A method is presented to reconstruct the geometry of specular reflectors with an ultrasonic array based on the image source principle. The ultrasonic beam is focused at a point in space emulating a point source within the medium. The transmitted wave interacts with the specular reflector and propagates back to the array as if it were generated by an image source. The reflected wave is analyzed with a sound source localization algorithm to estimate the image source location, and the reflector geometry is extracted using the mirror equation for spherical reflectors. The method is validated experimentally and its accuracy is studied. Under ideal conditions the method provides an accurate reconstruction of the position, orientation, and radius of curvature of specular reflectors, with errors Δr < 0.2 mm, Δα < 3°, and ΔR/R0 < 0.2, respectively. The method performs very well in the presence of high levels of thermal and speckle noise, with no degradation of the reconstruction as long as SNR(th) > -3 dB (signal-to-thermal-noise ratio) and SNR(sp) > 7 dB (signal-to-speckle-noise ratio). An iterative scheme based on the proposed method is presented to reconstruct the geometry of arbitrary reflectors by subdividing the reflector boundary into smaller segments. The iterative scheme is demonstrated both numerically and experimentally.