Reconstruyendo la diferencia de camino ´optico de un interferograma real degradado por ruido mediante la soluci´on de diferentes problemas de optimizaci´on


  • Juan Jaime Sánchez Escobar Centro de enseñanza técnica industrial
  • Liliana Ibeth Barbosa Santillán Universidad de Guadalajara, CUCEA.
  • Jorge Castro Ramos Coordinación de óptica.
  • Luis Francisco Barbosa Santillán Ingeniería en Mecatrónica



Reconstrucción numérica, problemas inversos, optimización estocástica, experimentos de demostración para estudiantes no graduados, estudiantes no graduados de ciencias e ingeniería.


This paper presents a comparative numerical study that demonstrates the feasibility of stochastic optimization (SO) for reconstructing the optical path difference (OPD) from a real interferogram degraded by noise, either by the maximization of the correlation coefficient or by the minimization of the Euclidean distance where the optimization achieved for each objective function corresponds to the near-optimal solution without being dominated by a local optimum. In order to show the efficacy of different SO algorithms based on evolutionary computation, we propose a solution to the maximization problem by using a genetic algorithm with the primary aberrations described by Kingslake, while for the solution of the minimization problem an evolutionary strategy with Zernike polynomials is proposed. The numerical results show the simplicity, robustness, and accuracy of both SO algorithms to calculate their corresponding aberration coefficients. Thus, this work offers an ideal opportunity to integrate the skills acquired by university students of science and engineering in subjects such as interferometric optical metrology, numerical methods, and programming with the purpose of performing interferogram analysis.

Author Biographies

Juan Jaime Sánchez Escobar, Centro de enseñanza técnica industrial

Subdirección de investigación; Docente con comisión para labores de investigación.

Liliana Ibeth Barbosa Santillán, Universidad de Guadalajara, CUCEA.

Departamento de Sistemas de Información; Profesora investigadora.

Jorge Castro Ramos, Coordinación de óptica.

Coordinación de óptica; Investigador Titular A.

Luis Francisco Barbosa Santillán, Ingeniería en Mecatrónica

Ingeniería en Mecatrónica; Docente-investigador.


J. J. Briers, Opt. Lasers Eng. 32 (1999) 111-138.

D. Malacara, M. Servin y Z. Malacara, Interferogram Analysis for Optical Testing, 2 Ed., CRC Press, Boca Raton, FL., (2005), pp. 1-62.

D. Malacara, J. M. Carpio y J. J. Sánchez, Opt. Eng. 29(6) (1990) 672-675.

J.Y. Wang y D. E. Silva, App. Opt. 19(9) (1980) 1510-1518.

X. Yu, Y. Yao, Y. Sun y J. Tian, Optik 122 (2011) 1701-1706.

X. Yu, Y. Yao, Y. Sun, J. Tian y C. Liu, Optik 123 (2012) 792-795.

N.S. Mera, L. Elliott y D.B. Ingham, Inverse Problems in Engng 11(2) (2003) 105-121.

M. Rivera, J. Opt. Soc. Am. A 22(6) (2005) 1170-1175.

M. B. Bernini, A. Federico y G.H. Kaufmann, Appl. Opt. 48(36) (2009) 6862-6869.

X. Liu y Y. Li, Opt. Express 11(14) (2003) 1677-1688.

A. Lara, G. Sánchez, C. A Coello y O. Schutze, IEEE Trans. Evol. Comput. 14(1) (2010) 112-132.

K. Sindhya, K. Miettinen y K. Deb, IEEE Trans. Evol. Comput. 17(4) (2013) 495-511.

J. C. Wyant and K. Creath, Applied optics and optical engineering VOLUME XI, 1 Ed., Academic Press, Inc., San Diego, California., (1992), pp. 1-53.

J.J. Sánchez, J.H. Alonso y S. Vázquez, Opt. Eng. 45(10) (2005) 105605-1.

J. J. Sánchez y L.I. Barbosa, Opt. Eng. 54(2) (2015) 094102-1.

J. J. Sánchez, L.I. Barbosa, J. Vargas y F. Aguilar, Appl. Opt. 55(22) (2016) 5806-5813.