This paper describes a new form of acoustical and microwave holography which obviates the need for a real or electronically simulated reference wave. The use of linear (rather than square-law) detectors permits recording of the instantaneous non-time-averaged object wave potential within the acoustic or microwave cycle rather than the intensity of the sum of an object wave and a reference wave time-averaged over many cycles. The time at which the recording is made is the reference rather than a real or electronically simulated reference wave. To achieve the effect of a plane reference wave making an angle &thgr; with the hologram plane, it is necessary to record the object wave potential instantaneously along a straight line on the hologram at the same time as the recording line is swept with velocity v across the plane in the direction perpendicular to the line. Then sin&thgr; = a/v, where a is the speed of the acoustic or microwave radiation. The feasibility of this method is demonstrated by recording and reconstructing a 4.8-MHz temporal reference acoustical hologram made with a Sokolov ultrasonic camera system.