  In this paper, we present the optimal use of coded signals in diverging wave
transmission for fast ultrasonic imaging. The performance of coded imaging with
diverging waves, quantified by SNR, CNR, speckle power and target signal
strength, is optimized in terms of code length, wave profile, aperture size and
field of view. We obtained one frame in 200 microseconds using coded diverging
wave transmission, equivalent to very high 5000 frames/s rate, where the
imaging depth is 7.5 cm. The performances of coded diverging wave transmission
and conventional single focused phased array imaging are compared on a single
frame basis. Complementary Golay sequences with code lengths ranging from 2 to
10 bits are used to code the signal. The signal strength and SNR obtained using
synthetic transmit aperture and conventional single focused phased array
imaging techniques, respectively, are used as reference in the performance
analysis. We present a method to determine the optimum diverging wave profile
to maximize the SNR across the entire viewing sector, which matches the
received signal strength distribution to that of synthetic transmit aperture
imaging. Optimum diverging wave profiles are determined for different sector
angles and for different array apertures. For 90{\deg} sector, the SNR of 8-bit
coded signal with optimized diverging wave profile is higher than that of
conventional single focused phased array imaging at all depths and regions
except the focal region, where it is 2-8 dB lower.
