*Appl Opt ; 58(2): 436-445, 2019 Jan 10.*

##### RESUMEN

When recovering smooth phases by phase unwrapping algorithms, many noniterative algorithms are available. However, normally those algorithms offer approximations of the current phase that cannot be accurate enough. This is because the majority of them are based on global approaches instead of local ones. Although smooth estimations are not often expected in phase reconstructions for real applications, a smooth initial guess could be useful for robust iterative techniques. Therefore, based on the most recent local polynomial approaches, we propose a simple least-squares fitting of the partial derivatives of the phase, normally estimated from the wrapped operator, by considering local polynomial models of the phase up to the third order. Synthetic and real data of wrapped phases are considered in our work.

*Appl Opt ; 57(10): 2727-2735, 2018 Apr 01.*

##### RESUMEN

In order to recover the holographic object information, a method based on the recording of two digital holograms, not only at different planes but also in a slightly off-axis scheme, is presented. By introducing a π-phase shift in the reference wave, the zero-order diffracted term and the twin image are removed in the frequency domain during the processing of the recorded holograms. We show that the zero-order elimination by the phase-shifted holograms is better than working with weak-order beam and average intensity removal methods. For recording experimentally two π-shifted holograms at different planes slightly off-axis, a single cube beam splitter is used. Computer simulations and experimental results, carried out to validate our proposal, show a high accuracy of π/14 that can be comparable with phase-shifting digital holography. For high fringe spacing, our proposal could be applied in electron holography, avoiding high voltage in a biprism.

*J Opt Soc Am A Opt Image Sci Vis ; 35(1): 35-44, 2018 Jan 01.*

##### RESUMEN

Several built-up indices have been proposed in the literature in order to extract the urban sprawl from satellite data. Given their relative simplicity and easy implementation, such methods have been widely adopted for urban growth monitoring. Previous research has shown that built-up indices are sensitive to different factors related to image resolution, seasonality, and study area location. Also, most of them confuse urban surfaces with bare soil and barren land covers. By gathering the existing built-up indices, the aim of this paper is to discuss some of their advantages, difficulties, and limitations. In order to illustrate our study, we provide some application examples using Sentinel 2A data.

*Appl Opt ; 56(4): 1215-1224, 2017 Feb 01.*

##### RESUMEN

In a previous work, we introduced the concept of transversal aberrations {U,V} calculated at arbitrary Hartmann-plane distances z=r [Appl. Opt.55, 2160 (2016)APOPAI1559-128X10.1364/AO.55.002160]. These transversal aberrations can be used to estimate the wave aberration function W, as well as the classical transversal aberrations {X,Y} calculated at a theoretical plane z=f, where f is the radius of a reference semisphere. However, when the ray identification is difficult to achieve at z=f, the use of {U,V} can be of great help. In the context of a least-squares fitting of the Hartmann data, the use of {U,V} is proposed by analyzing some simple examples for the case of a W with aberration terms up to the third order. These examples also consider the hypothesis fâ«W, as presented in the majority of the optical applications.

*Appl Opt ; 55(9): 2160-8, 2016 03 20.*

##### RESUMEN

In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z=f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X,Y} calculated at the plane z=f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U,V} calculated at any arbitrary Hartmann-plane distance z=r. We also show how to directly estimate the wavefront surface w from the information of {U,V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z=f.

*J Opt Soc Am A Opt Image Sci Vis ; 32(1): 35-45, 2015 Jan 01.*

##### RESUMEN

In optical design, many error functions can be used to generate an optical system with desired characteristics. These error functions are optimized by iterative algorithms. However, these error functions should be theoretically and mathematically differentiable to be optimized. In this paper, the differentiability of an error function is partially justified. The error function herein is called the projection functional. This proposed projection functional can be used to estimate the coefficients of an arbitrary lens with conic surfaces by means of the spot distributions on two planes produced by a fixed Hartmann plate. The differentiability of the projection functional is required to guarantee the existence of its Jacobian matrix, which is a suitable condition to minimize this functional by iterative methods. Numerical examples of the functional minimization are given.

*J Opt Soc Am A Opt Image Sci Vis ; 30(8): 1670-9, 2013 Aug 01.*

##### RESUMEN

The Fourier analysis of two-stage phase-shifting (TSPS) algorithms is growing in interest as a research topic, specifically, the algorithm's insensitivity properties to various error sources. The main motivation of this paper is to propose TSPS algorithms that perform well in the face of detuning and harmonics for each of the two sets of interferograms with different or equal reference frequencies. TSPS algorithms based on the development of generalized equations consider both the frequency sampling functions that represent them and nonconstant phase shifts.

*J Opt Soc Am A Opt Image Sci Vis ; 29(4): 431-41, 2012 Apr 01.*

##### RESUMEN

From generalized phase-shifting equations, we propose a simple linear system analysis for algorithms with equally and nonequally spaced phase shifts. The presence of a finite number of harmonic components in the fringes of the intensity patterns is taken into account to obtain algorithms insensitive to these harmonics. The insensitivity to detuning for the fundamental frequency is also considered as part of the description of this study. Linear systems are employed to recover the desired insensitivity properties that can compensate linear phase shift errors. The analysis of the wrapped phase equation is carried out in the Fourier frequency domain.

*Appl Opt ; 51(9): 1257-65, 2012 Mar 20.*

##### RESUMEN

A simple phase estimation employing cubic and average interpolations to solve the oversampling problem in smooth modulated phase images is described. In the context of a general phase-shifting process, without phase-unwrapping, the modulated phase images are employed to recover wavefront shapes with high fringe density. The problem of the phase reconstruction by line integration of its gradient requires a form appropriate to the calculation of partial derivatives, especially when the phase to recover has higher-order aberration values. This is achieved by oversampling the modulated phase images, and many interpolations can be implemented. Here an oversampling procedure based on the analysis of a quadratic cost functional for phase recovery, in a particular case, is proposed.

*Appl Opt ; 50(21): 4083-90, 2011 Jul 20.*

##### RESUMEN

In this manuscript, some interesting properties for generalized or nonuniform phase-shifting algorithms are shown in the Fourier frequency space. A procedure to find algorithms with equal amplitudes for their sampling function transforms is described. We also consider in this procedure the finding of algorithms that are orthogonal for all possible values in the frequency space. This last kind of algorithms should closely satisfy the first order detuning insensitive condition. The procedure consists of the minimization of functionals associated with the desired insensitivity conditions.

*Appl Opt ; 49(32): 6224-31, 2010 Nov 10.*

##### RESUMEN

In this work, we have developed a different algorithm than the classical one on phase-shifting interferometry. These algorithms typically use constant or homogeneous phase displacements and they can be quite accurate and insensitive to detuning, taking appropriate weight factors in the formula to recover the wrapped phase. However, these algorithms have not been considered with variable or inhomogeneous displacements. We have generalized these formulas and obtained some expressions for an implementation with variable displacements and ways to get partially insensitive algorithms with respect to these arbitrary error shifts.