Ultrasound Beam Physics: Resolution, Penetration & Focusing

simulator intermediate ~10 min
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Beam width = 2.25 mm at 60 mm focus

A 5 MHz transducer with 20 mm aperture focused at 60 mm produces a beam width of 2.25 mm at the focal point — sufficient resolution for most abdominal imaging.

Formula

λ = c / f (where c = 1540 m/s in soft tissue)
Beam width at focus: w = 1.22 × λ × F / D
Attenuation: I(z) = I₀ × exp(-2αfz)

Sound Beyond Hearing

Ultrasound — sound waves above 20 kHz — is one of medicine's most versatile imaging tools. Operating at frequencies of 1 to 15 MHz, medical ultrasound produces real-time images without ionizing radiation, making it safe for fetuses, children, and repeated examinations. The physics of beam formation, focusing, and tissue interaction determines what clinicians can see and at what detail.

Beam Formation and Focus

An ultrasound transducer emits a beam that naturally converges to a focal point in the near field, then diverges in the far field. Electronic focusing — achieved by delaying signals from individual array elements — can steer and focus the beam at any desired depth. The focal beam width, approximately 1.22λF/D, sets the lateral resolution. This simulation visualizes the beam profile and lets you optimize the frequency-aperture-focus trade-off.

Resolution vs Penetration

The fundamental trade-off in ultrasound is between resolution and penetration. Higher frequencies produce shorter wavelengths and finer resolution but are attenuated more rapidly by tissue. At 5 MHz, soft tissue attenuates the signal by about 2.5 dB per centimeter of round-trip travel. The maximum useful depth occurs where the returning echo is too weak to distinguish from noise — typically around 40 dB of two-way loss.

Clinical Applications

Ultrasound spans an extraordinary range of applications: obstetric imaging to monitor fetal development, echocardiography to assess heart function, musculoskeletal imaging to guide injections, and high-intensity focused ultrasound (HIFU) for non-invasive tumor ablation. Advances in contrast agents, elastography, and super-resolution imaging continue to expand what sound waves can reveal about the human body.

FAQ

How does ultrasound imaging work?

Ultrasound imaging sends high-frequency sound pulses (1-15 MHz) into the body. When the pulses encounter boundaries between tissues of different acoustic impedance, part of the energy reflects back. The transducer detects these echoes, and their timing and amplitude are used to construct an image of internal structures.

What determines ultrasound resolution?

Axial resolution (along the beam) depends on pulse length — shorter pulses (higher frequency) give better resolution. Lateral resolution depends on beam width at the depth of interest — narrower beams give finer detail. There is a fundamental trade-off: higher frequency improves resolution but reduces penetration depth.

What is the near-field of an ultrasound transducer?

The near field (Fresnel zone) extends from the transducer surface to the natural focal point at N = D²/(4λ). Within this region, the beam narrows. Beyond it (the far field), the beam diverges. Electronic focusing can place the focal point within or beyond the natural near-field length.

Why does ultrasound attenuate in tissue?

Tissue absorbs ultrasound energy and converts it to heat. Attenuation increases linearly with frequency — approximately 0.5 dB/cm/MHz in soft tissue. This means a 10 MHz signal loses 5 dB per centimeter, limiting practical imaging depth to about 3-4 cm at high frequencies.

Sources

Embed

<iframe src="https://homo-deus.com/lab/acoustics/ultrasound/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub