Single pixel quantitative phase imaging with spatial frequency projections

•Single pixel imaging is a powerful method that enables robust imaging in scattering media and integration of information not accessible to conventional camera imaging.•We demonstrate a method of common-path single pixel quantitative phase microscopy that opens the ability for phase imaging in new spectral regions, such as short wave infrared and mid infrared.•A general theory for single pixel intensity and quantitative phase microscopy is presented.•Simultaneous imaging of quantitative phase, absorption, and fluorescence through spatial frequency projections recorded on two separate detectors.•Single pixel quantitative phase images are presented in both forward and back scattered geometries, and quantitative images of absorption, phase, and fluorescence are shown in cultured cells.•Single pixel quantitative phase imaging is described with scattering theory to provide an intuitive understanding of the object spatial frequency information collected in both forward and back scattered geometries. We introduce a new single pixel imaging technique that automatically co-registers quantitative phase and incoherent image modalities through the simultaneous acquisition of identical object spatial frequency information. The technique consists of using a time varying groove density diffraction grating to produce a reference and scan beam. The interference between the beams produce time varying spatial frequencies in the sample. The collected light on a single pixel detector produces a time trace that allows easy recovery of coherent and incoherent contrast mechanisms. We derive theory for the quantitative phase and show excellent agreement with experimental data and numeric model. Additionally, we derive a general theory of single pixel quantitative phase theory that can be applied broadly to general methods that use a sequence of modulated light patterns for single pixel phase imaging.