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This paper demonstrates that the precise phase controllability of an opticalfrequency comb enables all-optical signal processing for the first time. Anovel all-optical Hilbert transform is presented with precise control ofrelative carrier-phase and envelope of optical pulse train based on frequencycontrol utilizing an optical frequency comb. With the proposed all-opticalsignal processing method, fully non-scanning one-shot three-dimensional (3D)imaging can be realized with high image resolution. The technique can beapplied to coherent phase imaging simultaneously. A precise pair of90$^\circ$-phase-shifted optical pulses over the entire spectral bandwidth canbe generated based on the precise optical phase controllability of an opticalfrequency comb, thereby facilitating a real-time and precise all-opticalHilbert transform to obtain amplitude and phase of optical signal in a singleshot of ultrashort pulses. In our experiments, we realized single-shot 3Dimaging with an uncertainty of 5 $\rm{\mu}$m and obtained a surface profilewith a resolution of 200 $\times$ 200 pixels.

Fully non-scanning three-dimensional imaging using an all-optical Hilbert transform enabled by an optical frequency comb