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.

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.

A simultaneous phase-shifting interferometer with a monitored spatial light modulator (SLM) flexible reference mirror is proposed to balance the flexibility and accuracy of aspheric-surface in-process measurements. In this method, polarization simultaneous phase-shifting camera systems are applied to reduce the influence of environmental vibrations on the in-process measurements. An SLM reference mirror is employed to improve the flexibility of in-process measurements. A device is integrated to monitor the SLM surface in order to improve measurement accuracy caused by the spatial phase nonuniformity and modulation instability of the SLM. Thus, the SLM surface is monitored and the aspheric surface is measured simultaneously in only one interferometer, which presents the advantages of a compact structure and simple calibration. A flat acrylic mirror with an unknown surface figure error is measured by the proposed interferometer. Cross tests demonstrate the feasibility of this interferometer.

Aspheric surface parameters, including vertex radius of curvature, conic constant, and high-order aspheric coefficients, decide the optical properties of aspheric surfaces. The measurement of aspheric surface parameter errors (SPEs) is a substantial issue for the fabrication of aspheric surfaces. Interferometry is a mature high-accuracy method in aspheric surface figure error measurement, but challenges still exist in the measurement of SPEs for high-order aspheric surfaces or convex aspheric surfaces. We propose an interferometric measurement method for high-order aspheric SPEs based on a virtual-real combination iterative algorithm (VRCIA). We also propose a recommended measurement system including a partial compensation interferometer to obtain the partial compensated wavefront and a laser differential confocal system to obtain the best compensation distance for calculating SPEs through the VRCIA. A high-order convex aspheric surface is measured to demonstrate the feasibility of the method. The relative accuracy of vertex radius of curvature error, conic constant error and fourth-order aspheric coefficient error can reach 0.025%, 0.095% and 3.02%, respectively.

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