Elementary-field analysis of partially coherent beam shaping

Abstract

We consider spatial shaping of partially coherent fields in two types of optical systems: a 2F Fourier-transforming system with the beam shaping element in the input plane and a 4F imaging system with the element in the intermediate Fourier plane. Different representations of the spatially partially coherent field in terms of fully coherent fields are examined to permit reduction of the dimensionality of the propagation integrals. The standard Mercer-type coherent-mode representation of the incident cross-spectral density (CSD) function is compared to expansions of CSD in either spatially or angularly shifted elementary field modes, all sharing the same spatial profile. In Fourier-transforming systems, the angular elementary-field representation proves computationally superior, while in imaging systems the spatially shifted elementary-field expansion is the best choice. Considering the Fourier-plane element as a generalized pupil, the latter leads to the concept's generalized amplitude associated with the elementary field and to a generalized transfer function of the system. These concepts reduce to the standard point spread function and the optical transfer function in the limit of spatial incoherence at the object plane. Examples of the effects of partial coherence in spatial beam shaping are given.

Pseudo-Schell model sources

“…The coherence characteristics of a light source affect the properties of the propagated field and, in particular, its irradiance profile, so that it is also possible to tune the beam shape by controlling the coherence of the source [1][2][3][4][5][6][7][8][9]. Such a feature is of a great interest in those applications, such as in remote sensing [10], free space optical communications [11][12][13], or optical trapping [14,15], just to mention some examples where the use of partially coherent sources have been proposed, due to the advantages they present if compared to their coherent counterparts.…”

The subtraction of mutually displaced Gaussian Schell-model beams

“…In classical optics, coherence theory [1][2][3] is a subject that continuously receives innovative contributions from countless authors, both within the scalar [4][5][6][7][8][9][10][11] and vectorial realm [12][13][14][15][16][17][18][19][20][21], including nonstationary states [22][23][24][25][26].…”

Genuine-field modeling of partially coherent X-ray imaging systems

“…The genuine approach, based on identical elementary modes, has been used to describe beam shaping (Singh et al, 2013) and imaging (Singh et al, 2015) systems in the visible spectral region. In this region conventional optical systems are essentially space-invariant over a considerable spatial domain, typically far in excess of the spatial extent of the elementary modes.…”