Second-order gradient (SOG) toroidal and unidirectional microphones derived using a first-order gradient sensor (FOG) and a reflecting plane are described. The FOG is positioned with its axis illustratively orthogonal to and suspended a few centimeters from a large acoustically reflecting surface. The resulting sensor image is phase reversed resulting in a transducer that is a linear quadrupole. The linear quadrupole can be described by two dimensions, the distance corresponding to the FOG's dipole distance and twice the distance from the reflecting plane. If the reflecting surface is large enough or if the wall of an enclosure is used, the resulting microphone becomes a SOG unidirectional microphone. The perfect match between the sensor and its image from a good acoustic reflector results in an ideal SOG microphone with 3 dB beam width of .+-.33.degree. and no grating lobes below about 3 kHz for a spacing from the reflecting plane of about 2.5 cm. A wall-mounted toroid can be formed by using two FOGs at right angles to each other and with the axis of each sensor at 45.degree. to the reflecting surface and a spacing between transducers that is twice the height of the transducers from the reflecting plane. A table-mounted toroid can be realized by properly combining a filtered version of a suspended FOG and an omnidirectional sensor flush mounted to the reflecting table-top. Other arrays of image-derived directional sensors are applied to hands-free telephoning and other noise and reverberation-reducing arrangements.