Echo Mapping

How time becomes
space on screen.

The machine measures one thing: when echoes return. From that single number — time — it constructs depth. And the amplitude of each echo is determined by a single equation: the mismatch in acoustic impedance at each tissue boundary.

d = c · t2
Time-of-Flight Depth
Z = ρ · c
Acoustic Impedance
R = (Z₂ − Z₁)²(Z₂ + Z₁)²
Reflection Coefficient
Scene View (left) — A-line Signal (right)
Vessel depth 2.5 cm
Vessel diameter 8 mm
Build a Tissue Stack — See the Reflection at Each Boundary
Acoustic Impedance & Reflection by Tissue Pair
Tissue ρ (kg/m³) c (m/s) Z (MRayl) Impedance (relative) Reflection vs Blood
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The 13 μs Rule

At 1540 m/s, round-trip travel to 1 cm depth takes 13 μs. The machine assumes exactly this. Every echo is time-stamped and converted to depth by this single constant — which is why speed artifacts from fat tissue shift structures deeper than reality.

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Why Blood Looks Dark

Blood and the surrounding soft tissue have very similar acoustic impedance (1.61 vs 1.63 MRayl). Almost no reflection occurs within the vessel lumen — so it appears anechoic (black) on screen. The bright walls are the tissue-blood boundaries.

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The Air Interface Problem

Tissue Z ≈ 1.6 MRayl. Air Z ≈ 0.0004 MRayl. Reflection coefficient approaches 1.0 — nearly total reflection. No signal penetrates. This is why gel is non-negotiable: it eliminates the skin-air interface entirely.

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Brightness = Impedance Mismatch

The grayscale value of any pixel encodes the amplitude of the returning echo, which directly encodes the acoustic impedance mismatch at that boundary. White = large mismatch. Black = no mismatch (or no structure). The image is literally a map of impedance gradients.