Ricardo Legarda-Sáenz

Autonomous University of Yucatán

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Carlos Brito‐Loeza

Autonomous University of Yucatán

A. Espinosa-Romero

Autonomous University of Yucatán

Mariano Rivera

Mathematics Research Center

Jorge L. Flores

Icahn School of Medicine at Mount Sinai

Anabel Martín-González

Autonomous University of Yucatán

Guillermo García–Torales

Universidad de Guadalajara

Ramón Rodrı́guez-Vera

National Institute of Cardiovascular Diseases

Francisco J. Hernandez–Lopez

Colegio de Postgraduados

Alejandro Téllez-Quiñones

Consejo Nacional de Humanidades, Ciencias y Tecnologías

Iván de Jesús May-Cen

Tecnológico Nacional de México

Cooperative Institutions

Centro de Investigaciones en Optica

Autonomous University of Yucatán

Universidad de Guadalajara

Instituto Tecnológico de Mérida

University of Vermont

Mathematics Research Center

Brunel University of London

Universidad de Guanajuato

Universidad Nacional Autónoma de México

Bremen Institute for Applied Beam Technology

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Wavefront Reconstruction of Discontinuous Phase Objects Using Directional Derivatives

Ricardo Legarda-Sáenz Jorge L. Flores Matías Fernández Lakatos

Here, we present a model that uses directional derivatives to recover wavefronts from discontinuous data, which leads to minimizing the noise contribution to the reconstruction. This model’s solution yields a nonlinear partial differential equation that is simple to solve using a well-established numerical technique. We give numerical reconstructions that show the potential of the proposed model using both synthetic and experimental data.

10.2139/ssrn.4673818

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Citations (0)

A Variational Model for Wrapped Phase Denoising

Mathematics (2023)

Iván de Jesús May-Cen Ricardo Legarda-Sáenz Carlos Brito‐Loeza

This paper presents a variational model for the denoising of wrapped phase images. By enforcing the required Pythagorean trigonometric identity between the real and imaginary components of the signal, this model improves the signal-to-noise ratio of the restored signal. To preserve phase map discontinuities, the model is based on total variation. The existence and uniqueness of the model’s solution are demonstrated using standard techniques. In addition, the convergence of a rapid fixed-point method to determine the numerical solution is demonstrated. Experiments on both synthetic and actual patterns validate the model’s performance.

Classification of discontinuities

SIGNAL (programming language)

Discontinuity (linguistics)

10.3390/math11122618

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Citations (1)

Nonparaxial method for computing the gradient field of a wavefront using moiré deflectometry

Optics Communications (1999)

Ricardo Legarda-Sáenz Ramón Rodrı́guez-Vera Mariano Rivera

Moiré pattern

Direction cosine

Wavefront sensor

10.1016/s0030-4018(98)00674-9

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Citations (3)

Iris Recognition Using Supervised Learning Based on Matching Features

Communications in computer and information science (2022)

Edgar Hernandez-Garcia Anabel Martín-González Ricardo Legarda-Sáenz

IRIS (biosensor)

Iris Recognition

10.1007/978-3-030-98457-1_4

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Citations (2)

Three-dimensional camera

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE (2003)

Thorsten Bothe Achim Gesierich Ricardo Legarda-Sáenz Werner P. O. Jueptner

Industrial- and multimedia applications need cost effective, compact and flexible 3D profiling instruments. In the talk we will show the principle of, applications for and results from a new miniaturized 3-D profiling system for macroscopic scenes. The system uses a compact housing and is usable like a camera with minimum stabilization like a tripod. The system is based on common fringe projection technique. Camera and projector are assembled with parallel optical axes having coplanar projection and imaging plane. Their axes distance is comparable to the human eyes distance altogether giving a complete system of 21x20x11 cm size and allowing to measure high gradient objects like the interior of tubes. The fringe projector uses a LCD which enables fast and flexible pattern projection. Camera and projector have a short focal length and a high system aperture as well as a large depth of focus. Thus, objects can be measured from a shorter distance compared to common systems (e.g. 1 m sized objects in 80 cm distance). Actually, objects with diameters up to 4 m can be profiled because the set-up allows working with completely opened aperture combined with bright lamps giving a big amount of available light and a high Signal to Noise Ratio. Normally a small basis has the disadvantage of reduced sensitivity. We investigated in methods to compensate the reduced sensitivity via setup and enhanced evaluation methods. For measurement we use synthetic wavelengths. The developed algorithms are completely adaptable concerning the users needs of speed and accuracy. The 3D camera is built from low cost components, robust, nearly handheld and delivers insights also into difficult technical objects like tubes and inside volumes. Besides the realized high resolution phase measurement the system calibration is an important task for usability. While calibrating with common photogrammetric models (which are typically used for actual fringe projection systems) problems were found that originate from the short focal length and the extreme opening angle of the system as well as the large depth of focus. The actual calibration method is outlined and current problems are shown. An improved calibration of the system is discussed for improved results in future.

USable

Digital Light Processing

Structured-light 3D scanner

Tripod (photography)

Camera lens

10.1117/12.501959

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Citations (4)

Robust wave-front estimation from multiple directional derivatives

Optics Letters (2000)

Ricardo Legarda-Sáenz Mariano Rivera Ramón Rodrı́guez-Vera Gerardo Trujillo-Schiaffino

A quadratic cost functional for computing an estimate of a wave front from multiple directional derivatives is presented. This functional is robust to noise and is specially suited for moiré deflectometry, Ronchi testing, and lateral shearing interferometry.

Shearing (physics)

Spatial frequency

10.1364/ol.25.001089

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Citations (28)

Direct phase unwrapping method based on a local third-order polynomial fit

Applied Optics (2019)

Alejandro Téllez-Quiñones Ricardo Legarda-Sáenz Adán Salazar-Garibay Juan C. Valdiviezo-N Miguel León-Rodríguez

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.

Operator (biology)

10.1364/ao.58.000436

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Citations (9)

Synchronous phase demodulation algorithm for conic carrier Hartmann topographer

Optics and Lasers in Engineering (2014)

Adonai Gonzalez Mariano Rivera Manuel Servı́n Ricardo Legarda-Sáenz Oscar Dalmau

Conic section

Ellipse

Position (finance)

10.1016/j.optlaseng.2014.11.012

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Citations (0)

Color deflectometry for phase retrieval using phase-shifting methods

Optics Communications (2014)

Jorge L. Flores Ricardo Legarda-Sáenz Guillermo García–Torales

10.1016/j.optcom.2014.08.030

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Citations (14)

Dynamic 3-D shape measurement method based on quadrature transform

Optics Express (2010)

Ricardo Legarda-Sáenz Ramon Rodriguez-Vera A. Espinosa-Romero

In this work, it is presented a combination of temporal phase unwrapping technique and Fourier-based quadrature transform to obtain the dynamic phase map from a vibrating object. The proposed combination results on a very simple algorithm which allows an accurate and versatile 3D reconstruction of the object under analysis.

Quadrature (astronomy)

10.1364/oe.18.002639

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Citations (4)