The resolution of the ultrasound system is a measure of how small details can be imaged. In an ultrasound system, there are different mechanisms that determine radial resolution (in the direction of the beam) and lateral resolution (across the beam). Figure 5 shows the relationships between an object under imaging (on the left) and the image. See the fact box for the relevant formulas. Normally, the resolution perpendicular to the beam (lateral resolution) is worse than the radial resolution. Radial resolution improves, the shorter the transmitted pulse waves are. 
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<img src="/elaring/fag/ultralyd/teknologi/figur5.jpg" height="250">
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Figure 5: a) Scanning of two point-shaped objects, the probe with the sound wave to the left. b) The resulting ultrasound image. Notice that the lateral resolution is significantly worse than the radial resolution. 
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Since a short pulse wave has a higher frequency than a long one, it requires a bigger frenquency bandwidth from the probe. In the 90s, new techniques and ceramic composite material made it possible to make probes with bandwidth 50-80% of the ultrasound frequency, and the trend is moving toward 100% relative bandwidth. Therefore, radial resolution is normally only a few wavelengths. Lateral point size is dependent on the relationship between the wavelength and the size of the probe, it increases linearly with the distance from the probe. This is in contrast to radial point size which is independent of distance. 
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In contrast to, for example radar and sonar, ultrasound displays objects near the probe. This is also a characteristic that is in common with optics, and therefore one needs to focus the beam. This is illustrated in figure 6. A probe with size D that is focused on depth F is shown. The figure shows lateral beam width with depth towards the right. Focusing results in an optimal depth area, depth sharpness, as shown in the figure. In the ultrasound instrument, this focusing is done automatically upon signal reception. This is called dynamic focusing. On larger probes, you can often adjust the transmitting focus manually. 
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<img src="/elaring/fag/ultralyd/teknologi/figur6.jpg" width="500">
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Figure 6: Beam width for a transducer with aperture D to the left in the picture. The focal point is at distance F and the depth sharpness is LF. 
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From what has been said about resolution, it should be an advantage to have the biggest possible probe in order to get the best possible lateral resolution. However, there are other limitations to take into account. In cardiology, the distance between the ribs restricts the size of the probe to ca 20 mm. Imaging of blood vessels in, for example, the throat and imaging of internal organs like the liver and kidneys do not have such restrictions. Other restrictions that can play a role are price of the equipment, as bigger probes generally require more electronical channels. For high quality equipment, physical limitations due to small aberrations in the tissue will limit the benefit of bigger probes.