In this paper, we demonstrated the design method of freeform unobscured reflective imaging systems using the point-bypoint Construction-Iteration (CI) method. Compared with other point-by-point design methods, the light rays of multiple fields and different pupil coordinates are employed in the design. The whole design process starts from a simple initial system consisting of decentered and tilted planes. In the preliminary surfaces-construction stage, the coordinates as well as the surface normals of the feature data points on each freeform surface can be calculated point-by-point directly based on the given object-image relationships. Then, the freeform surfaces are generated through a novel surface fitting method considering both the coordinates and surface normals of the data points. Next, an iterative process is employed to significantly improve the image quality. In this way, an unobscured design with freeform surfaces can be obtained directly, and it can be taken as a good starting point for further optimization. The benefit and feasibility of this design method is demonstrated by two design examples of high-performance freeform unobscured imaging systems. Both two systems have good imaging performance after final design.
Surface measurement and analysis are important to freeform surface optical systems. The deviation from designed
surface is generally regarded as a judging criterion of real surface quality. In off-axis optical systems, some freeform
surfaces contain no reference points. Measured data of such surfaces can only constitute a fitted surface, but the spatial
position of the fitted surface is difficult to be determined to make a smallest deviation from designed surface by internal
algorithms. In freeform surface optical systems, besides the surface deviations, the tangent vector variations of lattice
data of measured surface can also affect the image quality. Consequently the quality of freeform surface should be
appraised by both of tangent vector variations and surface deviations. This paper presents one method using first-order
differential to directly analyze and process the measured lattice data of freeform surfaces. This method assesses the
tangent vector variations of measured data and the smoothness of real surfaces, while does not involve the fitting
procedure with designed surfaces. In this paper, this method is applied to evaluate a set of measured lattice data of some
reflective freeform surfaces. Furthermore, some fitting algorithms are applied to assess the surface deviations between
the measured and designed surfaces as contrasts.