| With recent advances in technology, it is now possible to manufacture diffractive optical elements using VLSI techniques. Accordingly, there is renewed interest in diffractive optics. However, one of the major drawbacks for purely diffractive systems is their large chromatic aberrations. In addition, due to the idea's relative newness, not much is known about the tolerance of diffractive elements to manufacturing errors. This thesis addresses both of these problems.; First, a complete theory for a diffractive doublet design is introduced. The design is corrected at two wavelengths via a recursive ray tracing method. The design has three parameters: the two wavelengths to be corrected and the initial ray of the recursive ray trace. The different cases of on-axis and off-axis conjugate points are considered. The system geometry is used to compensate for the chromatic aberrations introduced by the diffractive elements. The first order theory of the design is also developed.; Next, the performance of the diffractive doublets is evaluated. The two on-axis designs are compared to refractive singlets, hybrid singlets and Fresnel singlets and doublets. Both designs perform approximately an order of magnitude better than the Fresnel designs. When compared to the refractive and hybrid singlets, the designs perform better at low F/#'s but worse at high F/#'s. We then analyze the off-axis performance of the designs. The designs have virtually no field of view (e.g., measured in minutes of arc for the F/3 case). However, they can be designed to image off-axis conjugate points with only a slight degradation in performance.; Finally, fabrication issues are examined. As a representative case, we look at the overall efficiency of a Fresnel lens. VLSI fabrication errors are modeled and then the fabrication process is simulated. The efficiency of the Fresnel lens falls as the square of errors in etch depth and linearly with lateral errors in the mask or mask alignment. We develop a model to successfully explain the results of the simulations. |
