This paper proposes a new method for the measurement of spherical coordinates by using capacitive sensors as a non-contact probe solution of measurement of aspheric surfaces. The measurement of the average effect of the capacitive probe and the influence of capacitive probe tilting were studied with respect to an eccentric spherical surface. Based on the tested characteristic curve of the average effect of the sphere and probe, it was found that nonlinear and linear compensation resulted in high measurement accuracy. The capacitance probe was found to be trying to fulfill a need for performing nm-level precision measurement of aspheric electromagnetic surfaces.

Error compensation technology is used for improving accuracy and reducing costs. Dynamic error compensation techniques of coordinate measuring machine (CMM) are still under study; the major problem is a lack of suitable models, which would be able to correctly and simply relate the dynamic errors with the structural and operational parameters. To avoid the complexity of local dynamic deformation measurement and modeling, a comprehensive calibration method is employed. Experimental research reveals specific qualities of dynamic Abbe errors; the results exceed the scope of ISO 10360-2 calibration method, showing the ISO 10360-2 dynamic error evaluation deficiencies. For calibrating the dynamic Abbe errors, the differential measurement method is presented based on the measurements of the internal and external dimensions. Referring probe tip radius correction, the dynamic Abbe errors compensation method is proposed for CMM end-users and is easy to use.

Integrated zoom and image stabilization system based on deformable mirrors (DMs) has advantages of miniaturization, rapid response and low energy consumption. Integrating the two capabilities on one DM-based imaging system poses considerable challenges. First, limited DM stroke will result in limited changeable aberration correction value for zoom and image stabilization. Second, the DM-based off-axis imaging system suffers a simple relative movement between optical axis and objects caused by carrier vibration may result in complicated optical system aberrations. To address these challenges, a reasonable assignment of the changeable aberration correction value for zoom and image stabilization is needed. Image stabilization and aberration correction in DM-based off-axis imaging system, should be considered when translation or rotation occurs. To troubleshoot the assignment issues of the correcting aberrations, we propose a graded optimization method which comprises two steps. To troubleshoot the image stabilization and aberration correction issues, we introduce vectorial ray tracing method and image point freezing principle to transform the aberration correction problem into an optimization problem of image coordinates. With the proposed method, we construct practical integrated freeform surfaces of DMs for a space camera with three mirrors. The sagittal heights of designed DM surface profiles are limited within their available stroke.