Abstract: Classical tomography method usually only considers the intensity reconstruction of the object, and often loses the phase, but the phase contains the information of the depth, shape, refractive index and so on of the surface of the object, which is more important than the intensity. As a classical phase retrieval algorithm,the Transport of Intensity Equation can directly calculate the phase from the known intensity. In this paper, a new algorithm can reconstruct the phase information of objects by tomography.The proposed algorithm is improved based on the high-order Transport of Intensity Equation to obtain higher precision phase results, and then reconstruct the three - dimensional phase information of the object through filtered back projection. Adding rotation center correction steps to the back projection reconstruction process makes the results more accurate. The experimental results show that the algorithm can obtain high precision three-dimensional phase reconstruction results while solving the low phase accuracy caused by intensity differential approximation constraints.

Key words: Tomography, High-order Transport of Intensity Equation, Multi-plane iteration, Phase retrieval, Intensity differential