The design issues for the technique of continuously programming a coherent transient spatial-spectral optical signal processor are discussed. The repeated application of two spatially distinct optical programming pulses to a non- persistent hole-burning material writes an accumulated, spatial-spectral population grating with low intensity optical pulses as compared to single shot programing. An optical data stream is introduced on a third beam, resulting in a processor output signal spatially distinct from all the input pulses. Programming and processing take place simultaneously, asynchronously and continuously. For accumulated gratings, the frequency stability of the optical source is an important consideration. Assuming a sufficiently stable optical source, simulations show that an accumulated (and maintained) grating in steady state, for both storage of a true-time delay and/or pattern waveform, can be highly efficient using currently available materials, on the order of that predicted for a perfect photon-gated device. An experimental demonstration of the continuous programming concept for true time delays programmed with chirped pulses is presented, showing the accumulation of the grating with low area pulses over time until it reaches steady state, for times longer than the persistence of the material.