Sound Beams and Ultrasound Resolution

Sound Beam Formation and Characteristics

• Sound beams are created through the combination of numerous small wavelets.
• These wavelets interact via constructive and destructive interference, resulting in an hourglass-shaped beam pattern.
• This specific formation is known as a diffraction pattern and is described by Huygens' Principle.
• The sound beam represents the width or diameter ($D$) of an ultrasound pulse as it moves away from the transducer face.
• The width of the sound beam is not constant; it varies based on its distance from the transducer.
• Because the beam diameter changes with distance, the sound intensity within the beam also varies accordingly.

Transducer Scanning Planes

• Ultrasound imaging utilizes two primary scanning planes:
• Main scanning plane: This plane is responsible for determining axial resolution and lateral resolution.
• Perpendicular plane: This is also known as the Z-axis, elevational resolution, or slice thickness. It contributes to the partial volume artifact.

Sound Beam Intensity and Artifacts

• Sound intensity within the beam is variable due to the changing beam diameter.
• Intensity is at its highest point at the focus.
• Some acoustic energy unintentionally travels outside the path of the main beam axis, resulting in side lobes or grating lobes.
• These lobes manifest as imaging artifacts.
• Side Lobes: These occur primarily with single-element or mechanical transducers.
• Grating Lobes: These are similar to side lobes but occur specifically in array transducers due to the presence of multiple active elements.

Methods for Lobe Reduction

• Side and grating lobes can be mitigated through two specific techniques:
• Apodization: This process involves applying higher electrical voltages to the central transducer elements and lower voltages to the outer elements. This distribution reduces the energy in the side lobes.
• Subdicing: This involves dividing a single crystal element into smaller sub-elements. These sub-elements are then electrically connected to function as a single unit, which helps reduce grating lobes.

Anatomy of a Sound Beam

• The sound beam is divided into specific regions:
• Near Zone: Also referred to as the Fresnel zone or near field. It is the region extending from the transducer face and narrowing gradually until it reaches the focus.
• Far Zone: Also referred to as the far field or Fraunhofer zone. This region starts beyond the focus, where the beam begins to diverge or spread out.
• Focal Zone: This is the specific region where the beam diameter is at its minimum; the diameter here is known as the beam diameter at the focus.
• Near Zone Length (NZL): The distance measured from the transducer face to the focal point.

Determining Near Zone Length (NZL)

• The NZL is influenced by three primary factors:
  1. Transducer crystal diameter.
  2. Transducer frequency ($f$).
  3. Transducer aperture.
• Frequency Relationship: Frequency and NZL are directly related. High frequencies result in a longer near zone length, while lower frequencies result in a shorter near zone length.
• Diameter Relationship: Transducer crystal diameter and NZL are directly related. A larger diameter provides a longer near zone length, while a smaller diameter results in a shorter near zone length.

Transducer Variable Aperture

• Also known as dynamic aperture, this refers to the number of active elements used to emit ultrasound pulses.
• When imaging shallow depths, a smaller aperture is used (fewer crystal elements are active).
• When imaging greater depths, a larger aperture is utilized (more crystal elements are active).
• Consequences of increasing the aperture:
  • The NZL is increased.
  • The focus is positioned deeper.
  • The beam diameter becomes narrower at the focus.
• The primary purpose of increasing aperture at depth is to maintain a narrow beam at the focus to improve lateral resolution.
• The ultimate limit for beam narrowing is determined by wavelength, aperture, and focal length.

Ultrasound Image Resolutions

• There are three types of imaging resolution:
  1. Detail resolution.
  2. Contrast resolution.
  3. Temporal resolution.
• Contrast and temporal resolutions are directly related to the ultrasound instruments.
• Detail resolution is more directly related to the transducer itself.
• Detail resolution encompasses two main aspects: Axial resolution and Lateral resolution.
• Traditionally, ultrasound transducers exhibit better axial resolution than lateral resolution.

Axial Resolution (LARRD)

• Axial resolution is also known by the acronym LARRD:
  • Longitudinal.
  • Axial.
  • Radial.
  • Range.
  • Depth.
• It is the ability to distinguish two closely spaced reflectors that are positioned along the direction of the ultrasound beam.
• Units: Measured in millimeters ($mm$).
• Typical Values: Ranges from $0.1 \dots 1\,mm$. A smaller numerical value indicates superior resolution.
• Formula:   $\text{Axial resolution (mm)} = \frac{\text{Spatial pulse length (SPL) (mm)}}{2}$
• Improvements: Axial resolution is enhanced by:
  • Shortening the Spatial Pulse Length ($SPL$).
  • Shortening the wavelength.
  • Damping (to provide shorter pulses).
  • Increasing the transducer frequency.

Lateral Resolution (LATA)

• Lateral resolution is also known by the acronym LATA:
  • Lateral.
  • Angular.
  • Transverse.
  • Azimuth.
• It is the ability to distinguish two closely spaced reflectors that are side-by-side, or perpendicular to the ultrasound beam.
• Units: Measured in millimeters ($mm$).
• Formula: $\text{Lateral resolution (mm)} = \text{beam diameter}$.
• Because beam width varies with distance from the transducer, lateral resolution also varies with distance.
• Improvements: Lateral resolution is enhanced by:
  • Focusing the beam.
  • Using multiple focal zones.
  • Increasing the transducer aperture.
  • Utilizing harmonics imaging.

Elevational (Z) Resolution and Slice Thickness

• This is considered the third aspect of detail resolution.
• It is measured perpendicular to the imaging plane.
• Higher resolution is achieved when the scan plane is thinnest.
• Poor elevational resolution contributes to the partial volume artifact.
• Partial Volume Artifact: This artifact causes the "filling in" of structures that should be anechoic (echo-free). It occurs because echoes from structures outside the actual imaging slice are included in the final image. An example is the appearance of debris at the base of the bladder.
• Improvements: Elevational resolution is enhanced by:
  • Focusing.
  • Using harmonics.
  • Using disc-shaped crystals (common in mechanical and annular transducers).
  • Using transducers with 1.5D ($1\,and\,\frac{1}{2}\,D$) crystal arrays.

Unfocused Sound Beams

• An unfocused beam has a "natural" focus.
• Characteristics of an unfocused beam diameter:
  • At the start of the near zone, the beam diameter equals the transducer diameter.
  • At the focus (the end of the near zone), the beam diameter is exactly $\frac{1}{2}$ the transducer diameter.
  • At a distance of two near zone lengths (into the far field), the beam diameter returns to a size equal to the transducer diameter.
• In these beams, divergence begins immediately after the natural focus.

Effects and Methods of Beam Focusing

• Focusing narrows the beam in the near field and the focal zone, leading to improved lateral resolution.
• Consequences of Focusing:
  • Reduced near zone length (the focus moves closer to the transducer face).
  • Widened beam diameter in the far zone (which degrades lateral resolution in the far field).
  • A smaller focal zone.
• Mechanical Focusing:
  • This is fixed or conventional focusing, typically used with single-element transducers.
  • The focal depth is determined at manufacturing and cannot be adjusted by the operator.
  • External Focusing: Achieved by applying a LENS.
  • Internal Focusing: Achieved by used a curved PZT (Piezoelectric Crystal).
• Electronic Focusing:
  • This is used in array transducers.
  • It involves the use of multiple crystal elements to steer and focus the beam electronically.