8.2 Acoustic Impedance, Reflection, Refraction & Scattering

Acoustic Impedance: The Property That Decides Everything

Acoustic impedance (symbol z) is the medium's opposition to the passage of sound, defined as:

z = density × propagation speed = ρ × c

It is measured in Rayls (kg/m²·s). Representative values: air ≈ 0.0004 × 10⁶ Rayls, fat ≈ 1.38 × 10⁶ Rayls, soft tissue ≈ 1.6–1.7 × 10⁶ Rayls, and bone ≈ 7.8 × 10⁶ Rayls. Impedance itself never generates an echo — echoes arise only at boundaries where impedance changes. A perfectly homogeneous medium, however dense, would return nothing. The grayscale image is literally a map of impedance mismatches.

Normal Incidence and the Reflection Coefficient

Normal incidence means the beam strikes the boundary at a 90° (perpendicular) angle. Here the behavior is simple: part of the intensity reflects straight back and the rest transmits onward with no change of direction. The intensity reflection coefficient (IRC) depends exclusively on the impedance mismatch:

IRC = [(z2 − z1) ÷ (z2 + z1)]² and ITC = 1 − IRC

where ITC is the intensity transmission coefficient. Conservation of energy demands that reflected plus transmitted intensity equal the incident intensity.

Mismatch Worked Examples

Work one through by hand. At a muscle/fat boundary with z₁ = 1.7 and z₂ = 1.38 (×10⁶ Rayls): the difference is 0.32 and the sum is 3.08, so IRC = (0.32 ÷ 3.08)² ≈ (0.104)² ≈ 0.011 — only about 1% of the intensity reflects, and 99% transmits to image deeper structures. Now the soft-tissue/bone boundary with z₁ = 1.63 and z₂ = 7.8: difference 6.17, sum 9.43, IRC = (0.654)² ≈ 0.43 — about 43% reflects from bone, far more than from any soft-tissue pairing, and the remaining beam is largely absorbed within bone, so almost nothing returns from behind it. At soft tissue/air the mismatch is so extreme the fraction approaches 1: virtually 100% reflects.

Two clinical corollaries follow. First, the soft-tissue/air mismatch is so extreme that even a microscopic film of air between transducer and skin reflects the entire beam — this is why coupling gel (impedance close to soft tissue) is mandatory to displace air. Second, gas-filled bowel and lung are impenetrable barriers, and bone casts the familiar acoustic shadow; scanning strategies in the abdomen are largely exercises in finding acoustic windows around these two obstacles.

Oblique Incidence: Reflection Angles and Refraction

Oblique incidence means the beam meets the boundary at any angle other than 90°. Two events occur:

• Reflection follows the mirror rule: incident angle = reflected angle, measured from the perpendicular. At oblique angles the reflected echo may travel away from the transducer and never be received — which is why specular boundaries (diaphragm, gallbladder wall, organ capsules) are brightest when interrogated perpendicularly and can fade when insonated obliquely.
• Refraction is the change in direction of the transmitted wave as it crosses a boundary where propagation speed differs. It obeys Snell's law: sin(transmission angle) ÷ sin(incident angle) = c2 ÷ c1. If the second medium is faster, the beam bends away from the perpendicular; if slower, toward it. Two conditions are required for refraction: oblique incidence AND a speed difference across the boundary. At normal incidence the transmission angle is 0° and no bending occurs, regardless of the speed change. If speeds are equal on both sides, oblique incidence still produces no refraction.

Refraction violates the machine's core display assumption that sound travels in straight lines. The resulting refraction artifact duplicates or laterally misregisters structures — a classic example is the duplicated (ghosted) aorta or SMA seen when the midline rectus muscles and fat refract the beam. Edge (refraction) shadowing is the same physics at the curved margins of round structures such as cysts, vessels, or the fetal head: the beam bends at the tangent, leaving a thin anechoic shadow fanning out from the edge. Unlike the dirty shadowing of air, edge shadows are thin, clean, and geometric.

Scattering and Rayleigh Scattering

Not all boundaries are large and smooth. When the beam encounters structures smaller than or comparable to the wavelength, or rough irregular surfaces, energy is redirected in many directions at once — scattering. The portion redirected back toward the transducer is backscatter, and it is responsible for the internal texture of solid organs: liver parenchyma, splenic architecture, and thyroid echogenicity are all rendered by scattered rather than specular echoes. Scattering is weaker than specular reflection and angle-independent, which is why parenchyma stays visible over a range of insonation angles.

Rayleigh scattering is the special case in which the scattering structure is much smaller than the wavelength. The definitive biological example is the red blood cell (≈ 7 µm across, versus a wavelength of hundreds of µm at clinical frequencies). Rayleigh scattering intensity rises with frequency to the fourth power (f⁴): doubling frequency increases scattered intensity sixteen-fold. This steep frequency dependence explains why higher frequencies are favored for detecting weak blood-flow echoes. Rayleigh scattering from moving red blood cells is the source of the blood-flow Doppler signal in vascular imaging — every spectral tracing and color pixel originates as this weak, omnidirectional backscatter from erythrocytes, not as specular reflections from vessel walls.