Planck pre-launch status: Low Frequency Instrument optics

We describe the optical design and optimisation of the Low Frequency Instrument (LFI), one of two instruments onboard the Planck satellite, which will survey the cosmic microwave background with unprecedented accuracy. The LFI covers the 30-70 GHz frequency range with an array of cryogenic radiometers. Stringent optical requirements on angular resolution, sidelobes, main beam symmetry, polarization purity, and feed orientation have been achieved. The optimisation process was carried out by assuming an ideal telescope according to the Planck design and by using both physical optics and multi-reflector geometrical theory of diffraction. This extensive study led to the flight design of the feed horns, their characteristics, arrangement, and orientation, while taking into account the opto-mechanical constraints imposed by complex interfaces in the Planck focal surface.