Fig. 6: Principle diagram of the high-throughput single-pixel compressive holography.

A complex-valued object \(O\left(\mathop{r}\limits^{ \rightharpoonup }\right)=A\left(\mathop{r}\limits^{ \rightharpoonup }\right){e}^{i\phi \left(\mathop{r}\limits^{ \rightharpoonup }\right)}\) can be expressed as the superposition of a complete set of orthogonal Hadamard basis \({H}_{n}\left(\mathop{r}\limits^{ \rightharpoonup }\right)\) with corresponding coefficients. To retrieve these coefficients, one can illuminate the object with a series of Hadamard-like patterns \({\widetilde{H}}_{n}\left(\mathop{r}\limits^{ \rightharpoonup }\right)\) (with components “0” and “1”) generated by the DMD. To implement heterodyne holography, a beat frequency \(\triangle f\) is introduced between the signal beam and the reference beam, enabling a time-varying signal that can be measured by the photodetector. The simple linear transformation between \({\widetilde{H}}_{n}\left(\mathop{r}\limits^{ \rightharpoonup }\right)\) and \({H}_{n}\left(\mathop{r}\limits^{ \rightharpoonup }\right)\) allows the reconstruction of holographic images with pure amplitude patterns. DMD: digital micromirror device; BS: beam splitter; PD: photodetector.