A system for the spatial recombining of pulse laser beams of same wavelength centered around λ 0, arising from N synchronized sources k, k varying from 1 to N, N being an integer >1, which has an optical axis and comprises: - a Fourier lens of focal length f 2, of predefined object plane and predefined image plane, the laser beams exhibiting at λ 0 a periodic spatial configuration of spacing P A in the object plane (plane A), - a recombining diffractive optical element with periodic phase profile, on which the N beams are intended to be directed by the Fourier lens according to an angle of incidence θ 2k that differs from one beam to the next, these angles of incidence being determined as a function of the period of the recombining diffractive optical element, characterized in that the sources are able to emit pulses of duration less than 10 -12 s, and in that it has: - N compensating diffractive optical elements with periodic grating with one compensating diffractive optical element per source, an angle of incidence θ 1k that differs from one beam to the next, and a grating spacing Λ 1k that differs between neighboring compensating diffractive optical elements, - an array of lenses with one lens per source, of predefined object plane and predefined image plane, forming with the Fourier lens a double-FT setup of predetermined magnification γ, able to image each compensating diffractive optical element on the recombining diffractive optical element, the compensating diffractive optical elements being situated in the object plane of the array of lenses, the recombining diffractive optical element being situated in the image plane of the Fourier lens, the image plane of the array of lenses coinciding with the object plane of the Fourier lens, and in that for each compensating diffractive optical element, the angle of incidence θ 1k of the beam on the compensating diffractive optical element, the angle of inclination Θ k of the compensating diffractive optical element on the optical axis, and the spacing Λ 1k of its grating, are determined on the basis of the following formulas: { Λ 1 k = λ 0 sin θ 1 k − Θ k + sin Θ k γ tan k P A f 2 1 + tan 2 k P A f 2 = tan Θ k + sin θ 1 k cos Θ k sin θ 1 k − Θ k cos Θ k + tan Θ k = γ tan k P A f 2 - a Fourier lens of focal length f 2, of predefined object plane and predefined image plane, the laser beams exhibiting at λ 0 a periodic spatial configuration of spacing P A in the object plane (plane A), - a recombining diffractive optical element with periodic phase profile, on which the N beams are intended to be directed by the Fourier lens according to an angle of incidence θ 2k that differs from one beam to the next, these angles of incidence being determined as a function of the period of the recombining diffractive optical element, - N compensating diffractive optical elements with periodic grating with one compensating diffractive optical element per source, an angle of incidence θ 1k that differs from one beam to the next, and a grating spacing Λ 1k that differs between neighboring compensating diffractive optical elements, - an array of lenses with one lens per source, of predefined object plane and predefined image plane, forming with the Fourier lens a double-FT setup of predetermined magnification γ, able to image each compensating diffractive optical element on the recombining diffractive optical element, the compensating diffractive optical elements being situated in the object plane of the array of lenses, the recombining diffractive optical element being situated in the image plane of the Fourier lens, the image plane of the array of lenses coinciding with the object plane of the Fourier lens,