Overview
This lecture covers the physics of echoes in ultrasound, focusing on reflection, transmission, and refraction at tissue interfaces, and explains key rules, terms, and calculations for understanding image formation.
What Are Echoes?
- Echoes are sound waves reflected back to the transducer after hitting tissue interfaces in the body.
- Ultrasound imaging relies on these echoes to create images, with different echo strengths producing various shades of gray.
- At each interface, sound can be absorbed, reflected, scattered, refracted, or transmitted.
Types of Reflection and Scattering
- Specular reflection occurs at large, smooth boundaries (e.g., diaphragm, vessel walls), creating strong, bright, linear echoes when sound is perpendicular.
- Diffuse reflection happens at large but rough surfaces, sending weaker echoes in many directions, making up much of tissue texture seen in images.
- Scattering comes from small, irregular structures, producing weak echoes in random directions, leading to the "acoustic speckle" pattern in images.
- Rayleigh scattering occurs with very small reflectors (like red blood cells) and increases drastically with higher frequency.
Reflection and Transmission Physics
- Most sound energy is transmitted deeper; only a small fraction returns as echoes.
- Reflection strength depends on the difference in impedance (resistance to sound) at the interface.
- Impedance (Z) is calculated as Z = density × propagation speed for the medium.
Key Rules of Reflection and Transmission
- Rule 1: Energy cannot be created or destroyed; incident intensity = reflected + transmitted intensity.
- Rule 2: With normal (90°) incidence, no reflection occurs if impedances are equal.
- Rule 3: With equal impedances and normal incidence, all energy is transmitted (100% transmission).
- Rule 4: Outcomes of reflection/transmission with oblique incidence are unpredictable.
- Rule 5: For oblique incidence, the angle of reflection equals the angle of incidence.
- Rule 6: Refraction (bending) occurs only if there is oblique incidence and different propagation speeds on either side.
Intensity Coefficients & Calculations
- Intensity Reflection Coefficient (IRC): % of incident intensity reflected; calculated as reflected intensity / incident intensity × 100.
- Intensity Transmission Coefficient (ITC): % of incident intensity transmitted; ITC = 100 - IRC.
- Small impedance mismatch = low IRC, large mismatch = high IRC, equal impedance = IRC of 0%.
Refraction and Snell's Law
- Refraction: Bending of the transmitted wave if sound crosses an interface at oblique incidence into a medium with a different speed.
- Snell's law: Relates incident and transmission angles to propagation speeds (not usually calculated directly in exams).
- Three refraction scenarios:
- Equal speeds: No refraction, incidence angle = transmission angle.
- Medium 1 speed > Medium 2: Incidence angle > transmission angle.
- Medium 1 speed < Medium 2: Incidence angle < transmission angle.
Key Terms & Definitions
- Impedance (Z) — Resistance to sound in a medium; Z = density × propagation speed.
- Incident Intensity — Original sound beam’s energy before hitting an interface.
- Reflection Intensity — Energy portion reflected back to the transducer.
- Transmission Intensity — Energy portion continued through the interface.
- Normal Incidence — Sound strikes the boundary at 90° (perpendicular).
- Oblique Incidence — Sound strikes the boundary at any angle other than 90°.
- Specular Reflector — Large, smooth boundary producing strong, organized echoes.
- Diffuse Reflector — Large but rough boundary creating scattered, weaker echoes.
- Scattering — Random reflection from small, irregular structures.
- Rayleigh Scattering — Organized scattering by very small structures, highly frequency-dependent.
- Refraction — Change in direction of transmitted sound due to speed difference.
- Snell’s Law — Formula describing relationship between angles and speeds across an interface.
Action Items / Next Steps
- Focus study on vocabulary, key rules, and understanding the principles (not complex calculations).
- Practice intensity coefficient calculations and review provided activity questions for further reinforcement.