Image Resolution in 2D Imaging: Spatial, Contrast, and Temporal Resolution

Spatial Resolution

• Spatial resolution is the ability to detect anatomically separate structures and display them distinctly.

• Types:

  • Axial Resolution

  • Lateral Resolution

Axial Resolution

• Definition: The ability to detect two structures along the axis of the beam as separate.

• Determined by spatial pulse length.

• Spatial Pulse Length:

  • The distance a pulse occupies in space (start to end).

  • Determined by wavelength and number of cycles in the pulse.

• Relationship between wavelength, propagation speed (c), and transducer frequency (f): $\lambda = \frac{c}{f}$

  • Inverse relationship between transducer frequency and wavelength.

  • Higher frequency → shorter wavelength → shorter spatial pulse length → improved axial resolution.

• High-frequency transducers improve axial resolution.

• Output Power and Gain:

  • Increased power/gain increases effective pulse length.

  • Optimized axial resolution: highest possible transducer frequency, low power, and low gain.

Lateral Resolution

• Definition: Ability to detect structures across the axis of the beam as separate.

• Related to beamwidth.

• A point structure appears as a short line on the screen, with the length equaling the beam width.

• Lateral resolution = beam width.

  • Best at the narrowest part of the beam (focal point).

• Beam can be narrowed by focusing and using higher frequency.

• Beam Width at Focus:

  • Determined by: $\lambda$ (wavelength), l (focal length), and d (diameter/aperture of the element).

• Higher frequency transducers improve lateral resolution.

• Optimized lateral resolution: focusing the beam, highest transducer frequency.

• Other factors also affect axial and lateral resolution.

Contrast Resolution

• Ability to differentiate anatomic structures with similar tissue characteristics and display them as different.

• Improved by:

  • Optimal machine settings (e.g., gain).

  • Reduction of electronic noise (e.g., harmonic imaging).

  • Harmonic imaging significantly improves contrast resolution.

Harmonic Imaging

• Reduces background noise.

• Fundamental Imaging:

  • A 3 MHz ultrasound pulse contains power in a range of frequencies around 3 MHz (bandwidth).

  • Sine wave distortion generates harmonics due to high-intensity transmit signals through tissue -> signal becomes more sawtoothed.

• Received echoes contain fundamental and harmonic frequencies.

  • Example: Transmitting at 3 MHz returns frequencies at 3 MHz (1st harmonic/fundamental) and 6 MHz (2nd harmonic).

  • Filtering out the fundamental frequency detects higher harmonic frequencies, ignoring weaker signals.

• Pulse Inversion Harmonics:

  • Two pulses are sent along each beam path at 180 degrees out of phase.

  • Fundamental frequency components cancel out during signal processing.

  • Second harmonic signals are added.

Temporal Resolution

• Ability to accurately portray moving structures.

• Related to frame rate (number of complete images displayed per second).

• Frame Rate:

  • Number of images produced per second.

  • Dependent on number of scan lines per frame and pulse repetition frequency (PRF).

• PRF is determined by the depth of penetration.

• Range Equation:

  • $Depth = \frac{Speed \times Time}{2}$

• Time to produce one scanline is calculated from a rearrangement of the range equation.

• Frame Rate Calculation:

  • $Frame Rate = \frac{1}{\text{Time to produce one image}}$

• Increasing imaging depth or number of scan lines will decrease the frame rate.

• Frame rate can be increased by:

  • Decreasing the depth of penetration.

  • Narrowing the 2D sector width (fewer scan lines).