The present subject matter provides apparatus and methods for physically fitting a hearing assistance device, including mathematically characterizing a person's ear canal. The apparatus includes a housing adapted to be mechanically coupled to the person in proximity to the person's outer ear. An ultrasonic transducer array is located within at least a portion of the housing. The apparatus includes electronics within the housing, the electronics adapted to control the transducer array to alternate between transmitting and receiving ultrasonic energy. In various embodiments, a processor is adapted to characterize geometry of the ear canal using information from the ultrasonic transducer array obtained from scans of the ear canal.