DESHIMA is a spectrometer for astronomical applications targeting sources at sub-mm wavelengths from 240GHz to 720GHz that will operate in the ASTE telescope in Atacama Desert, Chile. In this work, a quasi-optical system based on a hyper-hemispherical leaky lens antenna and a series of Dragonian reflectors is presented as the coupling chain for the EM radiation captured by the telescope into the detector. The design procedure is based on a field matching technique in reception. The achieved average illumination efficiency over the band is approximately 70%. The directivity patterns in the sky are also estimated. The side lobe, and cross-polarization levels, over the whole frequency band, are below-16dB, and-18dB, respectively. The measurement of the system is on-going, and will be presented at the conference.