TABLE OF CONTENTS Airy functions were introduced by G.B. Airy in 1838 in his article about the calculation of the light intensity in the neighbourhood of a caustic. We shall establish here the expression of this intensity (not in the way followed by Airy), but by the more "modern" approach of Landau & Lifchitz (1964).
Let us consider a monochromatic source and an aperture in an opaque screen. According to the laws of geometrical optics, beyond this screen, space is shared in two zones: the dark zone presenting a clear border with the enlightened zone. However the phenomenon of diffraction, as intense as the wavelength of the source, is large compared to the dimension of the opening, complicates the distribution of the light intensity in the neighbourhood of this border. According to the Huygens principle, we consider that each element of the surface d S of the opening is the source of a spherical wave. That is to say, u being the amplitude of the field on d S and k the wave number of the source of light, the electromagnetic field in a point P located at a distance R from the opening, is proportional to the sum of these spherical waves
where d S n is the projection of d S on the normal plane, corresponding to the direction of the ray resulting from the source, and arriving on the surface of the opening (cf. Fig. 7.1). If moreover...
