# Practical Guide to Ultrasound Beam Forming: Beam Pattern and Image Reconstruction Analysis
## 5 Synthetic Aperture Beam Forming  
Synthetic aperture is a beam-forming approach that originates from the world of radar and was first implemented for medical ultrasound imaging in the late 1960s and early 1970s [40; 41]. In its basic implementation, only one element is excited for every transmission event [42]. In the receive phase, all of the elements of the array are used to receive the echo signals, and a low quality image is generated for every transmission event. The key aspect is that every point of the image is obtained by taking into account the geometrical distance between each transmitting element and each receiving element. Thus, assuming a constant speed of sound through the imaging volume, appropriate phase sets are used to compensate for the differences in the arrival time. Subsequently, the received time-compensated signals are added together.  
As a result, the images that are obtained for each transmission are combined to obtain an image of higher quality in terms of spatial resolution, contrast, and penetration depth with respect to the images obtained for every transmission. Thus, focusing is performed for every pixel in the image, and applied both in the transmit phase (indirectly by recombining the images formed with a single emitter) and the receive phase. As a consequence, the highest possible spatial resolution for delay-and-sum beam forming is obtained everywhere in the image [43]. However, the signal-to-noise ratio and penetration depths are significantly degraded by the array aperture being minimized in transmission, since only one element is active. Transmitting with sub-apertures rather than with a single element can mitigate this phenomenon [44; 45; 46]. However, the accuracy in the image reconstruction given by the availability of the data as obtained from the entire transmitting-receiving pairs of elements is lost, which deteriorates the spatial resolution. Once again, improving the performance with respect to a given imaging feature implies accepting that there will be a loss in performance with respect to another.  
An interesting approach based on frequency division multiplexing has been proposed to improve the SNR and penetration depth without losing access to the full element-to-element data set [47]. Similarly to the case discussed for MLT, the available transducer bandwidth is divided into sub-bands. During each transmission, all of the elements are active, with each operating at one specific sub-band. During consecutive transmissions, every element is active at a different sub-band, and the entire bandwidth is covered. In the receive phase, band-pass filters are used to separate and identify the signal coming from the different elements. Using this approach, the entire aperture is active for every transmission event, and the achievable SNR and penetration depth are thus improved. Another possibility is to use chirp signals in transmission, and a matched filter in the receive phase. Particular attention to the signal properties is needed when chirp signals are used, so as to avoid temporal side lobes. Furthermore, additional processing steps and the ability of the hardware to generate well-controlled electrical signals is also required. However, this approach can improve penetration depth and axial resolution [48; 49; 50]. It is also important to note that if only one element is active for every transmission event, this implies that the time that is needed to collect all of the signals necessary to form an image is maximized, which in other words means minimizing the frame rate. However, not all of the elements of the array need to be used in transmission. In this way, a higher frame rate can be achieved. On the other hand, this will lower the spatial resolution and increase the amplitude of the side-lobes and their effect on the final image [51].