08 Ultrasound

Reflection and transmission

Intensity reflection at a normal planar interface.

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Simulation

Reflection and transmission — Change the numbers; the scene follows.

Where it works

Ultrasound

Tissue path

Along the beam in tissue — impedance mismatch, Doppler shift, MI/TI at the focus.

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Formula

R = \left(\frac{Z_2-Z_1}{Z_2+Z_1}\right)^2,\quad T=1-R

Variables

Z₁ · Impedance of medium 1MRaylZ₂ · Impedance of medium 2MRayl

Results

r
Amplitude reflection
-0.0831
R
Intensity reflection
0.0069
T
Intensity transmission
0.9931
R
Intensity reflection
0.69%

Explanation

R = \left(\frac{Z_2-Z_1}{Z_2+Z_1}\right)^2,\quad T=1-R

What it means

At a normal interface the intensity reflection coefficient is [(Z₂−Z₁)/(Z₂+Z₁)]² and T = 1−R (energy conservation, no absorption). Tissue–tissue interfaces reflect a few percent; tissue–air reflects ~99.9%. This is a working relation in Ultrasound.

Where it is used

Clinically it sits on the Ultrasound — Tissue path. Along the beam in tissue — impedance mismatch, Doppler shift, MI/TI at the focus. Ultrasound equations sit on the probe face and along the beam: impedance, Snell, Doppler, MI and TI. They explain why gel matters, why aliasing appears, and why a mechanical index is on the screen.

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How to use it

Enter Z in MRayl (from the impedance calculator). Amplitude reflection r can be negative (phase inversion, e.g. tissue → air). Change one input and watch the curve and the simulation follow.

Symbols

Z₁Impedance of medium 11.63 MRayl
Z₂Impedance of medium 21.38 MRayl

Worked example

A typical case from the default values: Z₁ = 1.63 MRayl (Impedance of medium 1); Z₂ = 1.38 MRayl (Impedance of medium 2). Substituting into the relation gives r = -0.0831; R = 0.0069; T = 0.9931; R = 0.69 %. These are teaching numbers — align them with your machine.

Typical values give

r = -0.0831
R = 0.0069
T = 0.9931
R = 0.69%

Where it comes from

The displayed formula is the working relation. Intensity reflection at a normal planar interface. Usual reference: Bushberg. Derive it in the specialty lesson, then return here to pin the numbers.

Reference: Bushberg

Assumptions & limits

Normal incidence, no roughness, no mode conversion. Oblique incidence needs the full Rayleigh/Zoeppritz set and Snell’s law (see refraction).

Pitfalls

Soft-tissue 1540 m/s is an assumption — not a measurement in that patient. Doppler angle 90° gives no shift. MI and TI are on-screen estimates, not absorbed dose. Normal incidence, no roughness, no mode conversion. Oblique incidence needs the full Rayleigh/Zoeppritz set and Snell’s law (see refraction).

Keep this

Gel, angle, and assumed speed of sound — get those three right before you trust a centimetre. Normal incidence, no roughness, no mode conversion. Oblique incidence needs the full Rayleigh/Zoeppritz set and Snell’s law (see refraction).

In this specialty

Ultrasound