  This paper demonstrates that the precise phase controllability of an optical
frequency comb enables all-optical signal processing for the first time. A
novel all-optical Hilbert transform is presented with precise control of
relative carrier-phase and envelope of optical pulse train based on frequency
control utilizing an optical frequency comb. With the proposed all-optical
signal processing method, fully non-scanning one-shot three-dimensional (3D)
imaging can be realized with high image resolution. The technique can be
applied to coherent phase imaging simultaneously. A precise pair of
90$^\circ$-phase-shifted optical pulses over the entire spectral bandwidth can
be generated based on the precise optical phase controllability of an optical
frequency comb, thereby facilitating a real-time and precise all-optical
Hilbert transform to obtain amplitude and phase of optical signal in a single
shot of ultrashort pulses. In our experiments, we realized single-shot 3D
imaging with an uncertainty of 5 $\rm{\mu}$m and obtained a surface profile
with a resolution of 200 $\times$ 200 pixels.
