The present disclosure is directed to a sun-sky-imitating illumination device (100) for generating natural light similar to that from the sun and the sky, comprising a direct-light generator (10) that comprises a first emitting surface (11) from which a direct light (13) is emitted and a collimated light source (20) configured to generate from a primary light a collimated light (23) which exits an output surface (22) positioned upstream from the first emitting surface (11) with respect to a direct light direction (15), wherein the direct light (13) has a luminance profile (Ldirect(x, y, θ, φ)) which has a first peak in the angular distribution around the direct-light direction (15) and the collimated light (23) exiting the output surface (22) has a luminance profile (Lcoll(x, y, θ, φ)) which has a second peak (14) in the angular distribution around the direct-light direction (15), the second peak being a narrow peak, and a diffused-light generator (50) that is at least partially light-transparent and is positioned downstream of the direct-light generator (10) and comprises a second emitting surface (51) and is configured to cause diffused light (53) at the second emitting surface (51), wherein the sun-sky-imitating illumination device is configured such that the direct-light generator (10) and the diffused-light generator (50) co-operate to form outer light (53,54) at the second emitting surface (51) which comprises a first light component (54) which propagates along directions contained within the narrow peak (14) and a second light component (53) which propagates along directions spaced apart from the narrow peak (14), wherein the first light component (54) has a CCT which is lower than a CCT of the second light component (53), wherein the direct-light generator (10) comprises an optical unit (30) positioned downstream of the output surface (22) of the collimated light source (20) and upstream from the first emitting surface (11) with respect to the direct light direction (15), wherein the optical unit (30) is configured to interact with the collimated light (23) exiting the output surface (22) to generate the direct light (13) emitted from the first emitting surface (11) so that the first peak of the luminance profile (Ldirect(x, y, θ, φ)) of the direct light (13) is larger than the second peak of the luminance profile (Lcoll(x, y, θ, φ)) of the collimated light (23), the optical unit (30) comprising a first planar light mixing element (33,33′) characterized by a first response function having a first angular profile with a peak having a first divergence angle (α1, α1′) measured as full width at half maximum (FWHM) of the peak, the first planar light mixing element (33,33′) being positioned so as to at least partially intercept the collimated light (23) exiting the output surface (22) of the collimated light source (20) and to define a unit input surface (31), and a second planar light mixing element (34) characterized by a second response function having a second angular profile with a peak having a second divergence angle (α2) measured as full width at half maximum (FWHM) of the peak, the second planar light mixing element (34) being positioned downstream of the unit input surface (31) so as to at least partially intercept the light crossing the unit input surface (31) and to define a unit emitting surface (32), wherein the first and second divergence angles (α1, α1′, α2) are equal to or smaller than 40° preferably smaller than 30°, more preferably smaller than 20°; and wherein the first (33,33′) and second (34) planar light mixing elements are spaced apart from each other at least of a minimum unit depth (z1) measured along the direct light direction (15), configured to obtain uniform luminance of the direct light (13) which exits the first emitting surface (11) of the direct light generator (10).