Sound Beams

Sound Beam Shape

• As ultrasound propagates, the beam’s width is not constant.
  • At the transducer face: width ≈ transducer diameter.
  • Immediately thereafter: beam narrows in a funnel-like fashion until it reaches its smallest diameter (the focus).
  • Beyond the focus: beam diverges or spreads out again.

Anatomical Regions of a Sound Beam

• Near Zone (Fresnel Zone)
  • Region from the transducer surface to the focus.
  • Beam gradually narrows.
• Focus / Focal Point
  • Location where the beam diameter is MINIMUM.
  • For a disc-shaped crystal: focal width = ½ of transducer diameter.
• Focal Zone
  • Region centered around the focus where the beam remains relatively narrow.
  • Produces the highest-quality echoes; best image detail.
  • ≈ ½ of the focal zone lies in the near field, ½ in the far field.
• Far Zone (Fraunhofer Zone)
  • Begins at the focus, extends deeper.
  • Beam diverges with increasing depth.
  • At a depth of two near-zone lengths (NZLs) the beam diameter ≈ transducer diameter.
  • Deeper than two NZLs: beam becomes wider than the crystal.

Near Zone (Fresnel) Characteristics

• Ends at the focus.
• Depth of this region is termed focal length / focal depth / near-zone length.
• Determined by transducer diameter & operating frequency (for fixed-focus probes).

Focal Depth (Near-Zone Length)

• Distance from crystal to focus.
• Adjustable on phased-array systems (electronic focusing).
• For fixed-focus probes the controlling factors are:
  • Transducer diameter (aperture).
  • Frequency of emitted sound.

Mathematical Relationships

• Direct relationships (fixed focus):
  • Larger diameter ⇒ deeper focus.
  • Higher frequency ⇒ deeper focus.
• Standard formulas
  • $Focal\ depth\,(cm)=\frac{\big(diameter\,(mm)\big)^2\times frequency\,(MHz)}{61.6}$
  • $Focal\ depth\,(cm)=\frac{\big(diameter\,(mm)\big)^2}{40\times wavelength\,(mm)}$

Far Zone (Fraunhofer) Characteristics

• Begins immediately after the focus.
• Divergence increases with depth.
• Focal zone occupies the very proximal portion of the far field.

Beam Divergence Relationships

• Small crystal diameter ⇒ greater divergence.
  • Diameter & divergence are inversely related.
• Low frequency ⇒ greater divergence.
  • Frequency & divergence are inversely related.
• Larger elements therefore improve far-field lateral resolution.

The Frequency Dilemma

• Imaging probes often need high frequency for resolution but small diameter for superficial focusing.
• Small, high-frequency crystals yield a shallower focus despite the higher frequency’s natural tendency toward depth.

Diffraction & Huygen’s Principle

• Huygen’s Sources: each tiny segment of the PZT acts as an individual point source generating V-shaped (spherical) wavelets.
• Interference of millions of wavelets combines to form the classic hour-glass beam profile observed in ultrasound.
• When crystal size ≈ wavelength, individual spherical waves dominate, producing wide “V” shaped beams (diffraction patterns).

Lateral Resolution ("LATA")

• Acronyms: Lateral, Angular, Transverse, Azimuthal.
• Describes the system’s ability to distinguish two reflectors that lie side-by-side (perpendicular) to the main beam axis.
• Units: distance (mm).
• Determined solely by beam width.
  • Narrower beam ⇒ better lateral resolution.
• Basic expression:
  • $Lateral\ resolution\,(mm)=Beam\ diameter\,(mm)$

Axial vs. Lateral Resolution

• Axial (along beam) resolution is usually better (numerically lower) because pulses are shorter than beams are wide.
• Lateral resolution is best at the focus/focal zone (where beam is narrowest).
• If two reflectors are closer together than beam width ⇒ only one echo displayed.

Effect of Frequency on Resolution

• Higher frequency probes:
  • Shorter pulses ⇒ improved axial resolution.
  • Less far-field divergence ⇒ improved lateral resolution.

Focusing Techniques (Improve Lateral Resolution)

• Goal: concentrate energy into a narrower beam.

Fixed (Mechanical/Conventional) Focusing

• Focal depth & extent of focusing are unchangeable.

1. External Focusing
   • Acoustic lens placed in front of PZT.
   • Greater lens curvature ⇒ stronger focusing.
2. Internal Focusing
   • Curved PZT surface itself concentrates energy.
   • Most common fixed-focus method.

Electronic (Phased-Array) Focusing

• Achieved by delaying excitation times across multiple elements.
• Allows operator to move focus and use multiple focal zones.
• Available only in multi-element (array) transducers.

Consequences of Focusing a Beam

• Near-field & focal-zone beam diameter ↓ (narrower ⇒ better lateral resolution).
• Focus moves closer to the transducer (shallower focal depth).
• Far-field diameter ↑ (divergence beyond focal zone increases).
• Overall focal-zone length (depth range of best resolution) ↓.

Practical, Ethical & Clinical Implications

• Optimal image quality hinges on correct selection of frequency, aperture, and focusing method.
• Over-focusing may compromise deeper structures (wider far field).
• Phased-array systems offer flexibility, but require diligent user adjustment to avoid diagnostic errors.

Numerical Quick-Reference

• Depth where beam = transducer diameter: ≈ 2 NZLs.
• Focal width (disc crystal): ≈ ½ transducer diameter.
• Lateral resolution ≈ beam width at any given depth.

Key Takeaways

• Beam shape transitions: wide (at crystal) → narrow (focus) → diverging (far field).
• Focal characteristics dictated by diameter & frequency; both directly proportional to focal depth.
• Divergence inversely related to diameter and frequency.
• Highest image detail arises in the focal zone; adjust focus to region of clinical interest.
• Focusing enhances lateral resolution but alters near/far field geometries—balance accordingly.