An ultrasonic transducer array, and a method for manufacturing it, having a plurality of transducer elements aligned along an array axis in an imaging plane. Each transducer element includes a piezoelectric layer and one or more acoustic matching layers. The piezoelectric layer has a concave front surface overlayed by a front electrode and a rear surface overlayed by a rear electrode. The shape of each transducer element is selected such that it is mechanically focused into the imaging plane. A backing support holds the plurality of transducer elements in a predetermined relationship along the array axis such that each element is mechanically focused in the imaging plane.