The Design of Lens Imaging System by Means of Fractional Fourier Transform

The relation between the 2nd fractional Fourier transform and the imaging process of an optical system is discussed. By changing the coordinate scales of the input plane in respect to the magnification of the optical imaging system, the fractional Fourier transform can be a powerful tool in designing a specific imaging system. The Gaussian imaging formula for single lens is obtained by using the tool. Finally the procedures are generalized for designing a double-lens imaging system with an example.