The comparison of phase-unwrapping algorithms has been an enigma because there has been no quantitative means of comparison. Noting that unwrapping routines are sensitive to noise and the local gradient of the phase array as well as fringe modulation, we have linked unwrapping performance to the gradient of first failure of the algorithm. When the gradient of first failure is plotted versus the signal-to-noise ratio, this can be used as an indicator of which algorithm to use in a given situation without the need for user intervention during the measurement and calculation. This study introduces three algorithms developed for their trade-offs in speed versus pixel noise (pointwise) sensitivity. The algorithms developed have been applied to live, noisy measurement data and have been proven to be robust.
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