Fast and accurate phase-unwrapping algorithm based on the transport of intensity equation

The phase information of a complex field is routinely obtained using coherent measurement techniques as, e.g., interferometry or holography. The obtained measurement result is subject to a 2π ambiguity and is often referred to as wrapped phase. Phase-unwrapping algorithms (PUAs) are commonly employed to remove this ambiguity and, hence, obtain the absolute phase. However, implementing PUAs can be computationally intensive, and the accuracy of those algorithms may be low. Recently, the transport of intensity equation (TIE) has been proposed as a simple and practical alternative for obtaining the absolute phase map. Nevertheless, an efficient implementation of this technique has not yet been made. In this work, we propose an accurate solution for the TIE-based PUA that does not require the use of wave-propagation techniques, as previously reported TIE-based approaches. The proposed method calculates directly the axial derivative of the intensity from the wrapped phase when considering the correct propagation method. This is done in order to bypass the time-consuming wave-propagation techniques employed in similar methods. The analytical evaluation of this parameter allows obtaining an accurate solution when unwrapping the phase map with low computational effort. This work further introduces the use of the iterative TIE-PUA that, in a few steps, improves significantly the accuracy of the final absolute phase map, even in the presence of noise or aliasing of the wrapped data. The high accuracy and utility of the developed TIE-PUA technique is proven by both numerical simulations and experiments for various objects.