## 1 Introduction  
Quantitative phase imaging is particularly useful for the investigation of biological thin tissue sections, which are generally transparent and hence do not show high amplitude contrast in a conventional optical microscope. It is therefore not easy to visualize such cells unless a staining is applied, which is time-consuming and may harm or even kill the cell and hence change their natural behavior. For translucent samples, the scattered light (which contains all the structural information about the object) is 90\({}^{\circ}\) out of phase to the unscattered light. When the object is weak (first Born approximation), this means that the modulus of the image (hence its intensity) is negligibly affected by the scattered waves. Conventional Zernike phase contrast microscopy [1] partly resolves this problem by reducing the amplitude of the undiffracted light and by introducing an additional 90\({}^{\circ}\) phase shift into the diffracted light. In the image, both terms (scattered and unscattered) now interfere strongly (they are in phase or anti-phase with one another), greatly increasing the visibility of the specimen. However, conventional Zernike phase contrast microscopy is not quantitative and suffers from artifacts, such as \"halos,\" which surround the edges of phase structures in the specimen and result in a reduced resolution. Other phase contrast imaging techniques such as differential interference contrast (DIC) do not suffer under loss of resolution, but DIC still does not yet result in quantitative phase imaging. In fact, DIC is a two-beam interference method with a lateral shear that approximately matches the microscope's resolution. It is hence sensitive to the phase gradient. Attempts have been made to recover the quantitative phase using spatial light modulators as an adjustable phase delay unit in Zernike phase contrast microscopy [2], called Spatial Light Interference Microscopy (SLIM) with the delay applied to phase ring, or in DIC, called Gradient Light Interference Microscopy (GLIM) [3] with the delay applied in the Fourier domain followed by an integration of the recovered phase gradient. However, SLIM still suffers from halo artifacts and loss of resolution, and GLIM suffers from the lack of directional sensitivity, which in detail means that it is insensitive to structural details oriented in a direction perpendicular to the shear direction. Instead of constant phases steps, various different shears have been applied in Reference [4] in order to recover the phase quantitatively. On the other hand, the well-established digital holography only works well outside the laboratory environment if measures, such as pulsed laser light (freeze the motion in time) or common path geometries (both arms experience same environment), are applied in order to reduce the impact of disturbing environmental conditions on the recorded hologram. In rare cases of single-cell imaging can Gabor holography or lateral shearing interferometry be applied to recover the phase quantitatively. In these particular cases, the specimen only covers a small fraction of the field of view. Hence, the specimen region can by means of lateral shearing be brought into interference with a neighboring region, where light has passed through in an undiffracted manner. This approach offers a robust and compact solution to recover the phase. However, it is limited to the imaging of a few cells only. Instead, our endeavor is the imaging of thin tissue in order to discard the labeling in histopathology. Iterative quantitative phase imaging can cover the aforementioned shortcomings via the recording of multiple diffraction patterns, which are then computer processed in an iterative manner to recover the quantitative phase. A key to phase retrieval imaging is the recording of the same information on multiple speckle decorrelated patterns. Many techniques have been developed based on this principle, such as the recording of two or more diffraction patterns at different planes [5].