Improving the accuracy of ultrasonic touch sensing and fingerprint imaging using acoustic impedance matching is disclosed. Acoustic impedance mismatches between an ultrasonic transducer array and a sensing plate can be reduced to maximize energy transfer and minimize parasitic reflections. A reduction in acoustic impedance mismatches can be accomplished using (i) a composite epoxy having a higher acoustic impedance than epoxy alone, (ii) one or more matching layers having an acoustic impedance that is approximately the geometric mean of the acoustic impedance of the sensing plate and the acoustic impedance of the transducer array, (iii) pores or perforations in the sensing plate, or (iv) geometric structures formed in the sensing plate. In addition, parasitic reflections can be suppressed using an absorbent layer.