Compressive sensing based on optical mixing using a spectral shaper with bipolar coding.

Photonic compressive sensing (CS) has attracted great research interest for its potentials in the acquisition of wideband sparse signals with relatively low sampling rate. The photonic CS scheme based on optical mixing using a spectral shaper can realize the mixing of a sparse signal with a high-speed pseudo-random bit sequence (PRBS), but avoids the use of high-speed electronics. In this approach, by utilizing the frequency-to-time mapping (FTTM) of chirped pulses, the spectral information on the spatial light modulator (SLM) within a spectral shaper can be projected into the time-domain waveform. However, the generated PRBS in the time domain is a unipolar sequence that alternates between 0 and 1, which leads to a nonzero-mean measurement matrix. This would result in a poorer performance of signal reconstruction compared to that with a zero-mean measurement matrix. Moreover, the length of PRBS that can be recorded in the SLM is also limited by the far-field condition. In this paper, we propose an optical mixer for photonic CS, which utilizes an SLM-based spectral shaper with complementary outputs as well as a balanced photodetector in order to generate bipolar PRBS. The performance of signal reconstruction can be significantly improved owing to the zero-mean measurement matrix induced by bipolar PRBS. In addition, the constraint on the length of PRBS can be greatly alleviated, since the obtained PRBS can still be kept zero-mean even if the PRBS is longer than that the far-field condition demands. Experimental and simulation results are presented to demonstrate the feasibility and advantage of the given approach.