Quantitative phase imaging in Hadamard-based active single-pixel microscopy by the motionless transport of intensity equation.

In this Letter, a method to achieve quantitative phase imaging (QPI) on Hadamard-based single-pixel microscopy (HSPM) is presented. A motionless implementation of the transport of intensity equation (TIE) supported by a focus-tunable lens (FTL) is reported for HSPM. The presented approach enables the use of digital micromirror devices (DMDs) instead of the typically implemented phase-only modulators utilized in QPI single-pixel imaging (SPI). Photobleaching and phototoxicity are minimized under the proposed approach. A minimal light-sample interaction is guaranteed by the DMDs' achievable frame rates, the structured illumination approach, and the use of high-sensitive photodiodes. The feasibility of this method is validated by imaging a calibrated phase-only USAF test target of different height steps. Additionally, epithelial cheek cells are imaged under low-power conditions, 240 µW, to validate the effectiveness of phase retrieval for biological samples.