer and balanced detector for each beam it reads in parallel, which is why FMCW development leans on photonic integration of the interferometers, detectors and beam steering.

Choosing between them

ToF suits applications where cost, simplicity and existing supply chains matter most and velocity can be inferred from successive frames: most robotics, mapping and many automotive sensors. FMCW suits applications that value per-point velocity and immunity to sunlight and to interference between many lidars on the road, and it is the approach most tied to silicon photonics. Both reach centimetre precision; neither is better in every respect.

References: B. Behroozpour, P. A. M. Sandborn, M. C. Wu and B. E. Boser, "Lidar system architectures and circuits," IEEE Communications Magazine 55(10), 135 (2017); M. I. Skolnik, Introduction to Radar Systems (3rd ed., McGraw-Hill, 2001); IEC 60825-1:2014, Safety of laser products: Equipment classification and requirements.