Abstract
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.
Highlights
Digital in-line holography often uses Fresnel and Fourier integrals, either to describe the light propagation and to calculate to the different expressions of amplitude distribution or to reconstruct the image of the object from the recorded holograms
We develop a vectorial model applied to the digital in-line holography
It should be noted that an optical system for digital in-line holography (DIH) is composed of two parts
Summary
Digital in-line holography often uses Fresnel and Fourier integrals, either to describe the light propagation and to calculate to the different expressions of amplitude distribution or to reconstruct the image of the object from the recorded holograms. The use of Hertz potentials allow to obtain a vectorial spherical wave which satisfy the Luneberg conditions. To illustrate the previous consideration about the kernels, holograms with Fresnel and Luneberg integrals have been simulated where the object is an opaque disk of diameter D illuminated by a wave of amplitude unity, i.e. Eδ = (Eδx, 0, 0) = (1, 0, 0) with δ = 0.
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