Assessment about Luneberg integrals and application to digital in-line holography

In this publication, the Luneberg integrals are revisited and the conditions of the using of such integrals have been recalled. Additivity law of Luneberg’s integrals and the link with the Frenel kernel for the propagation are discussed. By means of the definition of the Luneberg’s integrals, the propagation of a vectorial electromagnetic field (Hertz potentials) is developed and a new approach of the computation have been proposed based on Zernike polynomials. With this new approach simulations of holograms is illustrated in the case of the digital in-line holography with an opaque disk.