A method of aligning a diffractive optical system, to be operated with an operating beam, comprises: aligning (558) the diffractive optical system using an alignment beam having a different wavelength range from the operating beam and using a diffractive optical element optimized (552) to diffract the alignment beam and the operating beam in the same (or a predetermined) direction. In an example, the alignment beam comprises infra-red (IR) radiation and the operating beam comprises soft X-ray (SXR) radiation. The diffractive optical element is optimized by providing it with a first periodic structure with a first pitch (pIR) and a second periodic structure with a second pitch (pSXR). After alignment, the vacuum system is pumped down (562) and in operation the SXR operating beam is generated (564) by a high harmonic generation (HHG) optical source pumped by the IR alignment beam’ optical source.