2D Imaging – Comprehensive Study Notes

Principles of 2D Image Creation

• Ultrasound systems convert electrical energy → mechanical (sound) energy → back to electrical signals to form images.
• Fundamental assumptions:
– Sound travels in a straight line within tissue.
– Lateral resolution improves when the sound beam is narrow; therefore systems purposely narrow the beam through focusing.
• Challenge: A single pulse cannot cover a wide area; modern scanners emit many pulses in rapid succession and assemble them into a 2-D frame.
• Key term – “scan line”: the path traced by each emitted-and-received pulse pair.

Image Generation Workflow

• Step-by-step sequence:

1. Beam former sends precisely timed voltage spikes to active elements.
2. Elements vibrate, emit pulses that propagate into tissue.
3. Reflected echoes return; crystal elements convert mechanical vibrations to voltages.
4. Receiver applies time-varying gain, dynamic receive focusing, and digital signal processing.
5. Scan converter and display build a 2-D image from thousands of scan lines at video-rate (≈30–60 fps).

Transducer Fundamentals

• Characteristics governing image quality:
– Shape & number of active elements (PZT crystals).
– Ability to redirect (steer) beams.
– Degree and method of focusing for each beam.
– Consequent image shape (rectangular, sector, trapezoidal, blunted sector, etc.).
– Sensitivity to damage: loss of individual or all scan lines depending on array type.

Mechanical Transducers

• Hardware: Single round disc-shaped PZT crystal.
• Steering: Entire crystal physically rotates/moves by a motor, sweeping out a fan/sector pattern.
• Focusing options:
– Internal (concave PZT)
– External (acoustic lens)
• Image shape: Classic sector/fan with apex at transducer center.
• Failure mode: Any damage ruins the whole probe; no redundancy.

Linear Phased Arrays

• Construction: 100–300 small elements across a compact face, each \frac14–\frac12 λ wide.
• No mechanical parts; steering & focusing achieved electronically (phasing).
• Image: Sector or fan originating from a tiny footprint—useful between ribs or at cardiac windows.
• Sonographer control:
– Adjustable depth.
– Adjustable transmit focus; often offers multi-focus.
• Damage pattern: Loss or erratic lines corresponding to malfunctioning elements.

Phased Array Physics & Beam Manipulation

• All elements fire nearly simultaneously; each produces a spherical wavelet (Huygens’ Principle).
• Constructive/destructive interference → single, shaped beam.
• Beam steering:
– A linear time slope in excitation spikes = tilt; greater slope ⇒ larger steering angle.
– Electronics accomplishing this is the beam former.
• Transmit focusing:
– Outer crystals excited slightly earlier than inner ones, forming a curved wavefront.
– No slope (but curvature) focuses straight ahead; combined slope+curvature steers & focuses.

Multiple Foci & Dynamic Receive Focusing

• Multi-focus transmit:
– Same scan line fired several times with different curvatures.
– Greatest curvature → shallow focus; least curvature → deepest.
– Improves lateral resolution at many depths; cost = lower frame rate.
• Dynamic Receive Focusing:
– System introduces depth-dependent delays during reception.
– Occurs automatically; not user-adjustable.
– Continuously tightens the beam as echoes return, maintaining optimum focus for every depth.

Annular Phased Arrays

• Geometry: Concentric ring crystals (bull’s-eye).
• Steering: Mechanical only (rotate entire assembly); electronic steering not feasible ring-to-ring.
• Focusing: Each ring provides a different focal zone; activating inner→outer rings progressively deepens focus.
• Image: Fan/sector similar to mechanical probes.
• Failure mode: Damage to a ring causes an annular band of information loss.

Linear Sequential Arrays (LSA)

• Layout: 120–250 rectangular elements placed in a straight line; each ≈1 λ wide; footprint up to 10 cm.
• Firing pattern:
– Small groups (≈10 elements) fire in sequence → produce parallel beams yielding a rectangular image.
– Groups overlap to prevent gaps.
• Steering & focusing:
– Electronic focusing in the scan plane via curved excitation patterns.
– Receive focusing via variable delays.
• Damage: Vertical dropout (corresponding to element column).

Curvilinear (Convex) Arrays

• Same operational principles as LSA but elements arranged on a bowed surface.
• 120–250 crystals, each ≈1 λ wide; footprint as large as 10 cm.
• Firing groups generate beams that diverge, producing a blunted sector (“curved-top trapezoid”).
• Electronic focusing & dynamic receive focusing identical to LSA.
• Widely used for abdominal and obstetric scanning—large FOV with good near-field contact.

Vector Arrays

• Hybrid of LSA + phased array.
• 150–250 elements; combines group firing with electronic sloping delays.
• Produces trapezoidal images—rectangular near field, diverging far field.
• Clinically valuable when wide near-field plus extended sector are both needed (e.g., vascular access + deep survey).

Spatial Resolution Parameters

• Axial Resolution (depth): Determined by SPL; \text{Axial} = \frac{\text{SPL}}2. Constant for given probe & frequency.
• Lateral Resolution (azimuthal): Beam width within imaging plane.
• Elevational (slice-thickness) Resolution: Beam height above/below imaging plane; identical to lateral resolution when using a true disc crystal (mechanical or annular probes).
• Focal point: Depth where beam width/narrowness (and thus lateral resolution) is best.
• Diagram terms from slide 20: imaging plane, elevational plane, focal point, etc.

Side Lobes & Grating Lobes

• Side lobes: Produced by single-element transducers; off-axis energy → erroneous echoes → degrade lateral resolution.
• Grating lobes: Analogous phenomenon in arrays due to multiple elements.
• Both create artefactual structures because system assumes echoes originate along main axis.

Apodization (Lobe Suppression)

• Technique: Vary excitation voltage across array.
• Stronger voltages to inner elements; weaker to outer → smooth intensity profile, reducing grating lobes.

Dynamic Aperture

• “Aperture” = effective receiving (or transmitting) aperture = number of active elements engaged.
• System increases aperture size with depth to keep beam uniformly narrow.
• Improves lateral resolution over entire image without changing physical probe size.

Practical, Ethical, & Clinical Connections

• Probe care: Mechanical transducers are vulnerable—damage = total probe loss; arrays offer partial redundancy but still require gentle handling.
• Multi-focus & dynamic aperture enhance diagnostic confidence but lower frame rate—sonographer must balance resolution vs. temporal resolution (e.g., fetal heart vs. liver lesion).
• Understanding beam behaviour is essential for artefact recognition (side lobes, grating lobes) and safe operation (ALARA: adjusting depth, focus, power responsibly).

Key Numerical References & Equations

• Element width in phased array: 0.25\,\text{–}\,0.5\,\lambda.
• Element width in LSA/CSA: \approx 1\,\lambda.
• SPL (spatial pulse length): \text{SPL}=#\text{cycles}\times\lambda.
• Axial resolution: \text{R}_{axial}=\frac{\text{SPL}}2.
• Beam steering angle (simplified): \theta \propto \frac{\Delta t}{d} where \Delta t is time delay, d element spacing.

All numerical values and formulae derived from principles outlined in Edelman (2007), Understanding Ultrasound Physics, 3rd ed.