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This paper proposes a new approach for the analysis of reconstructed interference fields in digital holographic interferometry. In the proposed approach the interference phase to be estimated is conceived as a piecewise polynomial signal; consequently, each segment of the reconstructed interference field is modeled as a polynomial phase signal (PPS) with constant or slowly varying amplitude. The unwrapped phase distribution is then directly computed using the maximum likelihood estimation. Salient features of the proposed approach are: it provides accurate phase estimation from a single record of the interference field; it avoids cumbersome and error- prone filtering and 2D unwrapping procedures; and it paves the way to adapt well-established PPS analysis tools available in signal processing literature for the phase estimation in holographic interferometry.