Freeform surfaces are difficult to manufacture due to their lack of rotational symmetry. To reduce the requirements for manufacturing precision, a design method is proposed for freeform reflective-imaging systems with low surface-figure-error sensitivity. The method considers both the surface-figure-error sensitivity and optical specifications, which can design initial systems insensitive to surface figure errors. Design starts with an initial planar system; the surface-figure-error sensitivity of the system is reduced during construction. The proposed method and another that is irrelevant to figure-error sensitivity are used to design a freeform off-axis three-mirror imaging system. Comparison of the sensitivities of the two systems indicates the superiority of our proposed method.

Astigmatism is inevitable and inherent to progressive addition lenses (PALs), which are typically distributed in the lateral areas on both sides of the progressive corridor. In this study, we took into account the spectacle frame for the customized freeform PAL design with the variational-difference numerical approach. The PAL surface with minimized astigmatism, approximately equal to 84% of the added power, was numerically resolved without expending the zone for clear vision. We validated our approach by experimentally demonstrating the procedure from tool path generation to surface power measurement, thus providing an efficient solution to the personalization of astigmatism-minimized PAL design and manufacture.

In this Letter, we present a novel design method of image-side telecentric freeform imaging systems. The freeform surfaces in the system can be generated using a point-by-point design approach starting from an initial system consisting of simple planes. The proposed method considers both the desired object–image relationships and the telecentricity at the image-side during the design process. The system generated by this method can be taken as a good starting point for further optimization. To demonstrate the benefit and feasibility of our method, we design two freeform off-axis three-mirror image-side telecentric imaging systems in the visible band. The systems operate at F/1.9 with a 30 mm entrance pupil diameter and 5° diagonal field-of-view. The modulation-transfer-function curves are above 0.69 at 100 lps/mm.

In this Letter, a novel and compact freeform off-axis three-mirror imaging system and its detailed design method are proposed. The primary mirror and tertiary mirror of the system have the same surface analytical expression and they are integrated on one single freeform surface. In this way, the alignment process is made much easier due to the much fewer degrees of freedom. In addition, the difficulty and cost for the data handling, fabrication, and testing of the freeform surfaces and system can also be significantly reduced in some cases, especially compared with the configuration having multiple surfaces of different expressions integrated on one monolithic substrate. The final system has a 100 mm effective focal length and a 4°×3° field of view. The modulation transfer function of the system is close to the diffraction-limit.

In this Letter, we propose a novel configuration and design method of freeform, dual fields-of-view (FOVs), dual focal lengths, off-axis three-mirror zoom imaging systems. The switch of the two zooms is achieved by rotating a single mirror element. The design of a freeform, dual focal lengths zoom system is realized by a point-by-point design approach for the first time to our knowledge. This method enables the direct design of freeform surfaces from initial planes using given system specifications and configuration, and the designed system can be taken as a good starting point for further optimization. A freeform, dual FOVs, dual focal lengths, off-axis three-mirror zoom system is demonstrated. The F-numbers of the two zooms are 2 and 2.4. The dual FOVs are 3°×3° and 2.5°×2.5°. After final optimization, both of the zooms achieve high performances.