Holographic interferometry is an effective and rich method for measuring very small (order of a wavelength) deformations of an object and is widely used for non-destructive testing. In this work, the use of photorefractive materials for implementing real time phase shifting holographic interferometry is examined in detail. Bragg and non-Bragg orders generated during two-and multi-beam coupling in a photorefractive material can be used to retrieve the deformation of the object, or the phase information of the object. In previous work, it has been shown that object deformation can be determined from monitoring Bragg and non-Bragg orders. Preliminary experiments for determining the depth profile of an object have been reported, along with approximate analytic solutions for the Bragg and non-Bragg orders for the case of interacting plane waves. In this work, the exact solutions of Bragg and non-Bragg orders are found from numerically solving the interaction equations in a photorefractive material. It is shown that if the grating written in the material using two waves is read out by a reference and the object, the resulting Bragg and non-Bragg orders contain the information of the object phase, and is dependent on material parameters and the writing and reading beam intensities. Similarities and differences between this dynamic holographic technique and the traditional phase shifting digital holography are extensively discussed.