Asian Journal of Physics Vol 31, No 7 (2022) 677-686

Measurement of the displacement field of non-planar surfaces using ESPI

Juan Antonio Rayas1, Amalia Martínez-García1, Ana Karen Reyes1, and Miguel León-Rodríguez2
1Centro de Investigaciones en Óptica, A. C. Loma del Bosque 115, C.P. 37150, León, Guanajuato, México
2Universidad Politécnica de Guanajuato, Av. Universidad Sur 1001, Cortazar-Guanajuato, 38496, México

Dedicated to Prof Maria J Yzuel

Measurements of the displacement field by optical interferometry depend on the induced phase difference and on the interferometer’s sensitivity vector. In the case of out-of-plane interferometer, the latter depends in turn on the positions of the illuminating source and the observation, as well as the topography of the analyzed sample. The aim of this study is the quantification of the out-of-plane displacement field of a car fender subjected to mechanical loading. Special attention was paid to evaluating contributions to the displacement when the fender shape is considered. The displacement field is evaluated by using an electronic speckle pattern interferometer and the topography is obtained by a fringe projection technique. © Anita Publications. All rights reserved.
Keywords: Sensitivity vector, ESPI, Fringe projection, Phase stepping.

Peer Review Information
Method: Single- anonymous; Screened for Plagiarism? Yes
Buy this Article in Print © Anita Publications. All rights reserve


  1. Sirohi R S, Chau F S, Optical Methods of Measurement: Whole Field Techniques, (Marcel Dekker, New York, 1999), p 174.
  2. Martínez A, Rayas J A, Rodríguez-Vera R, Puga H J, Three- dimensional deformation measurement from the combination of in-plane and out-of-plane electronic speckle pattern interferometers, Appl Opt, 43(2004)4652–4658.
  3. Martínez A, Rayas J A, Cordero R, Electronic speckle pattern interferometer design to get maximum sensitivity on the measurement of displacement vector fields, Opt Commun, 262(2006)8–16.
  4. Martínez A, Rayas J A, Evaluation of error in the measurement of displacement vector components by using electronic speckle pattern interferometry,Opt Commun, 271(2007)445–450.
  5. Martínez A, Rayas J A, Cordero R, Genovese K, Analysis of optical configurations for ESPI, Opt Lasers Eng, 46(2008)48–54.
  6. Martínez A, Rodríguez-Vera R, Rayas J A, Puga H J, Error in the measurement due to the divergence of the object illumination wavefront for in-plane interferometers, Opt Commun, 223(2003)239–246.
  7. Puga H J, Rodríguez-Vera R, Martínez A, General model to predict and correct errors in phase map interpretation and measurement from out-of-plane ESPI interferometers, Opt Laser Technol, 34(2002)81–92.
  8. Gómez-Méndez G A, Martínez-García A, Reyes A K, Rayas J A, Relative error in out-of-plane measurement due to the object illumination, Appl Opt, 58(2019)4963–4968.
  9. Joenathan Ch, Pfister B, Tiziani H J, Contouring by electronic speckle pattern interferometry employing dual beam illumination, Appl Opt, 29(1990)1905–1911.
  10. Sciammarella C A, Lamberti L, Boccaccio A, General model for moiré contouring, part 1: theory, Opt Eng, 47 (2008)033605;
  11. Sciammarella C A, Lamberti L, Boccaccio A, Cosola E, Posa D, General model for moiré contouring, part 2: applications, Opt Eng, 47(2008)033606;
  12. Sciammarella C A, Computer-assisted holographic moire contouring, Opt Eng, 39(2000)99–105.
  13. Rodríguez-Vera R, Optical Gauging of Diffuse Surfaces by Electronic Speckle Contouring, Opt Lasers Eng, 26(1997)101–114.
  14. Genovese K, Lamberti L, Pappalettere C, A comprehensive ESPI based system for combined measurement of shape and deformation of electronic components, Opt Lasers Eng, 42(2004)543-562.
  15. Parra-Michel J, Martínez A, Anguiano-Morales M, Rayas J A, Measuring object shape by using in-plane electronic speckle pattern interferometry with divergent illumination, Meas Sci Technol, 21(2010)045303;
  16. Martínez A, Rayas J A, Puga H J, Genovese K, Iterative estimation of the topography measurement by fringe-projection method with divergent illumination by considering the pitch variation along the x and z directions, Opt Lasers Eng, 48(2010)877–881.
  17. Sirohi R S, Introduction to Optical Metrology, (CRC Press, Taylor & Francis Group, New York), 1999, p 96.