A miniature Free Piston Free Displacer (FPFD) Dual Opposed Stirling Cryocooler is designed for the applications in Infrared Imaging. Helium is used as a working gas, providing cooling effect at 80K operating under ambient conditions. A moving magnet linear motor drives the Cryocooler. Compressor and Expander are separate units connected via small diameter tube for minimum vibration export. The Cryocooler is modelled in Sage Software. Variation of the design parameters on the performance of the Cryocooler is studied. An optimization is done to maximize heat lift with frequency, displacer spring stiffness and negative facing area as optimization variables and work input as the constraint. Flexure spring is designed and analysed using Ansys. The variable features are the spiral angle, the number of arms and the gap width for the required stiffness and safe stress. Analysis of the moving magnet linear motor is done using Ansys Maxwell.