Development of freeform optical systems One of the essential properties of the freeform surface is that its asymmetric and locally variant surface profile breaks the symmetry of an optical system thus provoking unique issues that have never been considered in rotationally symmetric optical systems. This thesis focuses on developing an optimization algorithm that automatically eliminates the obscuration in the non rotationally symmetric reflective optical system as well as defining and computing the generalized chromatic aberrations in the non rotationally symmetric refractive optical system. Furthermore a comprehensive model for the tolerancing of freeform surface is put forward. When optimizing a three dimensional (3D) reflective optical system by tilting the mirrors the mirrors can block the ray path and in consequence reduce the image brightness and contrast. To take the degree of obscuration into consideration an error function that mathematically describes all the obscuration cases in 3D reflective systems is proposed. In order to analyze the generalized chromatic aberrations in 3D refractive systems the reference axis and reference plane are clarified to figure out the precise definition of the generalized chromatic aberrations. Both ray based and wavefront based methods are proposed to calculate the generalized chromatic aberrations surface by surface. In addition the influence of pupil aberration is discussed to improve calculation accuracy. The manufacturing error of the freeform surface can be transferred into the frequency domain by Fourier transform. The autocorrelation function (ACF) of the phase pattern is computed in different frequency ranges. By characterizing the width of ACF the boundary frequency between the deterministic and statistic errors can be found. A comprehensive model representing different types of surface errors is proposed to construct a synthetic freeform surface. By performing the Monte Carlo simulation tolerancing of the freeform system can be realized.