The quality-guided phase unwrapping algorithm is one of the most employed spatial algorithms due to its computational efficiency and robustness. It uses a quality map to guide the unwrapping process such that pixels are processed according to their quality values from highest to lowest. Several improvements have been proposed during the last few years with the purpose of using it in time-demanding applications. However, many of the proposals depend on the distribution of the values on the given quality map. In this paper, a novel pruning strategy based on a red-black tree data structure is proposed, whose complexity time is independent of the distribution of the given quality map. We take advantage of the partial ordering of the branches in a red-black tree together with a pruning strategy to speed up the unwrapping process. Experimental results, using real and simulated data, show that the complexity time of our proposal improves the existing quality-guide-based algorithms. Also, a series of interferometric patterns of a time-varying phase distribution experiment have been processed showing that our proposal can be used for real-time applications. The source code of the implemented algorithms is publicly available.

Single-pixel imaging is a technique that can reconstruct an image of a scene by projecting a series of spatial patterns on an object and capturing the reflected light by a single photodetector. Since the introduction of the compressed sensing method, it has been possible to use random spatial patterns and reduce its number below the Nyquist-Shannon limit to form a good quality image but with lower spatial resolution. On the other hand, Hadamard pattern based methods can reconstruct large images by increasing the acquisition measurement time. Here, we propose an efficient strategy to order the Hadamard basis patterns from higher to lower relevance, and then to reconstruct an image at very low sampling rates of at least 8%. Our proposal is based on the construction of generalized basis vectors in two dimensions and then ordering in zigzag fashion. Simulation and experimental results show that the sampling rate, image quality and computational complexity of our method are competitive to the state of the art methods.

In this work we present an experimental proposal to evaluate optical surfaces with high slopes or with infrared wavelengths based on the Ronchi test as well as on the concept of equivalent wavelength. A spatial modulator is used in the implementation of the Ronchi test, and a white LED with different color filters is employed in order to generate different wavelengths. Two Ronchigrams with incoherent light, each one for a different color, are registered and computationally processed, thus generating a third one with an equivalent wavelength. The results obtained show that it is possible to generate patterns with traditional rulings and substructured sequences of Katyl. Additionally, we discuss some of the limitations of employing different rulings. Finally, we found that appropriate image enhancing algorithms allow us to improve the visibility of the resulting fringes and thus obtain a better analysis.