THE FRESNEL DIFFRACTION : A STORY OF LIGHT AND DARKNESS

Claude Aime (1) , Eric Aristidi (1) , Yves Rabbia (1)

1 LAGRANGE - Joseph Louis LAGRANGE

In a first part of the paper we give a simple introduction to the free space propagation of light at the level of a Master degree in Physics. The presentation promotes linear filtering aspects at the expense of fundamental physics. Following the Huygens-Fresnel approach, the propagation of the wave writes as a convolution relationship, the impulse response being a quadratic phase factor. We give the corresponding filter in the Fourier plane. As an illustration, we describe the propagation of wave with a spatial sinusoidal amplitude, introduce lenses as quadratic phase transmissions, discuss their Fourier transform properties and give some properties of Soret screens. Classical diffractions of rectangular diaphragms are also given there. In a second part of the paper, the presentation turns onto the use of external occulters in coronagraphy for the detection of exoplanets and the study of the solar corona. Making use of Lommel series expansions, we obtain the analytical expression for the diffraction of a circular opaque screen, thereby giving the complete formalism for the Arago-Poisson spot. We include there shaped occulters. The paper ends with a brief application to incoherent imaging in astronomy.

Domaines: Astrophysique [astro-ph]

Claude Aime, Eric Aristidi, Yves Rabbia. THE FRESNEL DIFFRACTION : A STORY OF LIGHT AND DARKNESS. Summer school “Reconstruction d'images − Applications astrophysiques“, Jun 2012, Fréjus, France. ⟨10.1051/eas/1359003⟩. ⟨hal-02478976⟩