Instrumentación

 

Flatness measurement using a grazing incidence interferometer

 

N. Alcalá Ochoa*, G. Mendiola, and J.E.A. Landgrave

 

Centro de Investigaciones en Óptica, Apartado Postal 1–948, Leon, Guanajuato, México, *e–mail: alon@foton.cio.mx

 

Recibido el 12 de agosto de 2005
Aceptado el 30 de noviembre de 2006

 

Abstract

The purpose of this work is to report results of flatness measurements using a grazing incidence interferometer. We show that this interferometer provides enough accuracy to measure nominally flat polishing tools and rough surfaces. In order to calculate the deformation of the surface under test, an interferogram is analyzed with digital imaging techniques based on Fourier methods. We found experimentally that the entire surface topography can be recovered with errors lower than ~ 0.6 μm, or ~ λ_eqv/6, where λ_eqv = 3.6441 μm is the equivalent wavelength of the interferometer.

Keywords: Optical testing; interferometry; fringe analysis; laser applications.

 

Resumen

El propósito de este trabajo es el de reportar resultados de medición de planicidad usando un interferómetro de incidencia oblicua. Se muestra que este interferómetro proporciona la exactitud necesaria para medir la planicidad de herramientas de pulido y superficies rugosas. Con el propósito de evaluar las irregularidades de la superficie bajo prueba, el interferograma obtenido se analiza con técnicas de procesamiento digital de imágenes basadas en métodos de Fourier. Encontramos experimentalmente que la superficie completa se puede medir con errores menores a ~ 0.6 μm, o ~ λ_eqv/6, donde λ_eqv = 3.6441 μm es la longitud de onda equivalente del interferómetro.

Descriptores: Pruebas ópticas; intereferometría; análisis de franjas; aplicaciones de láseres.

 

PACS: 06.20.–f; 42.62.–b; 42.62.Cf

 

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Acknowledgements

The authors would like to express their gratitude to the members of the optical and the mechanical workshops at CIO, in particular to Carlos Perez Santos, and also to Zacarías Malacara Hernández, of the Optical Engineering Group, for their assistance in various tasks that were essential for the successful completion of this work.

 

References

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2. N. Alcalá Ochoa, G. Mendiola, E. Landgrave Manjarrez, and J.C. Sánchez Roldan, Cuantificación de planicidad de objetos usando un interferómetro de incidencia oblicua, Tech. Rep., CIO (2001).        [ Links ]

3. The cemented doublets of the GII were corrected for spherical aberration and coma for λ = 0.6328 μm.        [ Links ]

4. K.H. Womack, Opt.Eng. 23 (1984) 391.        [ Links ]

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6. N. Alcalá Ochoa, R. Rodríguez–Vera, M. Servín, and F. Mendoza Santoyo, Opt. Commun. 117 (1995) 213.         [ Links ]

7. By the variance of a function f(x, y) we shall mean

where the bar denotes average over the domain of the function f(x,y), denoted here by D, and

is the area of D. In our case, A is clearly the area under inspection.

8. K. Creath, "Temporal Phase Measurement Methods", in Interferogram Analysis, D.W. Robinson and G.T. Reid, Eds. (IOP Publishing, Bristol, UK, 1993) Chap. 4.        [ Links ]

9. N. Alcalá Ochoa, J.L. Marroquin, and A. Dávila, Opt. Commun. 163 (1999) 15.        [ Links ]

10. This expression for ψ(x, y) can be derived as we do in the case of interference in thin films. See, for instance, M. Born and E. Wolf, Principles of Optics, 6^th (corrected) ed. (Pergamon, Oxford, 1984) Chap. 7, p. 286.        [ Links ]

11. Wyko is a trademark. The Wyko interferometer is a Fizeau, phase–stepping, digital interferometer, used to test plane and spherical specular surfaces in an optical workshop.        [ Links ]