“…Starting from the pioneering works (Coisson & Walker, 1986;Kim, 1986;Kim, 1987a;Kim, 1987b), a lot of literature is available, which deals with the generalization of the concept of radiance to the case of partially transverse coherent sources as Synchrotron Radiation (SR) and Free-Electron Laser (FEL) sources (Coisson & Walker, 1986;Kim, 1986;Kim, 1987a;Kim, 1987b;Hulbert & Weber, 1992;Howells & Kincaid, 1994;Bahrdt, 1997;Hulbert & Williams, 1992;Hulbert & Williams, 1998;Bosch, 1999;Attwood, 1999;Bosch, 2000;Ciocci et al, 2000;Duke, 2000;Thomson & Vaugham, 2001;Wiedemann, 2002;Onuki & Elleaume, 2003;Hofmann, 2004;Clarke, 2004;Talman, 2006;Williams, 2006;Tanaka & Kitamura, 2009;Bazarov, 2012;Huang, 2013;Tanaka, 2014;Geloni et al, 2015;Vartanyants & Singer, 2018). This generalization process required changing the working framework from pure geometrical optics to wave optics, backed up by statistical optics.…”