A triacetone triperoxide cloud associated with a triacetone triperoxide explosive attached to a hard target is remotely detected by operating differential-absorption lidar lasers to transmit a laser beam toward the hard target at differing wavelengths. A backscattered laser beam reflected from the lidar target (hard target, person, aerosols, clouds, buildings) is detected because a cloud of triacetone triperoxide in front of the lidar target and between the lidar target and the differential-absorption lidar system produces a differential-absorption signal having characteristics that identify the triacetone triperoxide. In a second embodiment, a triacetone triperoxide cloud that is absorbing optical radiation from its ambient environment and which is attached to a hard target is detected from a location remote from the triacetone triperoxide explosive by detecting an optical radiation absorption signature characterized by triacetone triperoxide absorption lines.