Simultaneous estimation of multiple phases in digital holographic interferometry using state space analysis

• Published in: Optics and lasers in engineering Vol. 104; pp. 109 - 116
• Main Authors: Kulkarni, Rishikesh, Rastogi, Pramod
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2018
• Subjects: Exponential phase signal; Multi-beam digital holographic interferometry; Multiple phase estimation; Polynomial phase approximation; State space analysis; Polynomial phase approximation; Exponential phase signal; Multi-beam digital holographic interferometry; Multiple phase estimation; State space analysis
• ISSN: 0143-8166; 1873-0302
• DOI: 10.1016/j.optlaseng.2017.08.016

•An algorithm for multiple phase estimation from an exponential phase signal recorded in multi-beam digital holographic interferometry is proposed.•The phases within a small size window around each pixel are approximated as first order polynomial functions of the local spatial coordinates.•The polynomial coefficient estimation is performed based on state space analysis.•An amplitude discrimination criterion is utilized by setting distinct beam intensities in order to evaluate the phases of each signal component in an unambiguous manner. A new approach is proposed for the multiple phase estimation from a multicomponent exponential phase signal recorded in multi-beam digital holographic interferometry. It is capable of providing multidimensional measurements in a simultaneous manner from a single recording of the exponential phase signal encoding multiple phases. Each phase within a small window around each pixel is appproximated with a first order polynomial function of spatial coordinates. The problem of accurate estimation of polynomial coefficients, and in turn the unwrapped phases, is formulated as a state space analysis wherein the coefficients and signal amplitudes are set as the elements of a state vector. The state estimation is performed using the extended Kalman filter. An amplitude discrimination criterion is utilized in order to unambiguously estimate the coefficients associated with the individual signal components. The performance of proposed method is stable over a wide range of the ratio of signal amplitudes. The pixelwise phase estimation approach of the proposed method allows it to handle the fringe patterns that may contain invalid regions.