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Phase microscopy modalities are extensively used to image living transparent biological samples because of their ability to obtain high contrast images without the use of enhancing agents. Quantitative phase techniques in particular provide valuable information that can be interpreted easily when the imaged object is optically thin, that is, when the thickness of the object is much less than the depth of field of the imaging system. However, many biological objects of interest have thicknesses comparable to or larger than the depth of field. This work focuses on the initial development of inversion techniques for phase images to reconstruct features of thick transparent samples. Our goal is to estimate the unknown indices of refraction of the object. We use a constrained boundary iterative approach under the assumption that the index of refraction inside the object can be approximated as piecewise constant. The boundary location of all inhomogeneities are obtained by combining the information provided by several phase imaging modalities. Initial results indicate the ability of our approach to find the indices of refraction from images of uniform objects.