Outreach

Graduates of the INAOE, among the outstanding authors of the IOP Latin America magazine

Santa María Tonantzintla, May 25th, 2022. Dr. Jesús Alonso Arriaga Hernández, a doctoral graduate in Optics from the INAOE and currently a postdoctoral researcher at the BUAP, has been designated by the IOP Latin America magazine as a featured author for an article published in 2021. Dr. Bolivia Cuevas Otahola also participates in this work, a graduate of the doctorate in Astrophysics and a visiting professor researcher at the highest house of studies in Puebla.

This is a theoretical-experimental work in which the irradiance transport equation is applied to the study of wavefront propagation. (https://latinoamerica.ioppublishing.org/noticias/el-autor-dr-jesus-alonso-arriaga-hernandez-de-la-benemerita-universidad-autonoma-de-puebla-mexico/). The results were published in the aforementioned international publication in 2021.

Dr. Bolivia Cuevas Otahola is a graduate of the INAOE Astrophysics program. She did her master's degree in Physics at the Universidad de Los Andes (ULA) in Venezuela, where she also completed a Bachelor's degree in Mathematics. She worked during her thesis with Dr. Divakara Mayya and with Dr. Ivario Puerari, both INAOE researchers, studying the dynamical evolution of young star clusters. She also dabbled in Optics with Dr. Arriaga, working on ace propagation, medical image processing, and mathematical modeling. The constant in her research is the use of differential equations for solution and modeling of various phenomena, with special emphasis on software development. She is currently a visiting professor researcher in the mathematics department of the Faculty of Electronic Sciences of the BUAP.

Graduated from the Higher School of Physics and Mathematics of the IPN and from the doctoral program in Optics of the INAOE, Dr. Jesús Alonso Arriaga Hernández has worked with Dr. Ponciano Rodríguez in the manufacture of a laser, with Dr. Sabino Chávez in beam propagation, and did his thesis with Dr. Alejandro Cornejo. He highlights his training in mathematics and his passion for its formalism, with Dr. Cornejo he builds the thesis project for an equation in partial differences, the irradiance transport equation. A beautiful equation used in multiple areas of Physics.

During the interview, Dr. Cuevas Otahola refers: “All the work is around the irradiance transport equation, highlighting its importance in Optics, by relating the wave front and irradiance, without forgetting the wave nature of both concepts. What is the wavefront? Relating this to Astrophysics, we can think of an astronomical image taken with a telescope, and this in itself is a representation of the wavefront. Thus, what we observe, what reaches us as part of the electromagnetic radiation reflected in the image, is the wavefront of said astronomical objects and this is what we analyze. From this wavefront we process the image and what we obtain is information about what we are studying and applying in other areas. On the other hand, in the context of Optics, we can study how a beam propagates considering the nature of its source, which in Astrophysics we study as an object and its radiation, and in medicine we can also analyze it, but in a different way, studying the image according to the distribution of hot or cold areas as in an X-ray. Because the hot or more intense zones indicate the probable existence of an anomaly, as we have reported in a study in collaboration with Dr. Alberto Jaramillo, an INAOE researcher. We have been working on these topics within the multidisciplinarity that exists in the mathematical modeling and differential equations group at BUAP, where we use image processing techniques to be able to detect, for example, if there is any type of bone metastasis, anomaly in the mammary area, some tissue alteration, as well as being able to understand how SARS-CoV-2 modifies the areas where an individual is incubated or contaminated. On the other hand, using signal processing we analyze epileptic foci. An enormous virtue of this group in collaboration with Dr. Jacobo Oliveros and Dr. María Morín, both BUAP Researchers”.

In turn, Dr. Arriaga highlights: “In Optics it is very common to study the deformations of the wavefront from the polynomial of aberrations and in the case of some optical tests this is studied in other ways, obtaining it through transverse aberrations or from of some component or projection. However, in this work we make a more general representation of the wavefront because there are multiple forms and ways to describe it and what we did was, first of all, to obtain it from the solution of a differential equation with its respective conditions of edge throughout space, not without restricting ourselves to one or another projection of it. The foregoing is not because it is wrong or it is an erroneous conception of the problem, but in order not to restrict the calculations of the model considering the vector properties of space and the source that radiates to the object from which we obtain the wavefront so as not to forget that the phenomenon has a radiative and propagating nature. Thus, in this article, the first thing is the solution of the differential equation with its multiple conditions and the second is the propagation. How do we solve this? Analytically we propose our proposal in terms of series and numerically it was corroborated in her contribution to the investigation by Dr. Bolivia, resulting in the solution and observation of the wavefront that comes from the object from the multiple optical instruments of the experiment. And the great surprise is that the solution is so close to the physical phenomenon involved that in the area of ??the focus or where all the rays coming from the object of study are concentrated there is a very interesting phenomenon in the focus, in the Foucault test and the solution proposed in the investigation the sample; which was curious the way it was solved and modeled smoothly for Dr. Bolivia. I also did the simulation in the numerical solution but the elegance of Dr. Bolivia's solution is unmatched, obtaining the same results. We highlight the result of how the wavefront of an optical surface propagates as the object of study, before and after the focus in this first code, and we are already working on the next one to later interpret this in terms of the Zernike polynomials and concentrate in each aberration, to see how the wavefront is deformed as an entity whose nature is to be aberrated and is composed of multiple aberrations and whether each of them has an independent behavior or not. In addition, it is intended to evaluate if the equations in the model can be modified to obtain the same results, as a different method of studying the aberrations or deformations of the wavefront, that is, we can consider it ideal, except for deformations, whose integration shows its aberrated nature, to later apply it in Astrophysics in the analysis of some body that is very close to another object, or in medical image processing for the identification of some specific anomaly that is behind some tissue according to the convergence or divergence of the rays coming from the object under analysis.

Dr. Cuevas Otahola emphasizes that something important in her works is that they try to provide a strong, formal mathematical foundation: “since we started working with propagation, even much earlier, we have worked with Legendre polynomials because they are what we call in mathematics a generating base. A set of elements of a vector space that satisfy certain conditions to generate all the elements of the space. Something beautiful about this type of Legendre polynomials is that they allow us to represent any function, anything with them, they are a skeleton key. With them we have developed quite a few software tools and we have used them throughout the works and they allow us, for example, to increase the resolution of images, resolve two objects that are partially superimposed, in addition to the fact that together with the improvement of the computer equipment we also optimize some processing techniques to obtain results with which we can appreciate wonderful things”.

In turn, Dr. Arriaga highlights: “In Optics it is very common to study the deformations of the wavefront from the polynomial of aberrations and in the case of some optical tests this is studied in other ways, obtaining it through transverse aberrations or from some component or projection. However, in this work we make a more general representation of the wavefront because there are multiple forms and ways to describe it and what we did was, first of all, to obtain it from the solution of a differential equation with its respective conditions of edge. throughout space, not without restricting ourselves to one or another projection of it. The foregoing is not because it is wrong or it is an erroneous conception of the problem, but in order not to restrict the calculations of the model considering the vector properties of space and the source that radiates to the object from which we obtain the wavefront so as not to forget that the phenomenon has a radiative and propagating nature. Thus, in this article, the first thing is the solution of the differential equation with its multiple conditions and the second is the propagation. How do we solve this? Analytically we propose our proposal in terms of series and numerically it was corroborated in her contribution to the investigation by Dr. Bolivia, resulting in the solution and observation of the wavefront that comes from the object from the multiple optical instruments of the experiment. And the great surprise is that the solution is so close to the physical phenomenon involved that in the area of ????the focus or where all the rays coming from the object of study are concentrated there is a very interesting phenomenon in the focus, in the Foucault test and the solution proposed in the investigation of the sample; which was curious the way it was solved and modeled smoothly for Dr. Bolivia. I also did the simulation in the numerical solution but the elegance of Dr. Bolivia's solution is unmatched, obtaining the same results. We highlight the result of how the wavefront of an optical surface propagates as the object of study, before and after the focus in this first code, and we are already working on the next one to later interpret this in terms of the Zernike polynomials and concentrate in each aberration, to see how the wavefront is deformed as an entity whose nature is to be aberrated and is composed of multiple aberrations and whether each of them has an independent behavior or not. In addition, it is intended to evaluate if the equations in the model can be modified to obtain the same results, as a different method of studying the aberrations or deformations of the wavefront, that is, we can consider it ideal, except for deformations, whose integration shows its aberrated nature, to later apply it in astrophysics in the analysis of some body that is very close to another object, or in medical image processing for the identification of some specific anomaly that is behind some tissue according to the convergence or divergence of the rays coming from the object under analysis.

Dr. Cuevas Otahola emphasizes that something important in her works is that they try to provide a strong, formal mathematical foundation: “since we started working with propagation, even much earlier, we have worked with Legendre polynomials because they are what we call in mathematics a generating base. A set of elements of a vector space that satisfy certain conditions to generate all the elements of the space. Something beautiful about this type of Legendre polynomials is that they allow us to represent any function, anything with them, they are a skeleton key. With them we have developed quite a few software tools and we have used them throughout the works and they allow us, for example, to increase the resolution of images, resolve two objects that are partially superimposed, in addition to the fact that together with the improvement of the computer equipment we also optimize some processing techniques to obtain results with which we can appreciate wonderful things”.