Single-pixel complementary compressive sampling spectrometer

• A novel compressive spectroscopy method using complementary sampling is proposed.
• A single-pixel complementary compressive sampling spectrometer is presented.
• Only a single detector is required; this has implications for specialized cases.
• Extremely high-quality spectral recovery is achieved using the proposed design.
• This surpasses the performance of conventional single-pixel spectroscopy.

A new type of compressive spectroscopy technique employing a complementary sampling strategy is reported. In a single sequence of spectral compressive sampling, positive and negative measurements are performed, in which sensing matrices with a complementary relationship are used. The restricted isometry property condition necessary for accurate recovery of compressive sampling theory is satisfied mathematically. Compared with the conventional single-pixel spectroscopy technique, the complementary compressive sampling strategy can achieve spectral recovery of considerably higher quality within a shorter sampling time. We also investigate the influence of the sampling ratio and integration time on the recovery quality.