Various kinds of systems, that can do target recognition and position detection simultaneously by using infrared sensing detectors, have been developed. In this paper, the detection system TRSS (Thermal target Recognition by Spiral Scanning) adopts linear array shaped uncooled IR detector and uses spiral type fast scanning method for relative position detection of target objects, which radiate an IR region wavelength spectrum. It can detect thermal energy radiating from a 9 m-size target object as far as 200 m distance. And the maximum field of a detector is fully filled with the same size of target object at the minimum approaching distance 50 m. We investigate two types of lens systems. One is a singlet lens and the other is a doublet lens system. Every system includes one aspheric surface and free positioned aperture stop. Many designs of F/1.5 system with ${pm}5.2^{circ}$ field at the Efl=20, 30 mm conditions for single element and double elements lens system respectively are compared in their resolution performance [MTF] according to the aspheric surface and stop position changing on their optimization process. Optimum design is established including mechanical boundary conditions and manufacturing considerations.