Frequency-steered acoustic arrays transmitting and/or receiving multiple, angularly dispersed acoustic beams are used to generate 2D and 3D images. Input pulses to the arrays are generally non-linear, frequency-modulated pulses. Frequency-steered acoustic arrays may be provided in one-dimensional linear and two dimensional planar and curvilinear configurations, may be operated as single order or multiple order arrays, may employ periodic or non-periodic transducer element spacing, and may be mechanically scanned to generate 2D and 3D volumetric data. Multiple imaging fields of view may generated in different directions by switching the polarity of phase-shifted array transducer elements. Multiple frequency-steered arrays arranged in an X-configuration provide a wide, contiguous field of view and multiple frequency steered arrays arranged in a T-configuration provide orthogonally oriented fields of view. Methods and systems for operating acoustic arrays in a frequency-steered mode in combination a mechanical beam steering mode, electronic time-delay and phase shift beam forming modes, and phase comparison angle estimation modes are also provided.