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• The phase detection of physical lenses based on single-pixel common-path off-axis wavefront imaging is demonstrated. • The Fourier fringe analysis can avoid multi-step phase-shifting interference and reconstruct the target object more quickly. • Compared with the previously proposed SPI-based lens phase detection, the measurement speed of our method is increased by at least three folds. • A simple and cost-effective way for lens detection is proposed, which further propels the SPI technology toward practical application. The lens phase provides useful information about the optical path length, from which other key parameters of a lens can be calculated. Yet, the traditional 2D detector-based phase measurement methods are always limited by the specific spectral response range. Here, phase detection of the physical lens is accomplished via a single-pixel detector. The digital micromirror device (DMD)-based common-path off-axis single-pixel (DCOS) wavefront imaging system is established. Benefiting from the advantages of single-pixel detectors, this method is anticipated to be applied in specialist bands. In this method, the wavefront of a target object is reconstructed quickly by Fourier fringe analysis (FFA) from a hologram, which is obtained by the normal SPI technique. Thus, the measuring speed is at least three times faster than that achieved by multi-step phase-shifting. The average relative errors between the measured value and the calibrated value of focal lengths for 1000-mm and 500-mm optical lenses are 0.254% and 0.982%, respectively. Our work provides a fast, simple, and cost-effective way for phase detection of optical lenses and further enlarges the application scope of single-pixel wavefront imaging. [ABSTRACT FROM AUTHOR]

• Simultaneously amplitude and phase (i.e. spatial wavefront) imaging of a biological sample via DMD-based single-pixel phase-shifting interferometric techniques is demonstrated. • The experimental performances of those techniques for wavefront imaging of a biological sample are quantitatively and comprehensively compared, when different orthogonal bases, different reference strategies, and different modulation methods (i.e. binary grating, Lee, and super-pixel methods) are employed there. • Experimental results suggest that the grating-phase-shifting-based SWI using Hadamard basis (G-HSWI) performs best, in which one can use the checkerboard reference for the maximum field of view or select the peripheral reference for a better imaging resolution. • 2fps dynamic wavefront imaging of the sample at a 10 % downsampling rate with a resolution of 128 × 128 pixels can be realized by G-HSWI. Single-pixel wavefront imaging (SWI) is an innovative technique for simultaneously measuring the amplitude and phase of an unknown field, which is particularly important for wavefront imaging in invisible wavelengths and under low light conditions. However, most of the existing SWI techniques are still in the technical development stage. Here, we provide a comprehensive analysis and comparison of the SWI methods using DMD-based single-pixel multi-step phase-shifting interferometric techniques. Through experimental demonstrations, we first compare the performances of the techniques using the Hadamard basis, Fourier basis, and discrete cosine transform (DCT) basis. Further, the performances of the Hadamard basis-based SWI (HSWI) technique using phase-shifting interferometry with the different reference strategies are investigated while the binary grating, Lee, and super-pixel methods are applied to control the DMD for realizing the necessary complex amplitude modulations there. Experimental results suggest the grating-phase-shifting-based HSWI performs best, in which one can use the checkerboard reference for the maximum field of view or select the peripheral reference for a better imaging resolution; and it can do 2 fps wavefront imaging of the sample at 10 % downsampling rate with a resolution of 128 × 128 pixels. Our work provides researchers with a guideline to choose a suitable SWI technique for their applications. [ABSTRACT FROM AUTHOR]