For the holographic recording of the wave field of an object, a pattern created by the interference of the reference wave and the wave scattered by the object is used. Traditional holography requires mutual coherence of the reference and object-related beams. However, it has been shown in this work that the holographic recording of information concerning the object under study is possible without coherence between them, even by using radiation from different sources. Such recording can be carried out by employing subcycle or unipolar radiation pulses, when a resonant medium with a large phase memory time T₂ is used as the recording medium. In this case, the medium records the interference pattern formed by the subcycle or unipolar pulse reflected from the object and the polarization wave created by the same short pulse. Coherence is ensured by a polarization wave, which interacting with radiation reflected from the object induces a population grating in such a medium. This grating mimics the interference pattern in a similar holographic process with a monochromatic source having the wavelength equal to that corresponding to the resonant transition in the medium.