Signal and image processing operations, such as convolution, correlation, and phase conjugation, have been implemented by holographically recorded filtering elements placed in the Fourier plane of a coherent telecentric imaging system. ~1 The concept of holographic processing has been recently adopted for ultrafast temporal waveforms, generating a spectral hologram and achieving signal processing capabilities on ultrafast waveforms. ~(2,3) By recording spatial-domain holograms and reading them out with temporal waveforms, or vice-versa, the first spatial-temporal processors have been created.~(4-6) This interaction of spatial and temporal waves can be interpreted as a four-wave mixing process, a recording stage with two waves followed by readout with the third wave, generating the resultant output fourth wave.
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