This paper presents a 591×438-DPI ultrasonic fingerprint sensor. The sensor is based on a piezoelectric micromachined ultrasonic transducer (PMUT) array that is bonded at wafer-level to complementary metal oxide semiconductor (CMOS) signal processing electronics to produce a pulse-echo ultrasonic imager on a chip. To meet the 500-DPI standard for consumer fingerprint sensors, the PMUT pitch was reduced by approximately a factor of two relative to an earlier design. We conducted a systematic design study of the individual PMUT and array to achieve this scaling while maintaining a high fill-factor. The resulting 110×56-PMUT array, composed of 30×43-μm² rectangular PMUTs, achieved a 51.7% fill-factor, three times greater than that of the previous design. Together with the custom CMOS ASIC, the sensor achieves 2 mV kPa^-1 sensitivity, 15 kPa pressure output, 75 μm lateral resolution, and 150 μm axial resolution in a 4.6 mm×3.2 mm image. To the best of our knowledge, we have demonstrated the first MEMS ultrasonic fingerprint sensor capable of imaging epidermis and sub-surface layer fingerprints.