In the last few years, the efforts of many researchers have been focused on developing 3D real-time scanners. The use of 2D phased-array transducers makes it possible to steer the ultrasonic beam in all directions in the scanned volume. An unacceptably large amount of transducer channels (more than 4,000) must be used, if the conventional phased array transducers are extrapolated to the 2D case. To decrease the number of channels, sparse arrays with different aperture apodization functions in transmit and receive apertures have to be designed. The design is usually carried out in 1D, and then transferred to a 2D rectangular grid. In this paper, five different 2D array transducers have been considered and their performance was compared with respect to spatial and contrast resolution. An optimization of the element placement along the diagonals using vernier arrays is suggested. The simulation results of the ultrasound fields show a decrease in the grating-lobe level of 10 dB for the diagonally optimized 2D array transducers compared to the previously designed 2D arrays which did not consider the diagonals.