We present a quantitative phase imaging microscope based on a Shack-Hartmann sensor, that directly reconstructs the optical path difference (OPD) in reflective mode. Comparing with the holographic or interferometric methods, the SH technique needs no reference beam in the setup, which simplifies the system. With a preregistered reference, the OPD image can be reconstructed from a single shot. Also, the method has a rather relaxed requirement on the illumination coherence, thus a cheap light source such as a LED is feasible in the setup. In our previous research, we have successfully verified that a conventional transmissive microscope can be transformed into an optical path difference microscope by using a Shack-Hartmann wavefront sensor under incoherent illumination. The key condition is that the numerical aperture of illumination should be smaller than the numerical aperture of imaging lens. This approach is also applicable to characterization of reflective and slightly scattering surfaces.
We present a reference-less and time-multiplexing phase retrieval method by making use of the digital micromirror device (DMD). In this method, the DMD functions not only as a flexible binary mask which modulates the optical field, but also as a sampling mask for measuring corresponding phases, which makes the whole setup simple and robust. The DMD reflection forms a sparse intensity mask in the pupil which produces speckle pattern after propagation. With the recorded intensity on the camera and the binary pattern on the DMD, the phase in all the ‘on’ pixels can be reconstructed at once by solving inverse problems with iterative methods, for instance using Gerchberg-Saxton algorithm. Then the phase of the whole pupil can be reconstructed from a series of binary patterns and speckle patterns. Numerical experiments show the feasibility of this phase retrieval method and the importance of sparse binary masks in the improving of convergence speed.