A direct return and an indirect return can arrive with different delays. Four correlation taps recover their summed modulation phasor; its phase generally describes neither path by itself.
Mint is the direct path; violet is a delayed indirect path. Gold is what the demodulating sensor sees. Increasing the indirect contribution can change both recovered amplitude and phase.
P = A₀e⁻ⁱωτ₀ + A₁e⁻ⁱωτ₁
The depth estimate assumes a single round trip. Multipath violates that model even with noiseless taps. A known reference-phase change is removed during calibration; it does not physically move the surface.
z = c · mod(−arg P,2π) / (4πf)
The scene is monostatic: direct path length is 2z, while the second path length is 2z+ℓextra. With sinusoidal amplitude modulation, four ideal correlation taps at δ=0,π/2,π,3π/2 satisfy Cδ=B+½ Re(P eⁱδ). Their differences recover Re P and −Im P. The common DC offset B cancels.
These phasors describe intensity-modulation delay at MHz frequencies, not the optical electromagnetic carrier. Optical holography uses coherent field interference; CW-ToF uses temporal correlation. The Fourier algebra can be related without identifying the two physical measurements. A near-zero phasor amplitude makes its phase unstable.
Ideal four-tap CW-ToF model. CMU: time-of-flight image formation