A new type of transducer that measures the layer thickness at a small spot by spectroscopy is developed. It is made of piezoelectric copolymer film P(VDF-TrFE) with a concave annular structure. This transducer converges an ultrasonic wave on the specimen surface with oblique incidence. The layer thickness is estimated by means of a dip in the frequency spectrum of a reflected wave. Theoretical analysis using the angular spectrum theory and experimental evaluation of the transducer are described. The transducers operate in a frequency range from 7 MHz to 90 MHz. The output variation when the transducer scans a thin wire is in good agreement with a calculation of a line spread function. The lateral and axial resolutions estimated by the calculation of a point spread function are 0.61 lambda and 8.05 lambda, respectively.