Numerical calculation of near field scalar diffraction using angular spectrum of plane waves theory and FFT
A. Carbajal–Domínguezª, J.B. Arroyoª, J.E. Gómez Correaª, G.M. Niconoffª, G.M. Niconoffb
ª Universidad Juárez Autónoma de Tabasco, División Académica de Ciencias Básicas, Cunduacán, Tabasco, 86690, México e–mail: adrian.carbajal@dacb.ujat.mx
b Instituto Nacional de Astrofísica, Óptica y Electrónica, Departamento de Óptica, Grupo de Óptica Estadística, Apartado 51 y 216, Puebla, 72000 México.
Recibido el 14 de agosto de 2009 ]]> Aceptado el 29 de julio de 2010
Abstract
It is a known fact that near field diffraction or Fresnel diffraction calculations are difficult to perform exactly. It is in general necessary to make some approximations in order to obtain a more suitable form. In this work, a numerical implementation based on angular spectrum theory for near field diffraction is presented. The method uses Fast Fourier Transforms (FFT), and it turns out to be accurate and fast. In order to show the capabilities of the method, diffraction near field for a circular aperture and a spiral slit are studied. Numerical and experimental results are shown. This method could be useful to implement pc based physical optics learning.
Keywords: Scalar wave diffraction; Fresnel diffraction; near field diffraction; FFT; Helmholtz equation.
Resumen
Se sabe que los cálculos difracción de campo cercano o de Fresnel son difíciles de realizar de manera exacta. En general, es necesario realizar aproximaciones a fin de obtener expresiones con formas más manejables. En el presente trabajo se presenta una implementación numérica del cálculo del campo cercano usando la teoría del espectro angular. El método emplea la transformada rápida de Fourier (FFT) lo que le permite ser rápido y preciso. Con el propósito de mostrar la eficiencia del método, se presenta el estudio de la difracción producida por una abertura circular y por una rendija espiral. Se muestran los resultados numéricos y experimentales. Creemos que el presente método puede ser útil en la enseñanza de la óptica física en cursos soportados en el uso de pc.
Descriptores: Difracción de Fresnel; difracción de ondas escalares; difracción de campo cercano; FFT; ecuación de Helmholtz.
]]> PACS: 42.25.Bs; 42.25.Fx
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