Multi-Channel LiDAR

What is modelled

A spinning scanner sends a short laser pulse, times its echo and turns the delay into a distance. Stacked channels aimed at different elevation angles give rings, and the rotation gives the azimuth of every pulse. The spacing of the points depends on the rotation rate, the pulse rate and the channel angle; the reach depends on how weak an echo the detector can still notice; and a pulse rate that is too high makes distant echoes arrive after the next pulse has already left.

Equations

• Range R = c t / 2, unambiguous range Ru = c / (2 fp), a farther target appears at R − Ru floor(R / Ru).
• Azimuth step Δφ = 2π frot / fp, spacing on a wall R Δφ and R Δθ.
• Echo P = Pt ρ cos i Ar e−2αR / (π R2), reach where P = Pth; precision c σt / 2.
• Ground rings r = H / tan θ, gap r2 Δθ / H.

Checks run in the page

• A time-of-flight clock folded into one pulse period reproduces the ambiguity law.
• Ray casting against a flat wall gives d / cos(phi) and the 1 / cos^2 spacing growth.
• The log-log slope of the echo is -2 and the bisection reach equals the closed form.
• Vector intersection of rays with the ground equals H / tan(theta), with the derivative of the ring spacing.

Honest simplifications

Only the horizontal ring is ray cast in the top view, the laser power, receiver area and air loss are fixed, the echo is a Lambertian surface larger than the beam, multiple returns, motion of the head and sunlight noise are left out. It shows how the settings trade against each other.

• Press Fine metrology and compare the point spacing plot with Rapid sweep.
• Press Dark surfaces, far walls: the far walls drop out because their echo is below the threshold.
• Press High pulse rate, ghosts and see red ghost points appear inside the dashed unambiguous range.