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Revista mexicana de física

Print version ISSN 0035-001X

Rev. mex. fis. vol.55 n.5 México Oct. 2009




Bode plots applied to microscopic interferometry


J.M. Flores, M. Cywiak*, M. Servín, and L. Juárez


Centro de Investigaciones en Óptica, A.C., Loma del Bosque 115, Lomas del Campestre, León, Guanajuato, 37150 México, * e–mail:


Recibido el 16 de junio de 2008
Aceptado el 7 de septiembre de 2009



We describe a technique for using Bode plots in microscopic interferometry, in particular as applied to the three Gaussian beam interferometer recently reported in the literature. The technique is used in a similar manner to its application to an electric or electronic system in finding its frequency response. The Bode response is used to deconvolve the raw data obtained directly from the interferometer to compensate for the data in frequency, making it possible to obtain more realistic profiles of the samples under test. We apply this technique to obtain profiles of the inner reflective layers of two optical types of surfaces for data storage commercially available, namely, the compact disk (CD–R) and the digital versatile disk (DVD–R). We report the experimental results of radial scans of these devices without data marks, before and after applying the transfer function of the system. The measurements are obtained by placing the devices with the polycarbonate surfaces so as to aim the probe beam of the interferometer at them, taking advantage of the vertical depth discrimination of the microscope. We show that the resulting profiles, obtained across the Polycarbonate layer, measured with this interferometer, give valuable information of the real track profiles, making the combination of the Bode plots with this interferometer a suitable tool for quality control of the surface storage devices.

Keywords: Bode transform; gaussian beam; interferometry.



Describimos una técnica que permite utilizar las gráficas de Bode en interferometría microscópica, en particular aplicada al interferómetro de tres haces Gaussianos recientemente reportado en la literatura. La técnica es utilizada de una manera similar a la forma en que se hace para encontrar la respuesta en frecuencia de un sistema eléctrico o electrónico. La respuesta de Bode es utilizada para calcular la deconvolución de los datos crudos obtenidos directamente del interferómetro para compensar los datos en frecuencia, permitiendo obtener un perfil mas realista de las muestras bajo prueba. Aplicamos la técnica para obtener los perfiles de las superficies reflectoras internas de dos dispositivos ópticos comercialmente disponibles para almacenamiento de datos, el disco compacto (CD–R) y el disco digital versátil (DVD–R). Reportamos resultados experimentales de una exploración radial de estos dispositivos sin datos almacenados, antes y después de aplicar la función de transferencia del sistema. Las mediciones son obtenidas colocando los dispositivos con la superficie de Policarbonato apuntando al haz de prueba del interferómetro, aprovechando la ventaja de la discriminación de profundidad del microscopio. Mostramos que los perfiles resultantes, obtenidos a través de la capa del Policarbonato, medidos con este interferómetro, proporcionan información valiosa de los perfiles reales de las pistas de estos dispositivos, por lo que la combinación de Bode aunada al uso de este interferómetro representan una herramienta adecuada para el control de calidad de los dispositivos ópticos de almacenamiento de datos mencionados.

Descriptores: Transformar Bode; haz de Gauss; interferometría.


PACS: 07.60.; 42.79.Vb; 42.87.d





The authors thank CONACYT for financial support.



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