week 2- day 3 UT200

Refraction definition

The bending or alteration in propagation direction of a sound wave as it crosses a boundary into a second medium.

Two absolute criteria required for refraction

1. Oblique incidence (angle other than 90 degrees); 2. Different propagation speeds between the two media (c1 cannot equal c2).

Can refraction occur at normal incidence (90 degrees)?

No. Refraction NEVER occurs at 90-degree incidence, regardless of how different the sound speeds are.

Can refraction occur if propagation speeds are identical (c1 = c2)?

No. If sound speeds are identical, the sound beam travels straight through without bending, regardless of the incident angle.

Snell's Law equation

sin(theta_i) / sin(theta_t) = c1 / c2 (where theta_i is incident angle, theta_t is transmission angle, and c1/c2 are sound speeds).

Reference line used to measure acoustic angles in Snell's Law

The normal line, which is an imaginary perpendicular line drawn at 90 degrees to the tissue interface.

Refraction behavior when Medium 2 is faster than Medium 1 (c2 > c1)

Sound bends AWAY from the normal line; transmission angle is greater than incident angle (theta_t > theta_i).

Refraction behavior when Medium 2 is slower than Medium 1 (c2 < c1)

Sound bends TOWARD the normal line; transmission angle is less than incident angle (theta_t < theta_i).

Refraction behavior when Medium 2 equals Medium 1 speed (c2 = c1)

No bending occurs; the beam continues completely straight (theta_t = theta_i).

Degree of refraction definition and formula

The absolute difference between incident and transmitted beams: Degree of Refraction = |theta_t - theta_i|.

Calculate degree of refraction if incident angle is 60 deg and transmitted angle is 80 deg

|80 deg - 60 deg| = 20 degrees of refraction (bending away from normal).

Fundamental machine assumption violated by refraction

The assumption that sound travels in a straight line directly to and from a reflector.

Lateral displacement / duplication artifact mechanism

Sound bends upon oblique entry, but the ultrasound system assumes a straight path, mapping the returning echo side-by-side or duplicated laterally.

Classic clinical example of lateral duplication artifact

Duplicated gestational sac, bladder, or uterus caused by beam refraction through the paired rectus abdominis muscles.

Direction of image duplication in refraction artifacts

Lateral displacement (structures appear side-by-side, never deeper or shallower axial displacement).

Condition required for the Critical Angle to exist

Sound must travel from a SLOWER medium into a FASTER medium (c2 > c1) at an oblique angle.

Critical angle definition

The incident angle at which the transmission angle reaches exactly 90 degrees along the boundary interface.

Total internal reflection

Occurs at or beyond the critical angle when 100% of acoustic energy reflects back into Medium 1, with zero sound transmitted into Medium 2.

Edge shadowing (refractive shadow) mechanism

Sound strikes the curved margins of a cystic or rounded structure at grazing oblique incidence, causing sound divergence and total internal reflection away from the path.

Sonographic appearance of refractive edge shadows

Thin, hypoechoic or anechoic vertical acoustic dropout bands extending deep from the lateral curved margins of structures (e.g., cysts, gallbladder, fetal head).